Issues in Multiagent Resource Allocationstaff.science.uva.nl/~ulle/MARA/mara-survey.pdf · TFG-MARA...

TFG-MARA 1

Issues in Multiagent Resource Allocation

Yann ChevaleyreLAMSADE, Universite Paris-Dauphine (France)Email: [email protected]

Paul E. DunneDepartment of Computer Science, University of Liverpool (UK)Email: [email protected]

Ulle EndrissILLC, Universiteit van Amsterdam (The Netherlands)Email: [email protected]

Jerome LangIRIT, Universite Paul Sabatier, Toulouse (France)Email: [email protected]

Michel LemaıtreONERA, Centre de Toulouse (France)Email: [email protected]

Nicolas MaudetLAMSADE, Universite Paris-Dauphine (France)Email: [email protected]

Julian PadgetDepartment of Computer Science, University of Bath (UK)Email: [email protected]

Steve PhelpsDepartment of Computer Science, University of Liverpool (UK)Email: [email protected]

Juan A. Rodrıguez-AguilarArtificial Intelligence Research Institute (IIIA-CSIC), Barcelona (Spain)Email: [email protected]

Paulo SousaDEI, Instituto Superior de Engenharia do Porto (Portugal)Email: [email protected]

Keywords: resource allocation, negotiation, preferences, social welfare, complexity, simulation

The allocation of resources within a system of autonomous agents, that not only havepreferences over alternative allocations of resources but also actively participate in com-puting an allocation, is an exciting area of research at the interface of Computer Scienceand Economics. This paper is a survey of some of the most salient issues in MultiagentResource Allocation. In particular, we review various languages to represent the pref-erences of agents over alternative allocations of resources as well as different measuresof social welfare to assess the overall quality of an allocation. We also discuss pertinentissues regarding allocation procedures and present important complexity results. Ourpresentation of theoretical issues is complemented by a discussion of software packagesfor the simulation of agent-based market places. We also introduce four major applica-tion areas for Multiagent Resource Allocation, namely industrial procurement, sharingof satellite resources, manufacturing control, and grid computing.

2 TFG-MARA Chevaleyre et al.

Contents

1 Introduction 31.1 What is MARA? . . . . . . . . . . 3

1.1.1 Resources . . . . . . . . . . 31.1.2 Allocations . . . . . . . . . 31.1.3 Agent Preferences . . . . . 31.1.4 Allocation Procedures . . . 41.1.5 Objectives . . . . . . . . . . 41.1.6 Social Welfare . . . . . . . 41.1.7 The Role of Agents . . . . . 41.1.8 A Computational Perspective 4

1.2 Research Topics . . . . . . . . . . . 51.3 Paper Overview . . . . . . . . . . . 5

2 Application Areas 62.1 Industrial Procurement . . . . . . 6

2.1.1 Problem Description . . . . 62.1.2 Challenges . . . . . . . . . 6

2.2 Earth Observation Satellites . . . . 82.2.1 Problem Description . . . . 82.2.2 Modelling . . . . . . . . . . 8

2.3 Manufacturing Systems . . . . . . 92.3.1 Problems and Requirements 92.3.2 Manufacturing and Agents 10

2.4 Grid Computing . . . . . . . . . . 102.4.1 Scalability Issues . . . . . . 102.4.2 Market-based Allocation . . 11

3 Types of Resources 113.1 Continuous vs. Discrete . . . . . . 123.2 Divisible or not . . . . . . . . . . . 123.3 Sharable or not . . . . . . . . . . . 123.4 Static or not . . . . . . . . . . . . 123.5 Single-unit vs. Multi-unit . . . . . 123.6 Resources vs. Tasks . . . . . . . . . 13

4 Preference Representation 134.1 Quantitative Preferences . . . . . . 14

4.1.1 Bundle Enumeration . . . . 144.1.2 The k-additive Form . . . . 154.1.3 Weighted Prop. Formulas . 154.1.4 Straight-line Programs . . . 154.1.5 Bidding Languages . . . . . 16

4.2 Ordinal Preferences . . . . . . . . . 174.2.1 Prioritised Goals . . . . . . 174.2.2 Ceteris Paribus Preferences 17

4.3 Discussion . . . . . . . . . . . . . . 18

5 Social Welfare 185.1 Notation . . . . . . . . . . . . . . . 195.2 Pareto Optimality . . . . . . . . . 195.3 Collective Utility Functions . . . . 19

5.3.1 Utilitarian Social Welfare . 205.3.2 Egalitarian Social Welfare . 205.3.3 Nash Product . . . . . . . . 205.3.4 Elitist Social Welfare . . . . 205.3.5 Rank Dictators . . . . . . . 20

5.4 The leximin Ordering . . . . . . . 205.5 Generalisations . . . . . . . . . . . 215.6 Normalised Utility . . . . . . . . . 215.7 Envy-freeness . . . . . . . . . . . . 215.8 Example . . . . . . . . . . . . . . . 225.9 Welfare Engineering . . . . . . . . 22

6 Allocation Procedures 226.1 Centralised vs. Distributed . . . . 236.2 Auction Protocols . . . . . . . . . 236.3 Negotiation Protocols . . . . . . . 24

6.3.1 Contract-Net . . . . . . . . 246.3.2 Extensions . . . . . . . . . 246.3.3 Concurrent Contract-Net . 24

6.4 Convergence Properties . . . . . . 25

7 Complexity Results 267.1 Models and Assumptions . . . . . 267.2 Computat. vs. Comm. Complexity 267.3 Allocations with Given Properties 27

7.3.1 Representation Issues . . . 277.3.2 Quantitative Criteria . . . . 277.3.3 Qualitative Criteria . . . . 27

7.4 Path and Convergence Properties . 287.5 Open Problems and Conjectures . 29

8 Simulation Platforms 298.1 Simulation vs. Implementation . . 298.2 Simulating Time . . . . . . . . . . 30

8.2.1 Continuous Time Models . 308.2.2 Discrete-event Simulation . 31

8.3 Agent Modelling . . . . . . . . . . 318.4 Extensibility and Integration . . . 318.5 Software Listing . . . . . . . . . . 31

8.5.1 Swarm . . . . . . . . . . . . 318.5.2 Extensions to Swarm . . . . 328.5.3 RePast . . . . . . . . . . . 328.5.4 Desmo-J . . . . . . . . . . . 328.5.5 AScape . . . . . . . . . . . 328.5.6 DEx . . . . . . . . . . . . . 32

9 Conclusion 32

MULTIAGENT RESOURCE ALLOCATION TFG-MARA 3

1 Introduction

The allocation of resources is a central matterof concern in both Computer Science and Eco-nomics. To emphasise the fact that resources arebeing distributed amongst several agents and thatthese agents may influence the choice of alloca-tion, the field is sometimes called Multiagent Re-source Allocation (MARA). The questions inves-tigated by computer scientists are often of a pro-cedural nature (how do we find an allocation?),while economists are more likely to concentrateon qualitative issues (what makes a good alloca-tion?). A comprehensive analysis of the problemat hand, however, requires an interdisciplinaryapproach. Here the multiagent system (MAS)paradigm offers an excellent framework in whichto study these issues.

MARA is relevant to a wide range of applica-tions. These include, amongst others, industrialprocurement [45], manufacturing and schedul-ing [15, 71, 89], network routing [38], the fairand efficient exploitation of Earth ObservationSatellites [59, 60], airport traffic management [52],crisis management [62], logistics [49, 77], publictransport [16], and the timely allocation of re-sources in grid architectures [48].

This paper is a survey of some of the mostsalient issues in MARA. In the remainder of thisintroduction, we first give a tentative definition ofMARA and introduce its main parameters (Sec-tion 1.1). To illustrate the interdisciplinary char-acter of the field, we then list some of the researchquestions that we consider particularly interestingand challenging (Section 1.2). Finally, we give anoverview of the content of the main body of thepaper (Section 1.3).

1.1 What is MARA?

A tentative definition would be the following:

Multiagent Resource Allocation is theprocess of distributing a number of itemsamongst a number of agents.

However, this definition needs to be further qual-ified: What kind of items (resources) are beingdistributed? How are they being distributed (inother words, what kind of allocation procedure ormechanism do we employ)? And finally, why are

they being distributed (that is, what are the ob-jectives of searching for an allocation and how arethese objectives determined)?

1.1.1 Resources

We refer to the items that are being distributed asresources, while agents are the entities receivingthem. We should stress that this terminology isnot universally shared. In the context of applica-tions of MARA in manufacturing, for instance, weusually speak of tasks that are being allocated toresources. That is, in this context, the term “re-source” (i.e. the resources available to the manu-facturer for production) refers to what we wouldcall an “agent” here.

We can distinguish different types of resources.For instance, resources may or may not be divis-ible. For divisible resources (such as electricity),different agents may receive different fractions ofa resource. In the case of indivisible resources, itmay or may not be possible for different agentsto share (jointly use) the same resource (e.g. ac-cess to network connections as opposed to itemsof clothing). For many purposes, task allocationproblems can be regarded as instances of MARA(if we think of tasks as resources associated witha cost rather than a benefit).

1.1.2 Allocations

A particular distribution of resources amongstagents is called an allocation. For instance, inthe case of non-sharable indivisible resources, anallocation is a partition of the set of resourcesamongst the agents. The set of resources assignedto a particular agent is also called the bundle al-located to that agent.

1.1.3 Agent Preferences

Agents may or may not have preferences overthe bundles they receive. In addition, they mayalso have preferences over the bundles received byother agents (in the case of network connections,for example, the value of a resource diminishes ifshared by too many users). The latter type ofpreferences are called externalities.

Agents may or may not report their preferencestruthfully. To provide incentives for agents to betruthful is one of the main objectives of mecha-nism design.


1.1.4 Allocation Procedures

The allocation procedure used to find a suitableallocation of resources may be either centralisedor distributed. In the centralised case, a single en-tity decides on the final allocation of resourcesamongst agents, possibly after having elicitedthe agents’ preferences over alternative alloca-tions. Typical examples are combinatorial auc-tions. Here the central entity is the auctioneerand the reporting of preferences takes the form ofbidding. In truly distributed approaches, on theother hand, allocations emerge as the result of asequence of local negotiation steps.

1.1.5 Objectives

The objective of a resource allocation procedureis either to find an allocation that is feasible (e.g.to find any allocation of tasks to production unitssuch that all tasks will get completed in time); orto find an allocation that is optimal. In the lattercase, the allocation in question could be optimaleither for the central entity choosing the alloca-tion (e.g. a solution to a combinatorial auctionthat maximises the auctioneer’s revenue); or withrespect to a suitable aggregation of the prefer-ences of the individual agents in the system (e.g.an allocation of resources that maximises the av-erage utility enjoyed by the agents).

Combinations are also possible: The objectivemay be to find an optimal allocation amongst asmall set of feasible allocations; and what is con-sidered optimal could depend both on the pref-erences of a central entity and on an aggrega-tion of the other agents’ individual preferences(e.g. auction mechanisms aiming at balancing rev-enue maximisation and bidder satisfaction). Ofcourse, where computing an optimal allocation isnot possible (due to lack of time, for instance),any progress towards the optimum may be con-sidered a success.

1.1.6 Social Welfare

Multiagent systems are sometimes referred to as“societies of agents” and the aggregation of indi-vidual preferences in a MARA system can oftenbe modelled using the notion of social welfare asstudied in Welfare Economics and Social ChoiceTheory. Examples include utilitarian social wel-fare, where the aim is to maximise the sum of

individual utilities, and egalitarian social welfare,where the aim is to maximise the individual wel-fare of the agent that is currently worst off.

1.1.7 The Role of Agents

Our discussion shows that the term “multiagent”in Multiagent Resource Allocation can have dif-ferent interpretations:

– If a distributed resource allocation procedureis used, then the term “multiagent” indicatesthat the computational burden of finding anallocation is shared amongst several agents.

– If an aggregation of individual preferences isused to assess the quality of the final alloca-tion, then the term “multiagent” refers to thefact that the choice of allocation depends onthe preferences of several agents (rather thanon the preferences of a single entity).

Of course, the term “multiagent” could also bederived merely from the fact that resources arebeing allocated to several different agents. How-ever, if individual agents have no preferences (orsuch preferences are not taken into account) andthe allocation procedure is centralised, then usingthe term “multiagent” may be less appropriate.

1.1.8 A Computational Perspective

MARA, as introduced at the beginning of Sec-tion 1.1, may not seem to differ significantly fromwhat has traditionally been studied in Microeco-nomics. However, a distinctive feature of MARAis the focus on computational issues. For in-stance, with respect to the preferences of individ-ual agents, we are interested in representationsthat can be efficiently managed and communi-cated. Similarly, in the case of allocation proce-dures, MARA encompasses both the theoreticalanalysis of their computational complexity andthe design of efficient algorithms for scenarios forwhich this is possible. As a final example, con-cerning the strategic aspects of negotiation, wemay find that classical results in Game Theoryfail to hold due to the computational limitationsof the participating agents.


1.2 Research Topics

MARA is a highly interdisciplinary field; rele-vant disciplines include Computer Science, Ar-tificial Intelligence, Decision Theory, Microeco-nomics, and Social Choice Theory. Research inMARA can take a variety of forms:

– Preferences: What are suitable representa-tion languages for agent preferences? Issuesto consider include their expressive power,their succinctness, and their suitability inview of preference elicitation.

– Social welfare: What are suitable measuresof social welfare to assess the quality of an al-location for a given application? Under whatcircumstances can we expect an optimal al-location to be found?

– Complexity: What is the overall complex-ity of finding a feasible/optimal allocation?What is the complexity of the decision prob-lems that agents need to solve locally? Whatis the communication complexity (amount ofinformation to be exchanged) of negotiation?

– Negotiation: In particular for the distributedapproach, what are suitable negotiation pro-tocols? What are good strategies for agentsusing such protocols?

– Algorithm design: How can we devise effi-cient algorithms for MARA (e.g. algorithmsfor combinatorial auction winner determina-tion in the centralised case; algorithms tosupport complex negotiation strategies in thedistributed case)?

– Mechanism design: How can we devise nego-tiation mechanisms that force agents to re-port their preferences truthfully (both to re-duce strategic complexity and to allow for acorrect assessment of social welfare)?

– Implementation: What are best practices forthe development of prototypes for specificMARA applications and general-purposeplatforms to support quick prototyping?

– Simulation and experimentation: How do dif-ferent optimisation algorithms or negotiationstrategies perform in practice? How serious

is the impact of theoretical impossibility re-sults in practice? How prohibitive are the-oretical intractability results (computationalcomplexity) in practice?

– Interplay of theory and applications: Whatconstraints do real-world applications imposeon theoretical models for MARA? How cantheoretical results inform the development ofnew tools?

The aim of this survey is to provide a base linefor some of these issues. In particular, we presenta range of languages for representing preferences,we give an overview of the social welfare measuresmost relevant to MARA, and we review knowncomplexity results in the area. As it is often dif-ficult to make precise predictions on the perfor-mance of a resource allocation procedure by the-oretical means alone, we also discuss the require-ments to be met by software packages for MARAsimulations. To underline the importance of fur-ther research in the area, we introduce severalprestigious applications and discuss the challengesimposed on MARA models by these applications.

1.3 Paper Overview

The remainder of this survey paper is organised asfollows. In Section 2, we introduce four major ap-plication areas for MARA technology. These areindustrial procurement, the joint exploitation ofEarth Observation Satellites, manufacturing con-trol, and grid computing. Throughout Section 2,we highlight the specific challenges raised by theseapplications.

Next we review three important parametersthat are relevant to the definition of a MARAproblem. Firstly, in Section 3, we discuss genericproperties of resources, such as being indivisibleor sharable, and how such properties would affectthe design of a concrete MARA system. We thenmove on, in Section 4, to the issue of preferencerepresentation for individual agents. Each agentneeds to be endowed with a suitable representa-tion of preferences over alternative allocations andit is important to be able to express these prefer-ences in a compact way. We discuss both quanti-tative and ordinal preference languages. A thirdparameter in the definition of a MARA problemis the social welfare measure (or a similar tool) we


employ to assess the overall quality of a given allo-cations. A range of different concepts—includingcollective utility functions, Pareto optimality, andenvy-freeness—are reviewed in Section 5.

In Section 6, we attempt to give a shortoverview of the parameters that are relevant whenone chooses (or designs) an allocation procedure.We discuss the respective merits and drawbacks ofcentralised and distributed approaches to MARA,and we briefly introduce some (centralised) auc-tion protocols as well as (distributed) negotiationprotocols. We also report on results that establishunder what circumstances allocations can be ex-pected to converge to a socially optimal state ina distributed negotiation setting. Section 7 is asurvey of relevant complexity results. We mostlyconcentrate on the computational complexity ofproblems such as finding a socially optimal allo-cation, but we also briefly discuss issues in com-munication complexity for MARA, which is con-cerned with the length of negotiation processes.

Our presentation of theoretical issues is com-plemented by a discussion of software packagesfor the simulation of agent-based market places inSection 8. We start by giving an overview of thetypical requirements to be met by such packagesand then list the most relevant software productsavailable to MARA researchers interested in sim-ulation. Finally, Section 9 concludes.

2 Application Areas

As mentioned already in the introduction, MARAis relevant to a wide range of application domains.In this section, we introduce four of these prob-lem domains, all of which have recently been ad-dressed by (some of) the authors of this survey.

2.1 Industrial Procurement

The sourcing process of multiple goods or servicesusually involves complex negotiations that includediscussion of product features as well as quality,service, and availability issues. Consequently, sev-eral commercial systems to support online negoti-ation (e-sourcing tools) have been developed. Infact, e-sourcing is becoming an established part ofthe business landscape [90]. However, there arestill enormous challenges confronting users whowant to get the maximum value out of e-sourcing.

2.1.1 Problem Description

Traditionally, the core of the sourcing processcomprises the following tasks:

– request for quotation/proposal (RFQ/RFP);

– provider selection for RFQ/RFP delivery;

– offer generation;

– negotiation through offer/counter-offer inter-action or reverse auction; and

– selection of best offers.

Typically a buyer creates an RFQ by sequentiallyadding items. Each item specifies a product, beit a good or service. A paradigmatic example ofmulti-item RFQ occurs in industrial settings. Theproduction plan outlined by a company’s ERP(Enterprise Resource Planning) or SCM (Sup-ply Chain Management) application comes in theshape of a list of items to be produced along withthe parts required for each product, the so-calledbill of material. This is the basis for the buyer toinitiate multiple sourcing events, each devoted tothe procurement of the parts for each of the itemsto be produced.

Although several commercial systems to sup-port online negotiations have been released, tothe best of our knowledge, not a single systemcan claim to address the full complexity of onlinenegotiation. The first generation of sourcing toolsmerely incorporate single-item, price-quantity re-verse auction mechanisms. Others only offer ba-sic negotiation capabilities that are usually re-duced to a demand-offer matching tool. In generalterms, there is a lack of decision support function-alities (decision making in sourcing can involve afew hundred offers, each of which is described byseveral dozen attributes). Furthermore, there isa lack of technology support for computationallycomplex negotiation paradigms, which inhibit theapplication of promising mechanisms such as com-binatorial reverse auctions [24, 54].

2.1.2 Challenges

Although the degree of automation, namely ofdelegation to trading agents, in industrial pro-curement settings is still low, we do believe thatMARA techniques can contribute to improve this


situation. In what follows we identify several chal-lenges that any commercial tool aiming at thesuccessful implementation of resource allocationamongst several (human or software) agents in anindustrial procurement setting must address.

– Preferences of buyers and providers. How dowe best capture and represent trading agents’preferences so that they can effectively valuetheir trading partners’ offers, counter-offers,and RFQs? While recent advances in prefer-ence elicitation are encouraging (see, for in-stance, the work of Bichler et al. [6]), thisstill remains as the Achilles’ heel of indus-trial procurement applications.

– Business rules to constrain admissible alloca-tions. While in direct auctions, the items tobe sold are physically concrete (they do notallow configuration), in a negotiation involv-ing highly customisable goods, buyers needto express relations and constraints betweenattributes of different items. On the otherhand, multiple sourcing is common practice,either for safety reasons or because offer ag-gregation is needed to cope with high-volumedemands. This introduces the need to ex-press constraints on providers and on thecontracts they may be awarded. Providersmay also impose constraints on their offers.Therefore, highly expressive languages forboth buying and providing agents are re-quired.1 Incorporating business rules into al-location procedures can lead to more balancedand safer allocations.

– Automated negotiation strategies. There areseveral dimensions to take into account when

1Consider a buyer who wants to buy 200 chairs (anycolour/model is fine) for the opening of a new restaurantand who uses an e-procurement solution that launches areverse auction. If we employ a state-of-the-art combina-torial auction solver, a possible solution might be to buy199 chairs from provider A and 1 chair from provider B,simply because this is 0.1% cheaper than the next best al-location and it has not been possible to specify that, incase of buying from more than one provider, a minimumof 20 chairs purchase is required. In a different scenario,the optimal solution might tell us to buy 150 blue chairsfrom provider A and 50 pink chairs from provider B. Why?Because, although we had no preferences over the regard-ing colour, we could not specify that all chairs should be ofthe same colour. Although simple, this example shows thatwithout modelling natural constraints, solutions obtainedmay be mathematically optimal, but unrealistic.

designing negotiation strategies. Agents maynegotiate over multiple attributes of the sameitem, over a bundle of multiple items, or theymay hold separate but interdependent ne-gotiations. Negotiation techniques such astrade-off [37] or partial-order scheduling [102]are candidate techniques put forward fromthe research arena. The current procurementpractices tell us that the possibility of auto-matic offer submission is seen with interestfor repetitive sourcing events in private e-sourcing platforms where providers and busi-ness rules are well-known or result from aprovider qualification procedure or a framecontract. Nonetheless, the full application ofsuch automated trading still faces barriers,such as providers not wanting to reveal theircapabilities/preferences to third parties.

– Choice of mechanism. Commercial sourcingtools offer an ever increasing number of cus-tomisable negotiation mechanisms. Nonethe-less, market design is a highly complex, intri-cate task. New trends in automated mecha-nism design [22] as well as evolutionary mech-anism design [73] may prove valuable in as-sisting in the design of market scenarios thatensure certain global properties.

– Winner determination algorithms. Furtherresearch into algorithms capable of iden-tifying the optimal set of offers in multi-attribute, multi-item negotiation scenarioswith side constraints representing businessrules is required [45, 83].

– Bundling. Should a buyer (seller) conducta single negotiation or auction for an entirebundle of goods he or she is interested in pur-chasing (selling) or should they group itemsinto bundles and conduct several negotia-tions? Unfortunately, for complexity reasons,combinatorial bidding capabilities are rarelyfound on commercial systems. To overcomethis problem, we can think of a third ap-proach: Based on past market real data andknowledge, the whole bundle of items can bedivided into separate negotiations for whichthe appropriate providing agents are invitedand for which certain properties are satisfied(e.g. invite providing agents that can offer atleast 90% of the items in the bundle). These


properties model the expertise of e-sourcingspecialists in the form of rules of thumb [76].

Some of these challenges are already being tackledby recently developed negotiation support tools.iBundler [44, 44], for instance, is an agent-awaredecision support service acting as a combinatorialnegotiation solver for both multi-item, multi-unitnegotiations and auctions that can integrate busi-ness rules to constrain admissible solutions. iAuc-tionMaker [76] is a novel decision support tool formixed bundling that can help an auctioneer de-termine how to group items into promising bun-dles that are likely to produce a high revenue.Promising bundles are those that satisfy certainproperties believed to be present in competitivesourcing scenarios. These properties are definedby e-sourcing professionals and capture their ex-perience and knowledge in the domain.

2.2 Earth Observation Satellites

Next we consider another real-word application,namely the exploitation of Earth ObservationSatellites (EOSs) [10, 59, 60]. This applicationpertains to the problem of allocating a set of in-divisible goods to some agents with no possiblemonetary compensation between them. As wewill see, this is a typical case of a sharing problem,different from an auction situation, especially be-cause fairness is a key issue.

2.2.1 Problem Description

Due to their high cost, space projects such asEOSs are often co-funded and then exploited byseveral agents (countries, companies, civil or mil-itary agencies, etc.). The mission of an EOS isto acquire images (photos) of specified areas onthe earth surface, in response to observation de-mands from users. Such a satellite is operatedby an Image Programming and Processing Cen-ter. Each day, the Center collects a set of observa-tion demands from agents. Usually a demand canbe covered by a single image, but more complexdemands may arise, as we will see below. Eachdemand is given a weight (a positive integer), re-flecting the importance the requesting agent as-signs to the satisfaction of the demand. The dailytask of the Center is, amongst others, to build theimaging workload of the satellite for the next day,

by selecting the images to be acquired from theset of agent demands.

Naturally, the exploitation of the satellite mustobey a set of physical constraints, such as timewindow visibility constraints, minimum transitiontimes between successive image acquisitions, ormemory and energy management. Due to theseexploitation constraints, and due to the largenumber of (possibly conflicting) demands, a setof demands, each of which could be satisfied in-dividually, may not be satisfiable as a whole ona single day. All these physical constraints de-fine the set of admissible allocations of images toagents. The exploitation of an EOS must alsomeet the following requirements:

– Efficiency: The satellite should not be under-exploited.

– Equity: Each agent should get a return on in-vestments that is proportional to its financialcontribution.

2.2.2 Modelling

Let us first consider the simple problem whereonly one agent exploits the resource. In this case,the allocation problem consists of selecting, eachday, an admissible sequence of images that will beacquired by the satellite over the next day (andallocated to the agent). This agent measures itssatisfaction by a utility function which may bedefined as the sum of the weights of the allocatedimages. The efficiency requirement comes downto a simple optimisation problem: the utility func-tion of the agent must be maximised over the setof admissible allocations (see Lemaıtre et al. [61]for the description of some algorithms for solvingthis mono-agent allocation problem).

We now turn to the case where several agentsexploit the satellite. For simplicity, we assume inthis paper that the agents have equal rights overthe resource (we may assume, for example, thatthey have funded the satellite equally). Of course,each agent wants to maximise its own utility func-tion, but generally they are antagonistic: increas-ing the utility of one agent can lead to decreas-ing the utility of others. So a fair compromisemust be found, the realisation of which is the roleof a suitable preference aggregation mechanism.Such mechanisms will be discussed in detail in


Section 5. Here, the min function (egalitarian so-cial welfare) fits our requirements, as it naturallyconveys the equity requisite: we try to make theagent least happy as happy as possible (a refine-ment of this approach is given by the so-calledleximin ordering; see Section 5.4).

As mentioned before, weights of demands arefreely fixed by agents. In order to be able to com-pare individual utilities between agents, a com-mon utility scale must be set and used; that is,the same number should express the same level ofsatisfaction. To this end, Lemaıtre et al. [59, 60]have adopted an approach known as the Kalai-Smorodinsky solution (see Section 5.6), wherebyindividual utilities are compared relative to themaximum utility that each agent can receive. Itshould be noted that, unlike for auction problems,there are no preemptive constraints in this ap-plication: the same image could be requested byseveral agents, and allocated to them all (i.e. re-sources are sharable).

This application is also of interest because it of-fers real-word examples of dependencies betweendemands. As a first example, a request mayinvolve a pair of stereoscopic images; receivingonly one image would result in a poor satis-faction level for the agent. A second examplecomes from the fact that, for earth areas situ-ated in high latitudes, several images of the samearea can be taken from distinct angles during thesame day. Consider a stereoscopic demand con-cerning such an area, and suppose that it couldbe photographed from two angles. Let o11 ando12 be the pair of stereoscopic images from an-gle 1, o21 and o22 the images from angle 2.The demand can be quite naturally formulatedas (o11 ∧ o12) ∨ (o21 ∧ o22).

To sum up, our EOS multiagent fair resource al-location problem can be formally stated in the fol-lowing way. Agents express their (weighted) de-mands as simple logical propositions. An agent’sindividual utility is the sum of the weights of thesatisfied demands. The global utility is an ag-gregation of normalised individual utilities, theaggregation function being the min function (or,better, the leximin ordering).

2.3 Manufacturing Systems

Since the second half of the 20th century, the or-ganisation of mass production has been shifting

towards flexible manufacturing and customisedproducts. From a technological point of view,it has been observed that current manufacturingsystems (e.g. computer-integrated manufacturingarchitectures) have several drawbacks, in partic-ular excessive rigidity and centralisation [50, 71].Furthermore, future manufacturing systems areexpected to be characterised by globally dis-tributed production units, small quantities of alarge variety of products, the provision of individ-ual solutions tailored to each customer’s specificneeds, and concurrent execution of all the activi-ties in the manufacturing process [95].

2.3.1 Problems and Requirements

Future manufacturing systems therefore requirecoordination amongst production units and it isexpected that rigid, static, and hierarchical manu-facturing systems will give way to systems thatare more adaptable to rapid change [15]. In orderto overcome the identified problems with currentmanufacturing systems and prepare them for theexpected future scenarios, the new generation ofsystems must possess such attributes as decentral-isation, distribution, autonomy, adaptability, andincomplete information handling [88].

In manufacturing, the term resource allocationis usually synonymous for task scheduling. Fur-thermore, the term resource is understood as aphysical resource, i.e. a machine, of the manu-facturing plant. One of the problems in this areais that a task is a step of a production plan fora specific order (e.g. manufacture 100 chairs oftype P12-5), and there are usually dependenciesbetween tasks that must be obeyed (e.g. operation“drill hole 2” must be done before “cool surface”but after “drill hole 1”).

To further complicate things, the tasks involvedin a production plan will probably be done on dif-ferent production resources, thus creating a net-work of dependencies amongst resources.

One issue in the manufacturing area is that theschedule itself is only valid until the first distur-bance (e.g. machine or tool breakdown, rush or-der, etc.). Since manufacturing control and exe-cution is a real time application, the need to finda feasible solution is much greater than to findone that is optimal. The system as a whole mustreach a stable and feasible schedule without toomuch interruption of the shop floor.


2.3.2 Manufacturing and Agents

Physically, a manufacturing system involves sev-eral resources (numeric control machines, robots,automated guided vehicles, conveyors) and sev-eral tasks can be carried out at the same time.The number and configuration of these maychange of the lifetime of the system. Since themanufacturing process is dynamic (e.g. suppli-ers and consumers in a supply chain may changemany times) it is impossible to know the exactstructure or topology of the system in advance.The number of products and orders, as well asdifferent alternative production routes, accountfor the highly complex nature of manufacturingsystems.

All of the above make the design of manu-facturing systems an excellent candidate for theapplication of agent-based technology. In manyimplementations of multiagent systems for manu-facturing scheduling and control, the agentsmodel the resources of the plant and the schedul-ing and control of the tasks is done in a dis-tributed way by means of cooperation and coor-dination of actions amongst agents [15, 53, 72].As such, manufacturing scheduling and controltouches the areas of distributed planning and dis-tributed artificial intelligence. Nonetheless, thereare also approaches that use a single agent forscheduling (usually with a well-known centralisedscheduling algorithm) that dictates the schedulesthat the resource agents will execute [92]. Therationale for modelling resources as agents is tobetter mimic the actual real-world environmentand to allow for the modelling of the character-istics of each resource (e.g. available operations,own agenda of tasks to execute, cost of performingeach operation, etc.)

When responding to disturbances, the dis-tributed nature of multiagent systems can also bea benefit to the rescheduling algorithm by involv-ing only the agents directly affected, without dis-turbance to the rest of the community that cancontinue with their work. Typical approaches torescheduling include the removal of a late order,reallocation of low priority orders to make roomfor rush orders, shifting of tasks from one resourceto a similar one, etc.

An example for a MARA system for manu-facturing control is the Fabricare prototypesuite [89]. This a multiagent system for dynamic

scheduling of manufacturing orders. The agentsare modelled as extended logic programs with theability to handle negative and incomplete knowl-edge [88]. The system is very dynamic in whatconcerns its agents, i.e. resource agents dependon the system description file; task agents dependon the existing tasks (dynamic events). Each ne-gotiation uses the set of agents that are presentand available at that time, thus giving the sys-tem a high degree of adaptability to the dynamicnature of the manufacturing arena.

2.4 Grid Computing

Perhaps one of the most pressing applications forMARA techniques is grid computing [40]. It istrue that there are functioning systems for gridresource allocation, but these largely operate inbenevolent, cooperative subnets where partici-pants know and trust one another and there istypically no charge for the utilisation of resources,although perhaps some artificial accounting sys-tem is applied. Such frameworks are exactly whatis needed in order to test out many grid mid-dleware functions where the objective is to see ajob executed across a range of grid resources. Inmany respects, grid resource allocation—as dis-tinct from scheduling—and payment for resourceusage is an orthogonal problem to the actual pro-cessing of a job.

However, at some stage, if the vision of gridcomputing as a commodity not unlike energy is tobecome reality, then resource allocation, paymentand job processing will have to come together andcurrent research in MARA technology aims to laythe foundations for this union.

2.4.1 Scalability Issues

If the benevolent, cooperative network of mutu-ally trusting participants is discarded, the clientis faced with the problem of piecing together arange of disparate resources that are required tocomplete the processing of a particular job. Theparallels with markets, and especially commoditymarkets, as efficient (by economic measures) re-source allocation mechanisms in the presence oflarge numbers of traders and where possibly com-plex packages of goods are required, are striking.Grid networks have not yet become so large as tomake such approaches essential, but that time is


not far off, even in cooperative scientific researchnetworks, if one considers the grid that is foreseento support the analysis of results emerging fromCERN’s Large Hadron Collider [17].

The issues could be seen as a function of scale:Existing grids can handle resource allocationthrough single centralised mechanisms and (eco-nomic) efficiency of allocations may not be impor-tant. As grids become larger with a wider rangeof resources, and used for broader classes of tasks,centralised allocation and inefficient allocation ofresources are likely to become less tolerable. In re-sponse to this, various approaches need to be eval-uated and contrasted under carefully controlledconditions, from centralised systems seeking op-timal allocation to distributed mechanisms in-volving bilateral negotiation. Intuition—whichshould of course be treated with circumspection—suggests that neither of these can be entirely sat-isfactory, but each may act in different ways asbenchmarks against which to measure the rest:

– Centralised systems relying on combinatorialauction clearing algorithms can deliver opti-mal allocations, but are currently limited bycomputation costs to hundreds of items andthousands of bids [81].

– Distributed systems relying on bilateral ne-gotiation between consumer and serviceprovider for each component—that is, theconsumer constructs their own bundle—willalmost certainly scale, but the results aremuch less likely to be “good”. The risks in-herent in such an approach are significant:The order in which to undertake negotiation,the possibility that contracting for one re-source constrains the choice of subsequent re-sources, perhaps leading to incomplete bun-dles, the difficulty in assessing the quality ofa bundle or indeed the valuation of a bundleare all surrounded by uncertainty.

Implicit in both scenarios is that a client will needto combine a range of resources from the grid inorder to carry out their computation.

2.4.2 Market-based Allocation

In between the two extremes of centralised anddistributed lie the many variants of market-based allocation. And given the essentially de-centralised nature of (geographically dispersed)

grids, potentially with many administrative cen-tres and relatively weak control over individualnodes, the grid seems well suited to market-basedschemes, where the twin benefits of reputationand decentralised negotiation can facilitate thetrading of computational resources.

Among the different market schemes that ex-ist, one approach is to mimic ideas seen in com-modity trading [48]. While analogies are bothrisky and seductive, there do seem to be sufficientparallels to make more detailed exploration—andsimulation—desirable. Commodity markets are ablend of centralised and distributed in that thereare many commodity markets around the world,such that at any one time a significant subsetare trading, giving a 24/7 market, but withinany given market trades take place through bilat-eral mechanisms, typically continuous double auc-tions. However, a trader may participate in morethan one market at a time, giving rise to com-munication between markets as to current valua-tion trends along with the publication of “closingprices”.

But, commodity markets typically trade in lotsof a single kind and depending on the market,traders may be direct buyers and sellers with nomiddle-men or market-makers. Economic analy-ses and simulations indicate that market-makersincrease liquidity and enable the market to remain(economically) efficient at lower levels of partici-pation than in the presence of buyers and sell-ers alone [7]. Furthermore, in the case of bun-dles (lots of varying quantities of several kindsof goods), market-makers become repositories ofmarket memory, learning what bundles work (po-tentially a combination of reputation and fit ofresources) and identifying trends as new kinds ofbundles emerge. Thus they become more thanmediators between buyer and seller, fully justi-fying the epithet of “market-maker”. A tradingframework such as this seems highly applicable togrids and resource allocation within grid systems.

3 Types of Resources

A central parameter in any resource allocationproblem is the nature of the resources themselves.In this section, we give a brief overview of the (ab-stract) properties of different types of resources.Some of these properties are characteristics of the


resources (such as being perishable rather thanstatic, or continuous rather than discrete), whileothers are better understood as being characteris-tics of the chosen allocation system (for instance,whether or not a given item is sharable amongstseveral agents will typically depend on the allo-cation procedure rather than on characteristics ofthe item itself).

3.1 Continuous vs. Discrete

A resource may be either continuous (e.g. energy)or discrete (e.g. fruit). This “physical” propertywill typically influence how the resource is beingtraded, although this need not be the case. Forinstance, a continuous resource will typically beregarded as being (infinitely) divisible. Still, ina particular negotiation setting, it may only bepossible to buy or sell a certain quantity of such acontinuous resource as a whole. Individual unitsof a discrete resource, however, are always indi-visible (an apple that can be sold in small pieceswould not count as a discrete resource).

In a setting with several continuous resources,a bundle can be represented as a vector of non-negative reals (or, alternatively, numbers in theinterval [0, 1] to denote the proportion of a par-ticular resource owned by the agent receiving thebundle). Bundles of discrete resources can be rep-resented as vectors of non-negative integers. Ifthere is just a single item of each resource in thesystem, then vectors over the set {0, 1} suffice.

A continuous resource may be discretised bydividing it into a number of smaller parts to betraded as indivisible units. For instance, ratherthan treating 10.000 litres of orange juice as atruly continuous resource that could be dividedinto ever smaller subparts, we may agree to nego-tiate over 200 units of 50 litres each. This meansthat methods developed for discrete MARA areoften also applicable in the continuous case (al-though they may not be as efficient as methodsspecifically tailored to continuous resources).

The allocation of continuous resources (oftenjust a single continuous resource), has been stud-ied in depth in the classical literature in Eco-nomics. More recent work in Computer Scienceand Artificial Intelligence, on the other hand, hasoften focussed on discrete resources. In this pa-per, we also concentrate on discrete resources.

3.2 Divisible or not

As discussed above, resources may treated as be-ing either divisible or indivisible. While being ei-ther continuous or discrete is a property of re-sources themselves, the distinction between divis-ible and indivisible resources is made at the levelof the allocation mechanism. In this survey, weconcentrate on indivisible resources.

3.3 Sharable or not

A sharable resource can be allocated to a num-ber of different agents at the same time. An ex-ample of such sharable resources can be foundin the context of the Earth Observation Satelliteapplication discussed earlier (see Section 2.2): Asingle picture taken by the satellite can be allo-cated to several different agents (no preemptiveconstraints). The canonical case, however, con-siders resources as being non-sharable and in therest of this paper we also make this assumption.

3.4 Static or not

A resource may be consumable in the sense thatthe agent holding the resource may use up theresource when performing a particular action. Forinstance, fuel is consumable. Also, resources maybe perishable, in the sense that they may vanishor lose their value when held over an extendedperiod of time. Food is a classical example of aperishable resource.

We call resources that do not change theirproperties during a negotiation process static re-sources. In general, resources cannot be assumedto be static. In MARA however, it is often as-sumed that they are (that is, that resources areneither consumable nor perishable). The ratio-nale behind this stance is the fact that the ne-gotiation process is not really concerned with theactions agents may undertake outside the processitself. That is, even if a resource is either con-sumable or perishable, we can often assume thatit remains static throughout a particular negoti-ation process. In this paper, in particular, weconcentrate on static resources.

3.5 Single-unit vs. Multi-unit

In a multi-unit setting it is possible to have manyresources of the same type and to refer to these


resources using the same name. Suppose, for in-stance, there are a number of bottles of cham-pagne available in the system, but that agentscannot distinguish between these bottles. In asingle-unit setting, on the other hand, every itemto be allocated is distinguishable from the otherresources and has a unique name.

The differentiation between single- and multi-unit settings is a matter of representation. Anymulti-unit problem can, in principle, be trans-formed into a single-unit problem by introducingnew names for previously indistinguishable items.Vice versa, clearly, any single-unit problem is alsoa (degenerate) multi-unit unit problem. An im-portant advantage of working within a multi-unitsetting is that it may allow for a more compactway of representing both allocations and the pref-erences of agents over alternative bundles. Onthe downside, a richer language (variables rang-ing over non-negative integers, rather than binaryvalues) is required in this case.

3.6 Resources vs. Tasks

At a sufficiently high level of abstraction, a taskallocation problem can be reduced to a resourceallocation problem. Indeed, tasks may be con-sidered resources to which agents assign a nega-tive utility. However, an important characteristicof tasks as opposed to resources is the fact thattasks are often coupled with constraints regard-ing their coherent combination. For instance, atask may require the achievement of another taskas a precondition. In this respect, treating allo-cations merely as assignments of bundles of itemsto agents (without associated time constraints, forinstance) would be too simple a model.

In this paper, however, we concentrate on gen-eral resource allocation problems rather than is-sues that are specific to task allocation (and ex-ception is our discussion in Section 2.3).

4 Preference Representation

Preferences express the relative or absolute satis-faction of an individual when faced with a choicebetween different alternatives.2 In the context of

2This is the decision-theoretic view of preferences,shared by many communities, from mathematical eco-nomics to multi-criteria decision making.

MARA, these alternatives are the different poten-tial allocations of resources, or more concretely,the bundle of resources received by an agent foreach of the alternative allocations.

A preference structure represents an agent’spreferences over a set of alternatives X. Thereare several choices that can be made regardingthe definition of a mathematical model for pref-erence structures (this is an important questionthat has been discussed by researchers in decisiontheory for a long time). We can distinguish fourfamilies of preference structures:

– A cardinal preference structure consists of anevaluation function (generally called utility)u : X → Val , where Val is either a set ofnumerical values (typically, N, R, [0, 1], R+,etc.), or a totally ordered scale of qualita-tive values (e.g. linguistic expressions suchas “very good”, “good”, etc.). In the formercase the preference structure is called quan-titative, in the latter it is called qualitative.

– An ordinal preference structure consists of abinary relation on alternatives, denoted by�, which is reflexive and transitive (and usu-ally, although not necessarily, complete).3

We write x ≺ y (strict preference) if and onlyif x � y but not y � x, and x ∼ y (indiffer-ence) if and only if both x � y and y � x.

– A binary preference structure is simply a par-tition of X into a set of good and a set ofbad states. A binary preference structure canbe seen as both a (degenerate) ordinal pref-erence structure and a (degenerate) cardinalpreference structure.

– A fuzzy preference structure is a fuzzy rela-tion over X, i.e. a function µ : X×X → [0, 1].µ(x, y) is the degree to which x is preferredover y. Fuzzy preferences are more generalthan both ordinal and cardinal preferences.

Since fuzzy and qualitative preferences have notbeen used much as far as resource allocation isconcerned, we are going to neglect these in this

3Some work in preference modelling has also addressednon-transitive preference relations, arguing that humansoften exhibit non-transitive preferences—for the sake ofbrevity we will omit this issue here.


survey, and focus on quantitative and ordinalpreferences instead.

Observe that we have three “levels” for prefer-ence modelling, according to the possible opera-tions allowed by the preference structure: Ordinalpreferences allow only for comparing the satisfac-tion of a given agent for different alternatives, butcannot express preference intensity and do notallow for interpersonal comparison of preferences(that is, expressing statements such as “agent i ishappier with x than agent j with y”). Qualitativepreferences do allow for interpersonal comparisonof preferences, and can express a weak form ofintensity, but they do not allow for any “metric”use of preferences such as computing the differ-ence between two utility degrees so as to allowfor a monetary compensation—while quantitativepreferences do.

Note that any cardinal preference induces anordinal preference, namely for a utility function uwe can define the complete weak order �u givenby x �u y if and only if u(x) ≤ u(y).

The explicit representation of a preferencestructure consists of the data of all alternativeswith their associated utilities (for cardinal prefer-ences) or the whole relation � (for ordinal pref-erences). These representations have a spatialcomplexity in O(|X|) for cardinal structures andO(|X|2) for ordinal structures, respectively.

In many real-world domains, the set of alter-natives X is the set of assignments of a value toeach of a given set of variables. In such cases, thealternatives are exponentially many. It is not rea-sonable to ask agents to report their preferencein an explicit way when the set of alternativesis exponentially large, as this amounts to listingthe exponentially many alternatives together withtheir utility assessment or their ranking. This isthe case, in particular, when alternatives are allo-cations of resources (assignments of resources toagents). For this reason, the MARA project needslanguages for preference representation aiming atenabling a succinct representation of the descrip-tion of the problem, without having to enumer-ate a prohibitively large number of alternatives.Such preference representation languages often al-low for a much more concise representation of thepreference structure than an explicit enumeration.

In this section, we are going to give a briefsurvey of languages for preference representation.

We begin by discussing several ways of represent-ing compactly quantitative preferences (that is,utility functions), including languages specificallyintroduced for combinatorial auctions, and thenwe move on to languages for representing ordinalpreferences.

4.1 Quantitative Preferences

Let R = {r1, . . . , rm} be a set of indivisible re-sources. A quantitative preference structure fora resource allocation problem is a utility functionu : 2R → Val mapping bundles of resources (sub-sets of R) to numerical values (such as the reals).By defining utilities over bundles, we assume thatthe preferences of agents are free of so-called al-locative externalities. That is, the value that anagent assigns to a bundle R does not depend onthe allocation of the remaining resources amongstthe other agents.

In the case of task allocation (as opposed to re-source allocation), we may model the preferencesof agents using cost functions rather than util-ity functions. At the level of abstraction beingconsidered in the present survey, there is no ef-fective difference in the representation of utilityfunctions and cost functions. In the former case,agents would usually aim at maximising their util-ity, while in the latter case they would aim atminimising their costs.

Next we are going to review several languagesfor representing utility functions.

4.1.1 Bundle Enumeration

The most basic form of representing a utilityfunction is to enumerate the bundles to whichit assigns a non-zero value. That is, a utilityfunction u can be presented as the set of pairs〈R, u(R)〉 with R those bundles of resources forwhich u(R) 6= 0. We call this the explicit form, orthe bundle form.

The bundle form is obviously fully expressive inthe sense that any utility function may be so de-scribed. A serious drawback, however, is that thelength of such descriptions will typically be ex-ponential in the number of resources. This hasprompted researchers to develop more succinctlanguages for utility representation.


4.1.2 The k-additive Form

For some (but not all) utilities it is possible to ex-ploit regularities in the function structure in or-der to build succinct and efficiently computabledescriptions. Given k ∈ N, a utility function u issaid to be k-additive if and only if there exists acoefficient αT for each set of resources T of sizeat most k such that:

u(R) =∑T⊆R

αT

The coefficient αT represents the synergetic valueof owning all of the items in T together, beyondthe utility associated with any of its proper sub-sets. If a utility function is presented in terms ofsuch coefficients, then we say that it is given ink-additive form.

The k-additive form is also fully expressive, butonly in the sense that it can describe any utilityfunction provided k is chosen large enough (forany k less than the overall number of resourcesthere are functions that cannot be represented).It is typically considerably more succinct than thesimple bundles form (think of a function mappingbundles to the number of items in a bundle), al-though there are also counterexamples (such asfunctions mapping only bundles with a single el-ement to a non-zero utility value) [18].

In many application domains, it will be rea-sonable to assume that utility functions are k-additive with a relatively small value of k (whichwould allow for a very succinct representation).Indeed, the larger a bundle of resources, the moredifficult for an agent to estimate the additionalbenefit incurred by owning all the resources inthat bundle together (i.e. beyond the benefit in-curred by the relevant subsets).

The k-additive form of representing utilityfunctions is inspired by work in fuzzy measuretheory [47]. It has been introduced into theMARA domain by Chevaleyre et al. [18] and, in-dependently and in a combinatorial auction set-ting, by Conitzer et al. [23].

4.1.3 Weighted Propositional Formulas

Many languages for compact preference represen-tation make an explicit use of logic (for a survey ofsuch languages we refer to the work of Lang [57]).The basic idea of logic-based preference represen-tation for MARA is that each resource r can be

identified with a propositional variable pr, whichis true if the agent whose preferences we are mod-elling owns the corresponding resource, and falseotherwise.4 That is, every bundle R correspondsto a model. Agents can then express their prefer-ences in terms of propositional formulas (or goals)that they want to be satisfied. We write R |= Gto express that the goal G is satisfied in the modelcorresponding to the bundle R.

The simplest (and prototypical) logical repre-sentation of preferences simply consists of givinga single propositional formula G (representing theagent’s goal). The utility function uG generatedby G is extremely basic: uG(R) = 1 if R |= G,uG(R) = 0 if R |= ¬G. One possible refine-ment of this consists of considering a goal baseGB = {G1, . . . , Gn} and counting the number ofgoals satisfied by R.

In a further refinement, goals are associatedwith numerical weights, which tell how impor-tant the satisfaction of the goal is considered tobe. Formally, the preferences of an agent are ex-pressed by means of a finite set of such weighedgoals: GB = {〈G1, α1〉, . . . , 〈Gn, αn〉}, where eachαi is an integer and each Gi is a propositional for-mula. For every bundle R, we define the penaltyof R as follows:

pGB (R) =∑

{αi |R 6|= Gi} (1)

The penalty of R can be viewed as its disutility,that is, uGB (R) = −pGB (R). Many other oper-ators can be used, in place of the sum, for ag-gregating weights of violated (or symmetrically,satisfied) formulas [56].

4.1.4 Straight-line Programs

A further representation form for utility functionsis based on straight-line programs (SLPs). SLPsmay be viewed as directed acyclic graphs consist-ing of two distinguished types of vertex: inputswhich are sources (have in-degree 0) and gates,each of which has in-degree exactly 2. A sub-set of the gates (with out-degree 0) are distin-guished as the program outputs. In addition tothe graph structure an SLP is fully defined by as-sociating a binary Boolean operation with each

4In a multi-unit setting (see Section 3.5), we would haveto consider atomic sentences such as x ≥ 50, signifying abundle with at least 50 units of type x.


gate vertex. For an SLP, C, with m inputs, or-dered as 〈x1, x2, . . . , xm〉 and p gates, a topolog-ical labelling of the vertices assigns a unique in-teger in the range [1,m + p], λ(v), to each ver-tex of C in such a way that: λ(xi) = i; if v isa gate with 〈w1, v〉 and 〈w2, v〉 edges in C thenλ(v) > max{λ(w1), λ(w2)}. A topological la-belling may be efficiently computed for C usingdepth-first search.

An SLP, C with inputs 〈x1, x2, . . . , xm〉 andp gates, t of which are outputs labelled〈s0, s1, . . . , st−1〉 computes its result by execut-ing the program consisting of exactly m + plines, at each of which a single bit value (res(i))is computed. Given an instantiation of theinputs 〈α1, . . . αm〉, the ith line, li computes:res(i) := αi if 1 ≤ i ≤ m; and res(j1)θires(j2)if m + 1 ≤ i ≤ m + p, where θi is the binaryoperation associated with the ith gate and whoseinputs are the vertices labelled j1 and j2. Thenumerical value computed by C as a consequenceof a particular instantiation α of its inputs isval(C,α) =

∑t−1i=0 res(si) · 2i.

This model provides an alternative representa-tion for utility functions, u : 2R → N by a suit-able SLP, C: a subset S defines an instantiationof the inputs via its m-bit characteristic vectorα(S); the value u(S) is then simply val(C,α(S)).It is noted that, although this definition uses N asthe range, it is a trivial matter to extend to Z (al-low an additional output to act as a sign bit) andto Q (interpret the output bits as two groups, onedefining the numerator, the other the denomina-tor). As with the bundle form, the SLP form hasthe property of being fully expressive. In addi-tion, however, there are the following advantages:

– The number of bits needed to encode utilityfunctions can be exponentially smaller thanthat required in the bundle form.

– If the function u : 2Rm → Q is computableby a deterministic Turing Machine in timeT , then u may be represented by an SLP, Ccontaining O(T log T ) lines.

The first of these is easily seen by considering thefunction with value 1 if |S| is odd, and value 0 if|S| is even: the number of bundles to be listedis exactly 2m−1. The same function, however,is described by the program with 2m − 1 linescorresponding to the computation ⊕m

i=1 xi. The

second property is a consequence of the construc-tions presented by Schnorr [85] and Fischer andPippenger [39]. These simulations are effective(i.e. not simply existence arguments) and can beefficiently implemented.

In principle, other “program-based” formalismscan be defined, however, in order to be effectiveit must be possible efficiently to validate that agiven bit-string does describe a syntactically cor-rect program and to have an effective method ofdetermining the program output. For the SLPapproach above, both of these are satisfied, thelatter since the runtime of a given SLP is exactlythe number of program lines contained within it.

Extensive complexity-theoretic treatments ofthe SLP model (described in its usual terminologyof combinational logic networks) may be found inthe monographs of Savage [84], Wegener [96] andDunne [28]. In the context of MARA, the SLPform has been considered by Dunne et al. [32].

4.1.5 Bidding Languages

Bidding languages are used in combinatorial auc-tions to allow agents to communicate their pref-erences to the auctioneer.5 Preferences structureshere are valuation functions or, equivalently, pos-itive and monotonic utility functions on 2R.

Bids are expressed as combinations of atomicbids of the form 〈R, p〉, where p is the amount thebidder is prepared to pay for the bundle R. Twoprominent bidding languages are the OR and theXOR languages:

– The OR language is probably the mostwidely used bidding language. Here the valu-ation of a bundle is taken to be the maximalvalue that can be obtained when computingthe sum over disjoint bids for subsets of thebundle. For instance, a bid of the form

〈{a}, 2〉OR 〈{b}, 2〉OR 〈{c}, 1〉OR 〈{a, b}, 5〉

expresses that the bidder is willing to pay 2for a alone, 2 for b alone, 5 for both a and b,and 6 for the full set. Clearly, this languageis not fully expressive since it cannot repre-sent subadditive utility functions (for exam-ple, there is no way to specify that you wouldonly be prepared to pay 4 for the full set).

5Of course, strategic considerations may cause agentsnot to report their true preferences, but this issue is notrelevant from the viewpoint of preference representation.


– In the XOR language [80], atomic bids are as-sumed to be mutually exclusive. In this case,the valuation of a bundle is simply the high-est value offered for any of its subsets. TheXOR language can express any (normalised)monotonic utility function.

While the XOR language is more expressive thanthe OR language, it can also prove to be far lesscompact for certain types of preferences. For in-stance, the utility function u(R) = |R| requiresan exponential number of atomic bids in the XORlanguage, but only a linear number of OR bids.

Because the OR language is widely considereda simple and natural bidding language, there havebeen several attempts to extend its expressivenesswithout requiring an exhaustive listing of XORbids. It is, for instance, possible to combine thetypes of bids, and to thus to obtain OR-of-XORand XOR-of-OR bidding languages. For an ex-tensive discussion of such languages we refer tothe review article by Nisan [68].

An interesting alternative is to simulate XORbids by means of OR bids. The idea is simplyto introduce “fake” resources (or phantom goods,or dummy items), that have no function otherthan making bundles mutually exclusive, becausethe resource appears in both bundles [41]. Forinstance, if one wanted to express that the set{a, b, c} should be valued at 4, it would be pos-sible to add the fake resource f to obtain both〈{c, f}, 1〉 and 〈{a, b, f}, 5〉, and to bid in additionon 〈{a, b, c}, 4〉. This language, known as the OR∗bidding language (or OR with dummy items), isas expressive as the XOR language.

4.2 Ordinal Preferences

Next we are going to discuss the representation ofordinal preferences. Again, let R = {r1, . . . , rm}be a set of indivisible resources. An ordinal pref-erence structure � is a binary relation over 2R.Here, logic-based languages play a central role(see also our discussion of weighted propositionalformulas in Section 4.1.3).

4.2.1 Prioritised Goals

Prioritised goals are the ordinal counterpart toweighted goals: instead of numerical weights at-tached to goals (expressed as propositional for-mulas), we have a priority relation on goals, from

which a preference relation on the set of bundlescan be drawn.

While some approaches make use of partialpriority preorders, most of them make the as-sumption that the priority relation is complete.When this is the case, then priorities on formu-las can be expressed by a function r from in-tegers to integers. A goal base is then a fi-nite set of formulas with an associated function:GB = 〈{G1, . . . , Gn}, r〉. If r(i) = j, then j iscalled the rank of the formula Gi. By convention,a lower rank means a higher priority. The ques-tion is now how to extend the priority on goals toa preference relation over alternatives. The fol-lowing three choices are the most frequent ones:6

– best-out ordering [5]: R �boGB R′ iff

min{r(i) |R 6|= Gi} ≤ min{r(i) |R′ 6|= Gi}

– discrimin ordering [5, 14, 43]:Let d(R,R′) = min{r(i) |R 6|=Gi & R′ |=Gi}.R �dis

GB R′ iff d(R,R′) < d(R′, R) or{Gi |R |= Gi} = {Gi |R′ |= Gi}

– leximin ordering [5, 58]:7

Let dk(R) = |{Gi |R |= Gi & r(i) = k}|.R ≺lex

GB R′ iff there exists a k such thatdk(R) < dk(R′) and ∀j < k, dj(R) = dj(R′)R �lex

GB R′ iff R ≺lexGB R′ or ∀j, dj(R)=dj(R′)

Note that �lexGB and �bo

GB are complete prefer-ence relations while �dis

GB is generally not. Wemoreover have the following chain of implications:R ≺bo

GB R′ entails R ≺disGB R′ entails R ≺lex

GB R′.

4.2.2 Ceteris Paribus Preferences

In this language, preferences are expressed interms of statements like: “all other things be-ing equal, I prefer these alternatives over thoseother ones.” Formally, let C, G and G′ be threepropositional formulas and V a set of proposi-tional variables including those occurring in Gand G′. The ceteris paribus desire C : G > G′[V ]means: “when C is true, all irrelevant things be-ing equal, I prefer G∧¬G′ to ¬G∧G′”, where the“irrelevant things” are the variables that are notin V . The preference relation induced by a set

6We are using the convention min(∅) = +∞.7Not to be confused with (although related to) the lex-

imin ordering for the aggregation of individual preferencesin a society of agents presented in Section 5.4.


of such preference statements is then the transi-tive closure of the union of preference relations in-duced by individual preference statements. Thislanguage can also be extended so as to allow forindifference statements.

An important sublanguage of ceteris paribuspreferences is the language of (binary) CP-nets [9], which is obtained by imposing the fol-lowing syntactical restrictions:

– Goals G and G′ are literals speaking aboutthe same propositional variable.

– The variables mentioned in the context C ofa preference statement about variable p mustbelong to a fixed set, called the parents of p.

– For each variable p and each possible assign-ment π of the parents of p, there is one andonly one preference statement C : p > ¬p orC : ¬p > p such that π |= C.

Various extensions of CP-nets have been proposedso as to be more expressive. For instance, TCP-nets [12] are CP-nets with a dominance relationbetween variables. Languages for cardinal prefer-ence representation in the style of CP-nets havebeen defined as well, for instance UCP-nets [8],which are based on generalised additive indepen-dence.

4.3 Discussion

At least five very important issues should be ad-dressed when investigating preference representa-tion languages:

– Elicitation: How hard is is to elicit preferencefrom an agent so as to obtain a statementexpressed in a given preference language L?

– Cognitive relevance: How close is a given lan-guage L to the way in which humans wouldexpress their preferences?

– Expressive power: Given a representationlanguage L, a relevant question is whetherL can express all preorders and/or all util-ity functions, or only complete preorders, oronly a strict subclass of them, etc.

– Computational complexity: For a given lan-guage L, what is the computational complex-ity of comparing two alternatives, of deciding

whether a given alternative is optimal, or offinding an optimal alternative?

– Comparative succinctness: Given two lan-guages L and L′, determine whether everypreference structure that can be expressed inL can also be expressed in L′ without a sig-nificant (that is, supra-polynomial) increasein size (in which case L′ is said to be at leastas succinct as L).

A detailed discussion of these issues in view ofall the different representation languages we havecovered would be beyond the scope of this survey.We limit ourselves to a few indicative remarks.

With the exception of bidding languages, allthe languages for quantitative preferences pre-sented above are fully expressive and we havealready discussed several examples of compara-tive succinctness results for such languages. Aproblem with quantitative preferences in generalis the well-known difficulty of eliciting numericalpreferences from agents. Ceteris paribus prefer-ences, being rather close to human intuition andcomparatively easy to elicit, are interesting froma cognitive point of view. However, they havea high computational complexity in the generalcase, and furthermore, they generally leave manypairs of alternatives incomparable. As for pri-oritised goals, their lack of expressive power (nocompensation allowed between goals) somewhatlimits their range of use.

5 Social Welfare

A typical objective in MARA is to find an alloca-tion that is optimal with respect to a metric thatdepends, in one way or another, on the preferencesof the individual agents in the system. The aggre-gation of individual preferences can often be mod-elled using the notion of social welfare as studiedin Welfare Economics and Social Choice Theory.This view is in line with the widely used metaphorof multiagent systems as “societies of agents”. Forinstance, assuming that individual agents modeltheir preferences using utility functions mappingbundles of resources to numerical values, the con-cept of utilitarian social welfare, defined as thesum of individual utilities, can be used to mea-sure the quality of an allocation from the view-point of the system as a whole. This is probably


the most widely used interpretation of the term“social welfare” in the multiagent systems litera-ture [79, 97].

In Welfare Economics and Social Choice The-ory, on the other hand, many different notionsof social welfare and related concepts have beenstudied [2, 65, 86] and many of these are also ap-plicable to MARA systems [33]. In the contextof an e-commerce application, our aim may beto maximise the average profit generated by thenegotiating agents. In this case, utilitarian so-cial welfare provides a suitable metric for assess-ing system performance. In an application suchas that introduced in Section 2.2, where agentsneed to agree on the access to an Earth Observa-tion Satellite that has been jointly funded by theowners of these agents, on the other hand, it isimportant that each agent receives a fair share ofthe common resource (possibly reflecting the sizeof the financial contribution made by its owner).In this case, average utility is clearly not a goodindicator of performance.

Generally speaking, before sending a softwareagent into a system to negotiate on our behalf,we would like to know under what (social) rulesthat system operates. If these rules are not sat-isfactory, we may not be prepared to agree to bebound by the outcome of a negotiation.

In this section, we are going to review some ofthe notions of social welfare proposed in the lit-erature on Welfare Economics and Social ChoiceTheory that are relevant to MARA. More specif-ically, we are going to present and discuss differ-ent approaches to defining a social welfare order-ing, i.e. a mapping from the preferences of theagents in a society to the “preferences” of societyas a whole. Good references in this area are theHandbook of Social Choice and Welfare, edited byArrow, Sen and Suzumura [2], and the textbookby Moulin [65]. We are going to cover preferenceaggregation mechanisms for both ordinal and car-dinal agent preferences (utility functions). Giventhat every utility function also induces an ordinalpreference relation, any concept defined for ordi-nal preferences also extends to the cardinal case.

5.1 Notation

Let A = {1, . . . , n} be a set of agents. Dependingon whether we assume cardinal or ordinal prefer-ence structures, each of these agents i is equipped

with either a utility function ui or a preferencerelation �i. An allocation P is a mapping fromagents to bundles of resources; that is, P (i) is thebundle held by agent i in allocation P .

Our presentation is independent from the ex-act nature of the resources used (divisible or not,sharable or not, etc.). In most cases, we onlyassume that agents have preferences over alterna-tive allocations (only in the case of envy-freeness,discussed in Section 5.7, we need to assume thatagents have preferences over alternative bundles).For instance, P �i Q states that agent i likes allo-cation P no more than allocation Q. Despite suchgenerality, it makes sense to think of preferencesas being defined over bundles of resources (as dis-cussed in Section 4), i.e. to assume that there areno allocative externalities. That is, P �i Q maybe considered an abbreviation for P (i) �i Q(i)and ui(P ) is short for ui(P (i)).

5.2 Pareto Optimality

An allocation P is Pareto-dominated by anotherallocation Q if and only if the following hold:

– P �i Q for all agents i ∈ A; and

– P ≺i Q for at least one agent i ∈ A.

An allocation is Pareto optimal (or Pareto effi-cient) if and only if it is not Pareto-dominatedby any other allocation. That is, an allocationis Pareto optimal if and only if it is not possibleto (strictly) improve the individual welfare of anagent without making any of the others worse off.

Pareto optimality is generally regarded as themost fundamental criterion for efficiency. Notethat the concept of Pareto optimality is purely or-dinal: It does not require preferences to be numer-ical, not even interpersonally comparable. Alsoobserve that the notion of Pareto dominance onlygives rise to a partial (rather than a complete)ordering over alternative allocations.

5.3 Collective Utility Functions

If individual agents use utility functions to rep-resent their preferences, then every allocation Pgives rise to a utility vector 〈u1(P ), . . . , un(P )〉.A collective utility function (CUF) is a mappingfrom such vectors to numerical values (e.g. the re-als). Given that every allocation P determines a


utility vector, a CUF may also be regarded as afunction from allocations P to numerical values.Every CUF sw induces a social welfare ordering:The allocation Q is socially preferred over alloca-tion P if and only if sw(P ) ≤ sw(Q).

In the sequel, we list several examples for suchCUFs and indicate the kind of MARA applica-tions where they may be useful.

5.3.1 Utilitarian Social Welfare

The utilitarian social welfare is defined as the sumof individual utilities:

swu(P ) =∑i∈A

ui(P ) (2)

The utilitarian CUF is independent of the zerosof individual utilities. It can provide a suitablemetric for overall (as well as average) profit in arange of e-commerce applications.

5.3.2 Egalitarian Social Welfare

The egalitarian social welfare is given by the util-ity of the agent that is currently worst off:

swe(P ) = min{ui(P ) | i ∈ A} (3)

This CUF offers a level of fairness and may be asuitable performance indicator when we have tosatisfy the minimum needs of a large number ofcustomers. Fair division [13, 66, 101] is an impor-tant area with many potential applications in thefield of MARA.

5.3.3 Nash Product

The Nash product is defined as the product ofindividual utilities:

swN (P ) =∏i∈A

ui(P ) (4)

This notion of social welfare favours both in-creases in overall utility and inequality-reducingredistributions. In this sense, it may be regardedas a good compromise between the utilitarian andthe egalitarian agendas. Another interesting as-pect of this CUF is that it is independent of theindividual scales of agent utility functions.

Observe that the Nash product can only pro-vide a meaningful metric of social welfare if all in-dividual utilities are non-negative (or better even,if they are all positive).

5.3.4 Elitist Social Welfare

The elitist social welfare is given by the utility ofthe agent that is currently best off:

swel(P ) = max{ui(P ) | i ∈ A} (5)

The elitist CUF is clearly not a fair measure forsocial welfare, but it can be useful in cooperation-based applications where we require only oneagent to achieve its goals.

5.3.5 Rank Dictators

The egalitarian and the elitist CUFs are bothrepresentatives of the family of k-rank dictatorCUFs, which we are going to define next. Let(v↑P )k denote the kth smallest utility assigned toallocation P by any of the agents in A (this is thekth coordinate in the ordered utility vector for al-location P ; see also Section 5.4). Then the k-rankdictator CUF swk is defined as follows:

swk(P ) = (v↑P )k (6)

A special case of particular interest is the medianrank dictator CUF which is defined as swk withk = n

2 in case n is even and k = n+12 in case n is

odd. Indeed, for certain applications the individ-ual level of welfare on an agent that does at leastas well as half of the agents in the system but notbetter than the other half may be considered assuitable indicator for overall system performance.

5.4 The leximin Ordering

The leximin ordering is a social welfare orderingthat refines egalitarian social welfare. It works bycomparing first the utilities of the least satisfiedagents, and in case these utilities coincide, com-pares the utilities of the next least satisfied agents,and so on. This idea is formalised as follows.

Suppose agents use utility functions to expresstheir preferences. Then every allocation P givesrise to an ordered utility vector v↑P , which is theresult of first computing ui(P ) for every agent i ∈A and then arranging these values in ascendingorder. For example, v↑P = 〈3, 5, 20〉 means thatthe agent worst off enjoys utility 3, the one bestoff utility 20, and the third one utility 5.

Then Q is leximin-preferred to P if and only ifthere exists an integer k ∈ {1, . . . , n} such that:


– (v↑P )i = (v↑Q)i for all i < k; and

– (v↑P )k < (v↑Q)k.

In other words, the leximin ordering is the lex-icographic ordering over ordered utility vectors.It favours the reduction of inequalities betweenagents. An allocation is leximin-optimal if andonly if it is not leximin-preferred by any otherallocation.

5.5 Generalisations

It is possible to build families of parametrisedCUFs able to induce a continuous collection ofsocial welfare orderings, including most of thosedefined above. Let us describe briefly two suchfamilies. The first one is defined by the followingadditive CUF [65]:

sw(p)(P ) =∑i∈A

g(p)(ui(P )) (7)

The parameter p is a real number, p 6= 0, andg(p)(x) = sgn(p) · xp (where sgn(p) = 1 if p > 0and sgn(p) = −1 if p < 0), with the conventiong(0)(u) = log u. Obviously, sw(1) measures utili-tarian social welfare, and sw(0) induces the samesocial welfare ordering as the Nash product. Theleximin ordering is the limit of the social welfareordering induced by sw(p) as p goes to −∞.

The other family of CUFs is a particular caseof what is known as ordered weighted averaging(OWA) operators [99]. With the notation intro-duced above, let us define:

sww(P ) =∑i∈A

wi · (v↑P )i (8)

Here, w = (w1, w2, . . . , wn) is a vector of realnumbers. Let us consider the vector w such thatwi = 0 for all i 6= k and wk = 1, then we haveexactly the k-rank dictator CUF (including theegalitarian and the elitist CUFs, which are specialcases of rank dictators). Consider now the vectorw such that wi = αi−1, with α > 0, then the caseα = 1 corresponds to the utilitarian CUF, and theleximin ordering is the limit of the social welfareordering induced by sww as α goes to 0.

5.6 Normalised Utility

It can often be necessary to normalise utility func-tions before aggregating individual preferences us-ing any of the methods presented here, because

many of them require individual utilities to be in-tercomparable. For instance, if P0 is the initialallocation of resources, then we may restrict ourattention to allocations P that Pareto-dominateP0 and use the utility gains ui(P )−ui(P0) ratherthan the utilities ui(P ) themselves as input to ei-ther a collective utility function or the leximinordering.

A further normalisation step would be to eval-uate an agent’s utility gains relative to the gainsit could expect in the best possible case. Moreprecisely, let us define the maximum individualutility for each agent as:

ui = max{ui(P ) |P ∈ Adm} (9)

Here, Adm is the set of admissible allocations.That is, ui is the utility that agent i could enjoyif it were the sole agent exploiting the availableresources. Then we define the normalised indi-vidual utility of an agent i as follows:

u′i(P ) =ui(P )

ui(10)

Observe that max{u′i(P ) |P ∈ Adm} = 1, forall agents i. In other words, the maximum nor-malised utility is the same for all agents.

The optimum of the leximin ordering with re-spect to normalised utilities is known as the Kalai-Smorodinsky solution [66].

5.7 Envy-freeness

An allocation is envy-free if and only if each agentis at least as happy with its share than it wouldbe with any of the bundles allocated to one ofthe other agents [13]. That is, an allocation Pis envy-free if and only if P (j) �i P (i) holds forall agents i and j. Envy-freeness is a propertythat does not require the intercomparability ofthe utilities of different agents.

If we require all items to be allocated, then anenvy-free allocation does not always exist (con-sider, say, a an allocation problem with a singleresource that is desired by all agents in the sys-tem). But even when not all items need to beallocated, it is well-known that there are alloca-tion problems for which there exists no allocationthat is both Pareto optimal and envy-free. Onecould therefore aim at finding (Pareto optimal) al-locations that would, at least, minimise the over-all “degree of envy” as much as possible. There


are several candidate definitions for minimal envy.Two possible approaches would be the following:

– Minimise the number of envious agents.

– Minimise the average degree of envy (the dis-tance to the most envied competitor) of allenvious agents.

5.8 Example

To exemplify some of the concepts introduced inthis section, consider a scenario with two agents,1 and 2, and a set of three resources {a, b, c} thatare indivisible and cannot be shared. Suppose thepreferences of the two agents are represented bythe utility functions u1 and u2:

u1({a}) = 18 u1({b}) = 12 u1({c}) = 8u2({a}) = 15 u2({b}) = 8 u2({c}) = 12

Furthermore, suppose u1 and u2 are additive, i.e.ui(R) =

∑r∈R ui({r}), and thereby fully speci-

fied by the above values. Let P be the allocationgiving a to 1 and b and c to 2.

Allocation P has maximal egalitarian socialwelfare (18). Utilitarian social welfare, on theother hand, is not maximal for this allocation (38rather than 42) , and neither is elitist social wel-fare (20 rather than 38).

P is Pareto optimal as well as leximin-optimal,but not envy-free, since agent 1 would be hap-pier with the share of 2 than with its own. Infact, there is no allocation that would be bothPareto and and envy-free for this problem. Onthe other hand, for the slightly different problemwhere u1({a}) = 20 instead of 18 (leaving the restunchanged), allocation P would be both Paretooptimal and envy-free.

5.9 Welfare Engineering

The insight that very different notions of socialwelfare may be appropriate for different applica-tions of MARA has provided the impetus for thedevelopment of the Welfare Engineering frame-work [19, 33], which addresses two issues:

– the systematic choice of suitable social wel-fare orderings for a given application ofMARA (and possibly the application-drivendesign of new orderings); and

– the design of appropriate rationality criteriaand social interaction mechanisms for nego-tiating agents in view of different notions ofsocial welfare.

By “appropriate” we mean criteria and mecha-nisms that ensure the convergence of the negotia-tion process to an allocation that is optimal withrespect to the chosen social criterion (see also Sec-tion 6.4). Of course, depending on the applicationin question, such criteria need to be balanced withthe autonomy requirements of individual agents.

An example for the first aspect of Welfare Engi-neering would be the elitist collective utility func-tion discussed earlier, which seems unethical forhuman society, but it may be just the right per-formance indicator for a distributed computingapplication where several agents are working to-wards their own goals, but the system designer isonly interested in (at least) one of them achievingtheir objective as quickly as possible. This aspectof Welfare Engineering may be characterised as“welfare economics for artificial agent societies”.

An example for the second aspect would be thefollowing convergence result: To achieve Paretooptimal outcomes in negotiation without mone-tary side payments, ask agents to negotiate mu-tually beneficial deals involving any number ofagents or resources, but also to participate indeals that do at least not lower their own levelof utility [35]. This aspect of Welfare Engineer-ing can be summarised as “inverse welfare eco-nomics”, alluding to the characterisation of mech-anism design as “inverse game theory” [70].

6 Allocation Procedures

Generally speaking, the allocation procedure usedto find a suitable allocation of resources could beeither centralised or distributed. In the centralisedcase, a single entity decides on the final allocationof resources amongst agent, possibly after havingelicited the preferences of the other agents in thesystem. Typical examples for the centralised ap-proach are combinatorial auctions [24]. Here thecentral entity is the auctioneer and the report-ing of preferences takes the form of bidding. Intruly distributed approaches, on the other hand,allocations emerge as the result of a sequence oflocal negotiation steps. Such local negotiation is


often restricted to bilateral trading as in the clas-sical Contract-Net approach [87], but systems al-lowing for multilateral exchanges of resources be-tween more than two agents are also possible.

A comprehensive survey on allocation proce-dures for MARA would be beyond the scope ofthis paper. Any such survey would have to ad-dress at least the following three issues:

– Protocols: At this level, we need to addressontological issues (what types of deals arepossible?) and devise communication pro-tocols accordingly (what messages do agentshave to exchange to agree on one such deal?).

– Strategies: When designing individualagents, we need to devise strategies for agentsthat allow them to best exploit a given ne-gotiation protocol. This can also providefeedback to the first level: Where possible,protocols should be designed in such a waythat they provide incentives to the negoti-ating agents to adopt a particular desirableprofile of behaviour (mechanism design).

– Algorithms: At this level, we need to pro-vide algorithms to solve the computationalproblems faced by agents when engaged innegotiation. This includes both algorithmsto decide how to respond to a proposal ina distributed negotiation scenario and win-ner determination algorithms for combinato-rial auctions. Again, this level may providefeedback to the other two levels: If a partic-ular computational problem proves too hardto be solved in a reasonable amount of timethen this may call for a simplification of thenegotiation protocol (or strategy).

In this paper, we concentrate on the first of theseissues. The most fundamental question to con-sider before devising a protocol for a MARA sys-tem is whether to adopt a centralised or a dis-tributed design. We therefore start with a shortdiscussion of the respective merits and draw-backs of centralised and distributed approachesto MARA. This is followed by an introductionto protocols for combinatorial auctions and anoverview of the Contract-Net and related proto-cols for distributed resource allocation. Finally,we make a connection to our discussion of social

welfare measures in Section 5 and review a num-ber of results concerning the convergence to a so-cially optimal allocation for different protocols inthe distributed setting.

6.1 Centralised vs. Distributed

Both the centralised and the distributed approachto MARA have their advantages and disadvan-tages. Possibly the most important argumentin favour of auction-based mechanisms concernsthe simplicity of the communication protocols re-quired to implement such mechanisms. Anotherreason for the popularity of centralised mecha-nisms is the recent push in the design of power-ful algorithms for combinatorial auctions that, forthe first time, perform reasonably well in prac-tice [41, 80]. Of course, such techniques are, inprinciple, also applicable in the distributed case,but research in this area has not yet reached thesame level of maturity as for combinatorial auc-tions. An important argument against centralisedapproaches is that it may be difficult to find anagent that could assume the role of an “auction-eer” (for instance, in view of its computationalcapabilities or in view of its trustworthiness).

The distributed model seems also more naturalin cases where finding optimal allocations may be(computationally) infeasible, but even small im-provements over the initial allocation of resourceswould be considered a success. Step-wise im-provements over the status quo are naturally mod-elled in a distributed negotiation framework.

6.2 Auction Protocols

Auctions [24, 54, 55, 94, 98] are centralised mech-anisms for the allocation of goods amongst sev-eral agents. Agents report their preferences andwait for the final allocation to be made by theauctioneer (whether there is an initial allocationof goods, as in combinatorial exchanges, or not,as in regular combinatorial auctions). The act ofreporting preferences is called bidding and, natu-rally, agents are not required to reveal their truepreferences during bidding, but they may submitwhatever bid(s) they believe to best serve theirown interests.

Bidding may be public (open-cry) as in thewell-known English auction model or private(sealed bids). In the case of open-cry bidding,


we can further distinguish between ascending bids(English auction) and descending bids (Dutchauction) [94]. In combinatorial domains, whichis what we are interested in here (i.e. there aremany goods and agents can submit bids for differ-ent combinations of goods), typically, most auc-tion protocols foresee only a single round of bid-ding using sealed bids. The bidding language (seeSection 4.1.5) determines what types of bids areadmissible (and how to interpret them).

The auction protocol also specifies which agentwould be awarded which goods, based on the bidsreceived in time, and what price they should payfor the bundles allocated to them. In some cases,this decision can be left entirely to the auctioneer(who will seek to maximise her revenue). In othercases, it is important that the auctioneer followsthe rules specified by the protocol, as these ruleshave been designed in such a way as to provideincentives to the bidders to bid truthfully. This isthe case for the Vickrey auction model [94], andits extensions to combinatorial scenarios, wherethe winning agents pay less then the prices theyspecified in their bids.

For an extensive review of different auctionmodels for resource allocation in combinato-rial domains we refer to the forthcoming bookon Combinatorial Auctions, edited by Cramton,Shoham and Steinberg [24], and the review ar-ticle on the same topic by Kalagnanam andParkes [54].

6.3 Negotiation Protocols

We now give a brief overview of some of the pro-tocols developed for negotiation over resources ina distributed setting.

6.3.1 Contract-Net

Perhaps the most popular negotiation protocol isthe Contract-Net protocol [87]. Although the pro-tocol was primarily designed for task allocation,it is also perfectly suited to MARA. The protocolconsists in four interaction phases, involving tworoles (manager and bidder):

– Announcement phase: The manager adver-tises the resource to a number of partneragents (the bidders).

– Bidding phase: The bidders send their pro-posals to the manager.

– Assignment phase: The manager elects thebest bid and assign the resource accordingly.

– Confirmation phase: The elected bidder con-firms its intention to obtain the resource.

Any agent can initiate an interaction following theprotocol by assuming the adequate role. The pro-tocol is really a one-to-many protocol, leading tothe assignment of a single task (or resource) to asingle contractor (that is, the resulting deal is aone-to-one agreement regarding a single item).

6.3.2 Extensions

Many different extensions to this protocol havebeen proposed and we briefly review some of thesehere. The TRACONET system developed bySandholm [77], for instance, uses a variant of theclassical Contract-Net protocol to allow negotia-tion over the exchange of bundles of resources.

Golfarelli et al. [46] have proposed an exten-sion where the bidders have no explicit mech-anism for utility transfer (in other words, theycannot use money). The first phase remains thesame as in the original Contract-Net: the man-ager announces a (bundle of) resource(s). Butthe protocol is based on exchanges: instead ofbidding money, the agents will bid for one ormore resources they are interested in exchanging.This extension allows agents to agree on swap-ping resources (rather than buying them fromeach other).

Sousa et al. [89] have designed a version of theContract-Net protocol where bidders first propa-gate constraints between them in order to guar-antee the coherence of different operations relatedto the same task.

6.3.3 Concurrent Contract-Net

As pointed out by Aknine et al. [1], when manymanagers negotiate simultaneously with manycontractors, using the Contract Net protocol canlead to unsatisfactory results. In particular, be-cause contractors are required to answer a singlebid at a time, they may miss some contracts. Toovercome this, they have proposed an extensionto in which a pre-bidding and a pre-assignment


phase are added before the final bidding and as-signment phase of classical Contract-Net proto-cols. During the pre-bidding and pre-assignmentphases, which can last a long time, agents pro-pose temporary bids and managers temporarilyaccept (or reject) these bids. These new phaseshave several positive effects:

– After a deal has been temporarily accepted, ifthe manager receives a better offer, this dealcan be turned into temporarily rejected offer.It turns out that when many negotiations areconducted simultaneously, by delaying the fi-nal acceptance, better deals (from the man-ager’s point of view) may be negotiated.

– Contractors can modify their offers manytimes by making temporary offers. If the con-tractor receives a better new offer from an-other manager, it can modify its temporarybids before sending a definitive bid.

– The pre-bidding phase may be quite long.This has the positive effect of reducing therisk of decommitment.

An alternative way to tackle this latter problem isto allow agents to decommit, but to apply penal-ties when they do so. This route has been followedin the levelled commitment approach proposed bySandholm and Lesser [82].

6.4 Convergence Properties

As discussed earlier, once a particular negotiationprotocol has been fixed, we need to devise strate-gies for the agents using that protocol. Work inthis area is often of a game-theoretical nature.A different line of research has analysed how thenegotiation behaviour of individual agents affectsthe quality of the overall distribution of resources(with respect to some of the social welfare mea-sures introduced in Section 5) by abstracting awayfrom the details of individual negotiation strate-gies [35, 78].

For instance, a rational agent may be defined asan agent that will only agree to deals that result ina positive payoff for itself. That is, a set of ratio-nal agents will only agree on mutually beneficialdeals. Which of the possibly many mutually ben-eficial deals agents will actually agree on dependson the concrete strategies they use, and overly ag-gressive negotiation strategies may even prevent

agents from identifying any mutually beneficialdeal at all [67]. However, in cases where it is ad-missible to assume that agents will agree on somedeal meeting certain rationality criteria (such asresulting in a strictly positive payoff for every-one involved) whenever such a deal exists, it issometimes possible to prove so-called convergenceproperties of a negotiation framework.

For instance, in the context of negotiation overfinitely many indivisible resources, an importantresult, due to Sandholm [78], states that any se-quence of deals that are mutually beneficial willeventually result in an allocation with maximalutilitarian social welfare, provided that agentscan use monetary side payments to compensatetheir trading partners for otherwise disadvanta-geous deals (and each agent’s payoff is linear inthe amount of money received). That is, therecan be no infinite sequence of mutually beneficialdeals, and if agents keep on making such deals thesystem will converge to an allocation that max-imises the sum of individual utilities. A similarresult states that any sequence of mutually ben-eficial deals without side payments will convergeto a Pareto optimal allocation [35].

An important caveat is that these results applyto negotiation settings where agents can agree ontruly multilateral deals: A single deal may involveany number of agents (as well as any number ofresources). Decomposing such a multilateral dealinto a sequence of bilateral deals is not always pos-sible, because some of the bilateral deals makingup the overall deal may not be mutually benefi-cial to both agents. Hence, myopic agents thatrequire a positive payoff for every single deal theytake part in will not accept such a deal.

Given the difficulty of implementing such gen-eral deals, it is important to understand underwhat circumstances sequences of structurally sim-ple deals suffice to guarantee convergence to a so-cially optimal allocation of resources. Recent re-sults in this area show that mutually beneficialdeals with side payments that involve only a sin-gle resource each (and thereby only two agentsat a time) suffice to reach allocations with maxi-mal utilitarian social welfare in case all agents usemodular utility functions [35].8 In fact, the class

8A utility function u is said to be modular if and onlyif we have u(R1∪R2) = u(R1)+u(R2)−u(R1∩R2) for allbundles R1 and R2. This means that the utility assigned


of modular utility functions is also maximal in thesense that for no class of functions strictly includ-ing that class it would still be possible to guaran-tee that agents using utility functions from thislarger class and negotiating only mutually ben-eficial deals over single resources will eventuallyreach an allocation with maximal utilitarian so-cial welfare in all cases [21]. Related work has alsoidentified classes of utility functions (and ordinalpreference relations) that guarantee the conver-gence to optimal allocations for sequences of dealsinvolving at most k resources each [20].

7 Complexity Results

A growing body of work within the study ofMARA considers various concepts of complexity,not only in the standard sense of computationalcomplexity theory but also in terms of conceptssuch as communication complexity. Such workcomprises both positive results—e.g. algorithmswith provably efficient performance characteris-tics, properties of restricted classes of allocationsettings, etc.—and a large collection of negativeresults that suggest many naturally arising de-cision and optimisation problems are unlikely toadmit generally applicable algorithmic solutions.Within this section our aim is to review extantwork that has addressed such questions and tocatalogue related open problems.

7.1 Models and Assumptions

The structure we consider in the subsequent textwill be referred to as a resource allocation setting,by which we mean a triple 〈A,R,U〉 where:

– A = {1, 2 . . . , n} is a set of n agents;

– R = {r1, r2, . . . , rm} is a collection of m re-sources; and

– U = {u1, u2, . . . , un} describes the utilityfunction ui : 2R → Q for the agent i ∈ A.

We assume that each r ∈ R is indivisible and non-shareable, i.e. at most one agent at a time will“own” r (see also Section 3). An allocation of

to a bundle of resource can be computed as the sum of theutilities of the individual resources in that bundle, i.e. theclasses of modular and 1-additive functions coincide.

the resources in R among the agents in A is amapping P : A → 2R with P (i) ∩ P (j) = ∅ forany i 6= j. The set of all allocations of R among Awill be denoted by Πn,m. From the fact that thereare n choices of agent for each of the m resources,it is easily seen that |Πn,m| = nm.

7.2 Computational vs.Communication Complexity

In very informal terms, traditional computationalcomplexity theory is concerned with the issue ofclassifying computational problems with respectto how much of a particular computational re-source is required for their solution. Typically,computational problems are phrased as decisionquestions, i.e. given an input instance I, is it thecase that some property φ holds true of I? Forexample, given a directed graph H(V,E) and avertex s in V , is it the case that every vertexin V can be reached by some path that startsin s? The concept of computational resource ismodelled via some formal model of computation.Thus, time (space) as the (worst-case) number ofmoves (tape cells) made by a (deterministic) 2-tape Turing machine (DTM) that correctly clas-sifies input instances, i.e. accepts if φ(I) = >,rejects if φ(I) = ⊥. For further introductionsto computational complexity theory we refer thereader to the textbook by Papadimitriou [69].

In the context of MARA problems, computa-tional complexity results have tended to addresswhat might be termed “global” properties of givenresource allocation settings, e.g. whether alloca-tions satisfying particular criteria exist. Recentwork, however, has begun to address computa-tional properties of abstract high-level negotiationprotocols as reviewed in Section 6.4 above, e.g.given some constraint, χ, that allowed deals mustsatisfy, a number of decision problems may be for-mulated regarding allocations that are reachablefrom a starting allocation via sequences of χ-deals.

This view of complexity has not, in general,needed to be concerned with “localised” ques-tions, e.g. the overheads involved in describingand implementing proposed deals; how manydeals may be needed in order to reach an allo-cation with desirable properties, etc. In the workof Endriss and Maudet [34] the term communica-tion complexity, deriving from the model put for-ward by Yao [100], is introduced to capture the


combination of number of deals and communica-tion to agree a deal that could be needed in orderfor an allocation to be finalised. While the bulkof the survey below is concerned with complex-ity issues from the perspective of computationalcomplexity, we also discuss some results relatedto communication from the works of Endriss andMaudet [34] and Dunne [29], that consider upperand lower bounds on the number of deals neededin various contexts.

7.3 Allocations with Given Properties

Given a resource allocation setting, 〈A,R,U〉, theagents concerned seek to bring about an alloca-tion that will satisfy certain criteria. As discussedin Section 5, such criteria may be purely quanti-tative (e.g. the sum of the individual utility valu-ations (utilitarian social welfare) is maximal (or isabove a given amount), but so-called qualitativeproperties (Pareto-optimal or envy-free outcomes,for instance) are also of interest.

7.3.1 Representation Issues

Standard computational complexity theory con-siders properties of algorithms implementedwithin some “well-defined” model of computation,e.g. Turing machines. In order sensibly to con-sider the performance of a specific algorithm, thisis reported as a function of the algorithm’s inputlength. This convention presumes that, in com-paring different algorithmic approaches to a par-ticular problem, such comparisons are only “rea-sonable” if the representation of input instancesis similar, or that (at worst) different formats canbe translated between efficiently.

In considering how instances are to be repre-sented in the case of decision problems concern-ing resource allocation settings, a significant is-sue that arises is the encoding of the collectionof utility functions U . The domain of a utilityfunction is 2R: thus (from the viewpoint of upperbounds on complexity) the characteristics of algo-rithms employing an enumerative form (listing allsubset/value pairs) may not be comparable withalgorithms employing some compact representa-tion. We therefore give complexity results for thethree different forms of representing utility func-tions discussed in Section 4.1: the bundle form,the SLP form, and the k-additive form (here the

2-additive form is of particular interest).

7.3.2 Quantitative Criteria

Two natural decision questions regarding themeasure swu of utilitarian social welfare, havebeen considered with regard to each of the threeformalisms for representing utility functions:

Welfare Optimisation (WO)Instance: 〈A,R,U〉; K ∈ QQuestion: ∃P ∈ Πn,m : swu(P ) ≥ K?

Welfare Improvement (WI)Instance: 〈A,R,U〉; P ∈ Πn,m

Question: ∃Q ∈ Πn,m : swu(Q) > swu(P )?

WI and WO are both NP-complete for the repre-sentation of utility functions in bundle form (re-duction from Set Packing [18]); for the SLPform (reduction from 3-Sat [32]); and for 2-additive functions (the simplest proof is via areduction from Max-2-Sat [18]). Both the 2-additive and SLP results apply even in systemscontaining only 2 agents; the SLP reduction showsthat the problems remain NP-complete when(both) utility functions are monotonic.

7.3.3 Qualitative Criteria

The qualitative measures of Pareto optimalityand envy-freeness give rise to the following de-cision problems:

Pareto Optimality (PO)Instance: 〈A,R,U〉; P ∈ Πn,m

Question: Is P Pareto optimal?

Envy-Freeness (EF)Instance: 〈A,R,U〉Question: ∃P ∈ Πn,m : P is envy-free?

Deciding PO is coNP-complete for both SLPand 2-additive utility functions. The former wasshown by Dunne et al. [32] (reduction from 3-UnSat restricted to instances with clause andvariable numbers equal); the latter, although notexplicitly stated by Chevaleyre et al. [18], is animmediate consequence of their proof that WI isNP-complete. Again both continue to hold in 2-agent contexts, with the SLP reduction also ap-plying to monotonic utility functions.


EF is examined in a variety of cases in thework of Bouveret and Lang [11]. They considera representation based on concise logic-based de-scriptions of agent preferences (as discussed inSection 4.1.3 above). In addition to the ba-sic question of whether envy-free allocations arepossible—shown to be NP-complete even within2-agent settings—the question of allocations thatcombine envy-freeness with Pareto optimality isexamined (termed efficient envy-free, or EEF,allocations). For such decision problems theydemonstrate completeness results ranging fromNP-complete up to Σp

2-complete, depending onthe restrictions placed on the preference relations.That NP-completeness also holds for the ques-tion EF within the SLP model in 2-agent settingshas been shown by Dunne [30] (reduction from3-Sat).

7.4 Path and Convergence Properties

The collection of results referred to above, holdindependently of the regime used to negotiate al-locations. There are, however, a number of ques-tions that arise specifically in the context of dis-tributed negotiation when the structure of ad-missible deals is constrained. Thus suppose thatonly individually rational deals may be used, i.e.deals that are beneficial to all the agents involved.If monetary side payments are allowed, then in-dividually rational deals are deals 〈P,Q〉 underwhich swu(Q) > swu(P ) [35]. As has been shownby Sandholm [78], if additional constraints, suchas “all deals are bilateral and involve exactly oneresource changing” (sometimes called the class ofO-contracts), then there are cases where some ra-tional deals cannot be implemented. A furtherproblem that arises is that, even when there is arational O-contract path to go from P to Q thismay involve an agent repeatedly making deals in-volving the same resource, i.e. such paths maycontain more than m distinct deals.

In general, given some predicate Φ on deals, thefollowing decision problem arises:

Φ-PathInstance: 〈A,R,U〉; P (s), P (t) ∈ Πn,m with

swu(P (t)) > swu(P (s))Question: ∃∆ = 〈P (0), P (1), . . . , P (r)〉 s.t.

P (0) = P (s) and P (r) = P (t) and∀1 ≤ i ≤ r, Φ(P (i−1), P (i))?

Dunne et al. [32] consider the complexity of Φ-Path where Φ(P,Q) holds only if the deal is indi-vidually rational and involves at most some givennumber k of the resources being passed from oneagent to another. Within 2-agent settings usingSLP representation it is shown that Φ-Path is NP-hard for all k ≤ m

3 (and for the case k = m2 ). In

the special case of O-contracts (i.e. k = 1) NP-hardness holds with both utility functions beingmonotonic. Recent work, presented in Dunne andChevaleyre [31], improves this NP-hardness lowerbound and obtains an exact complexity classifi-cation: Φ-Path is PSPACE-complete for Φ(P,Q)holding if the deal is an individually rational O-contract.

Introducing the idea of a maximal Φ-path (froman initial allocation P ) as a sequence of deals ev-ery one of which satisfies Φ and with the finalallocation, P (t) being such that for every Q it isthe case that ¬Φ(P (t), Q), leads to the followingrelated problem:

Φ-ConvergenceInstance: 〈A,R,U〉Question: Is it the case that ∀P ∈ Πn,m, for

all maximal Φ-paths ∆ startingfrom P , the allocation last(∆)these terminate in, is one whichmaximises swu?

For instance, the basic convergence result firstproved by Sandholm [78] (discussed in Sec-tion 6.4) shows that the answer to the above ques-tion is always “yes” when Φ does not restrictthe range of admissible deals in any way. Φ-Convergence is the subject of ongoing work whichhas already established the following: For Φ corre-sponding to individually rational O-contracts, Φ-Convergence is coNP-complete for the SLP modeland for 4-additive utility functions [31] Both re-sults hold in 2-agent settings. If all utility func-tions are modular (i.e. 1-additive), then the an-swer to Φ-Convergence is always “yes” [21].

We now return to an issue relating to the ideasof communication complexity discussed above.The question of interest also has a bearing onestablishing upper bounds on the complexity ofΦ-Path. Given a resource allocation setting andΦ, consider the (rational) deals that can be im-plemented by Φ-paths. Dunne [29] has introducedthe following measures:


– Lopt(P,Q): the length of the shortest Φ-pathrealising 〈P,Q〉.

– Lmax(A,R,U): the maximum value ofLopt(P,Q) over those deals for which a Φ-path exists.

– ρmax(n, m): The maximum value (takenover all choices of utility function) ofLmax(A,R,U).

– ρmaxC (n, m): As ρmax, but with the maximi-

sation taken over utility functions belongingto some class C.

A related study (employing different terminology)is given by Endriss and Maudet [34], where atten-tion is focussed on utility functions which allowany rational deal to be implemented via some se-quence of rational O-contracts; the main case be-ing considered in this respect is that of 1-additivefunctions.

Let Φ(P,Q) hold if and and only if the deal〈P,Q〉 is an individually rational O-contract:

– ρmax(n, m) ≤ nm −m(n− 1) [78]

– ρmax(n, m) ≥ 772562m − 1 [29]

– ρmax1−add(n, m) = m [34]

– ρmaxmono(n, m) ≥ 77

1282m2 − 3 [29]

The latter two results pertain to the classes of 1-additive and monotonic utility functions, respec-tively. The constructed rational paths in the gen-eral and monotonic lower bound cases are unique.

7.5 Open Problems and Conjectures

Given the existing results concerning the measureswu wherein exact complexity classifications havebeen derived for each of the three representationstyles for utility functions, the following conjec-tures seem plausible and ought to be straightfor-ward to verify.

Conjecture 1 Deciding if there is an allocationP with swe(P ) ≥ K is NP-complete (whether U isgiven in bundle form, SLP form, or is 2-additive).

Conjecture 2 Given K ∈ Q, deciding ifmax{swu(P ) |P ∈ Πn,m} = K is DP -complete(again in all three representation formalisms).

Conjecture 3 EF is NP-complete for 2-additiveutility functions.

8 Simulation Platforms

Theoretical work in Microeconomics and Auc-tion Theory provides a very strong foundationfor analysing many resource allocation problems.However, on occasion we may be faced with aproblem in which some of the assumptions un-derlying the theory are violated. This is espe-cially the case in MARA scenarios where compu-tational concerns are prominent [25]. For exam-ple, mechanism design as originally developed inEconomics is not concerned with computationalissues such as algorithmic or communication com-plexity. In a conventional auction design scenarioissues such as the speed of winner determinationand the communication costs of submitting bidsare often not of significant concern since they arenot typically a bottleneck with respect to the en-tire auction process which can involve protractedand lengthy decision making by human traders.However, in a market place run entirely by au-tomated trading agents, such issues are likely tobe of more concern since their performance costscan sometimes be of similar order of magnitudeas the overall computational costs of running theauction. Once these costs are taken into ac-count many of the results in auction theory be-come somewhat brittle. For example, the revela-tion principle no longer applies when transaction-throughput and reduction in communication com-plexity are adopted as design goals [74].

In such cases experimental work using simula-tions of agent-based market places—Agent-basedComputational Economics (ACE) [93]—can shedlight on some of the grey areas that are difficultto analyse using existing theoretical tools.

As with any software engineering problem, inchoosing an appropriate software framework inwhich to implement an ACE simulation it is im-portant to consider the requirements that thesoftware needs to meet. In this section, we givean overview of the typical requirements addressedby ACE software, and we then proceed to givean overview of some commonly-used simulationframeworks.

8.1 Simulation vs. Implementation

Software for simulating multiagent systems typ-ically addresses different requirements from thatdesigned to implement multiagent systems. Al-


though it is natural to view a MAS implementa-tion as its own simulation, there are a number ofproblems with such an approach, which we shalladdress in turn.

Firstly, ideally we would like the outcome of asimulation experiment to be exactly reproduciblegiven the initial conditions of the experiment.This is not always possible in a MAS implemen-tation since many environmental factors will bebeyond the experimenter’s control. For example,the precise outcome of an experiment may dependon the exact timing with which an agent respondsto a particular message, and this time intervalwill depend on factors beyond the experimenter’scontrol, such as the memory and CPU currentlyavailable to the agent.

Secondly, when we come to analyse the resultsof a simulation, we often need to generalise be-yond a single run of an experiment with a singleset of initial conditions. Typically, we generaliseby taking many samples of free initial variablesand running the experiment many times for eachsample. Simulation frameworks are equipped tolog data from the outcome of each experiment to aformat suitable for analysis using statistical anal-ysis software, such as MATLAB.

Thirdly, the performance considerations of asimulation are qualitatively different to that ofan implementation. The software architecture ofa MAS implementation is driven by real-worldrequirements that do not always hold in a sim-ulation context. For example, trading agentsneed to be able to run on different machinesdue to commercial and practical considerations.This distributed parallelism is detrimental to rawsystem-level performance however, since inter-host network communication overheads dominateother performance considerations. By running allagents on the same host we can achieve severalorders of magnitude performance increase. Thiswould be an impractical solution for a real MAStrading implementation. However, such consider-ations do not apply in a simulation context, andby relaxing these constraints we can achieve a sig-nificant gain in performance.

Similarly, much of the technical complexity of areal MAS implementation addresses requirementsthat are not present in a simulation context. Forinstance, MAS implementations need to be ro-bust against system failures, and they need to re-

spond quickly to real-time asynchronous events.This necessitates a highly parallel software archi-tecture, involving, for example, many threads ofexecution running simultaneously. Such consid-erations do not apply in agent-based simulation,since real-time parallelism can be simulated usinga sequential program, and this greatly reduces thecomplexity of the software (and hence the poten-tial for bugs).

Finally, any MAS interacts at some point withthe environment. In a MARA scenario, for exam-ple, the environment might constitute economi-cally relevant characteristics of the human ownersof agents, such as their utility functions. Unlikethe agents in a MAS implementation, the environ-ment is not a software entity in a MAS implemen-tation, and cannot be directly ported to an agent-based simulation. Rather, the environment itselfmust be simulated. Agent-based simulation toolk-its allow for the abstract statistical simulation ofenvironmental factors. Hence a key feature of anysimulation toolkit is a library of pseudo-randomnumber generators (PRNGs). A good simulationtoolkit will provide high quality PRNGs, such asthe Mersenne Twister PRNG [64], with extremelylarge periods, low statistical correlation, and theability to produce random numbers according toarbitrary (non-uniform) distributions.

In summary, when developing a system to simu-late a MARA scenario, it is important to choose aframework or toolkit that is specifically designedfor agent-based simulation, as opposed to toolkitssuch as JADE [51] that are designed for imple-menting multiagent systems.

8.2 Simulating Time

For practical purposes we often prefer to simulatethe parallelism of events using sequential com-putation, rather than execute the simulation ofmultiple simultaneous events in parallel in real-time. This necessitates a framework for comput-ing the outcome of events that occur simultane-ously. There are several approaches to simulatingtime in a model.

8.2.1 Continuous Time Models

Many physical processes are characterisedby smooth and continuous changes in time-dependent variables. Differential equation models


are common in analytical microeconomics. Suchmodels are applicable approximations of realmarket places when there are very large numbersof participants in the market since individualcharacteristics of the participants play a lesssignificant role and the entities in the system canbe treated as simple and homogeneous particles.However, these models break down when thenumber of participants becomes very small andthe individual and strategic characteristics of theparticipants become more prominent.

Agent-based models address this issue by pro-viding a richer structure with which to modelmarket participants. In such models, macro-levelvariables describing the ensemble of agents nolonger vary smoothly with time. This necessitatesalternative approaches to temporal modelling.

8.2.2 Discrete-event Simulation

Discrete-event simulation frameworks [4, 42]model time in discrete quanta called ticks. In-tuitively, a tick can be thought of as an “instant”of time. During the simulation of a tick—the tickcycle—entities (agents) in the simulation signalwhich agents they interact with during that in-stant of time by sending events to each other.Individual events specify the exact nature of theinteraction between agents. In an auction simula-tion, for example, an auctioneer agent may sendan end-of-auction event to all trading agents inthe auction when it has closed. At the end of atick cycle, once events have been exchanged, eachentity updates its internal state in response to anyevents it has received.

8.3 Agent Modelling

In a MARA simulation, agents often need tomake intelligent decisions in their resource util-isation and acquisition behaviour. The intelligentagents community has traditionally favoured sym-bolic approaches, such as the class of BDI (Belief-Desire-Intention) models. In a MARA scenario,however, an agent’s goals are often quantitative innature; for example, agents act to maximise theirexpected utility. In the field of agent-based elec-tronic commerce, this has led to the adoption ofBayesian approaches to agent’s decision problemssuch as (multiagent) reinforcement learning.

Many agent-based simulation frameworks have

been developed by the Artificial Life (ALife) com-munity. Agents in ALife models are imbuedwith very little intelligent behaviour at the out-set; rather, intelligent behaviour emerges col-lectively from the complex interactions betweenagents equipped with relatively crude decisionmaking machinery. Connectionist approachessuch as neural networks and evolutionary ap-proaches such as genetic algorithms, are popularin such models.

Since simulation is the main methodology usedin ALife research, ALife software toolkits tend tobe the most mature in terms of simulation func-tionality. Correspondingly, since empirical meth-ods are relatively rare in MAS research, there arefew frameworks for simulating BDI agents, as op-posed to implementing BDI agents.

8.4 Extensibility and Integration

When conducting research via simulation it is of-ten necessary to extend the existing functionalityof the system. Although all frameworks providethe ability to configure simulations, the desiredbehaviour cannot always be implemented by con-figuring the existing components provided by theframework. In this case it is necessary for the re-searcher to implement the desired behaviour bywriting their own code. Toolkits take two mainapproaches to allowing extensibility: They alloweither for scripting in a custom language or forthe introduction of new classes and methods viainheritance.

8.5 Software Listing

We are now going to give a brief overview ofsome commonly used general-purpose simulationframeworks that might be suitable for analysingMARA problems.

8.5.1 Swarm

Swarm [91] is one of the most famous ALife soft-ware toolkits and has been continually improvedby an active community of users and develop-ers since the early 1990s. It provides an APIfor discrete-event simulation, uses high-qualityPRNGs, allows for spatial modelling, and includesreal-time visualisation tools. Swarm is an open-source project written in the Objective-C pro-gramming language.


8.5.2 Extensions to Swarm

The Evo toolkit [36] is an extension to Swarmthat provides agents with the ability to mate andevolve new behaviour over time using a systemsimilar to genetic programming.

MAML [63] is an extension to Swarm that pro-vides a higher-level scripting language that is sim-pler to use than Objective-C. The goal is to allowresearchers from the social sciences, who are notnecessarily skilled programmers, to quickly de-velop simulations.

8.5.3 RePast

RePast [75] is another toolkit inspired by Swarm,but is written entirely in Java, and the ulti-mate design goals of this system are more MAS-rather than ALife-oriented. It offers similar fea-tures as Swarm (discrete-event simulation, high-quality PRNGs, spatial modelling, visualisationtools) and it is also open-source and extensible.

The core simulation functionality of RePast isparticularly mature and robust (it use the COLTlibrary for high-performance scientific comput-ing). The MAS-oriented features, on the otherhand, are still relatively immature (no explicit re-inforcement learning, no BDI support).

8.5.4 Desmo-J

Desmo-J [26] is implemented in Java and pro-vides raw discrete-event simulation functionality.While only providing minimal functionality, thesystem comes with a highly flexible, well-designedAPI. It uses the standard Java PRNG, but theAPI should allow other (more advanced) PRNGsto be plugged in as well.

8.5.5 AScape

AScape [3] is a Java-based discrete-event simula-tion framework with an emphasis on spatial mod-elling of agents.

8.5.6 DEx

DEx [27] is a high-performance toolkit provid-ing high-quality PRNGs, discrete-event simula-tion, spatial modelling, and real-time visualisa-tion tools (including 3D representation).

9 Conclusion

We have presented a survey of salient issuesin Multiagent Resource Allocation (MARA), atimely and fast-developing area of research at theinterface of Computer Science and Economics.Naturally, the choice of topics selected for detailedpresentation has been driven, at least in part, bypersonal interests and preferences. Nevertheless,we are confident that this material will prove use-ful to many researchers working on different as-pects of MARA and related disciplines.

In the first part of the paper, after a short in-troduction to the field, we have highlighted fourmajor application domains, which together bothdemonstrate the wide scope of MARA and under-line the urgent need to further advance the fieldto meet the enormous challenges still posed bythese applications. The second part of the pa-per serves as a catalogue of fundamental conceptsin MARA: generic properties of resources charac-terising a MARA problem at hand; languages forpreference representation to model the interests ofindividual agents; and social welfare measures andrelated tools to assess the overall quality of an al-location of resources. The third part of the paperthen addresses actual MARA techniques. This in-cludes, in particular, an introduction to allocationprocedures and a selection of relevant complexityresults. Where theoretical results alone are notsufficient, our survey of simulation platforms canserve as a starting point for experimental work.

Two important issues that we have not cov-ered are the algorithmics of MARA and the game-theoretical analysis of negotiation (and bidding)strategies. The former includes the design of al-gorithms for the winner determination problemin combinatorial auctions, and a survey of recentwork in this area is available elsewhere [81]. Theliterature on game-theoretical issues in negotia-tion, multiagent systems, and Computer Sciencein general is vast and fast-developing. A goodstarting point for readers interested in the com-putational approach to Game Theory (and thegame-theoretic approach to Computer Science) isthe short paper by Papadimitriou [70].

Acknowledgements. This survey has beenwritten in the context of the activities of theAgentLink Technical Forum Group on MultiagentResource Allocation (TFG-MARA).


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