COMPLEX AGENT-BASED MODELS: APPLICATION … AGENT... · Theoretical models are usually developed...

Informaãní management

152 2014, XVII, 1 DOI: 10.15240/tul/001/2014-3-012

Introduction

Economies constitute complex and dynamicsystems, which have been studied from multipleperspectives and with various tools, techniquesand methods. They encompass behaviouralpatterns, interaction among particular subjects,or several functional principles [34]. There aretwo dominating issues related to modelling ofeconomic systems. Firstly, study of economicsystems is traditionally based on analytical andeconometric tools, which have been the mainarbiters of the veracity or plausibility ofassumptions and hypotheses in economics.Theoretical models are usually developed foranalytical tractability and offer internalconsistency within prescribed conditions andassumptions [28]. This approach is highlysuitable for theory development. However, inpractice the pace of change and existinguncertainty about the way in which markets willevolve has made it increasingly important forcompanies to be aware of modelling techniques,which would enable support of decision-makingprocesses. Due to this necessity variousmodelling tools, methods, or techniques havealready been applied in the business realm,ranging from standardised tools and techniquessuch as Unified Modelling Language (UML) orPetri nets [30], to non-standardised “fundiagrams” helping managers to capture mentalmodels and ideas [5]. Moreover, the pool ofapplied techniques comprises both modelsgrounded in exact mathematical representationof reality, which can be further simulated (e.g.Markov chains), and more or less vague modelshelping only to express significant elements

and relations in the studied business domain(e.g. flow charts, or causal-loop diagrams).Secondly, majority of these approaches andtechniques usually fail when coping with oneparticular attribute of real economic systems –complexity [6]. These two gaps might bebridged with the help of new modelling paradigmsthat have been established only recently.Application of agent-based modelling in therealm of economic systems is labelled asAgent-based Computational Economics (ACE).Current ACE research divides into four streamsdistinguished by objectives [34]:1) Empirical understanding.2) Normative understanding.3) Qualitative insight and theory generation.4) Methodological advancement.

This paper purpose is to supportconstructivist approach to economic theory andit aims to apply basic ACE principles in newlydeveloped and original model of a complexeconomic system. In particular sections itintroduces results of experiments run on thecreated model. As such, it contributes to thesecond and fourth ACE objectives.

The paper is organised as follows. Theliterature review focused on ACE and researchalready done in this realm is provided in thenext section. Whereas the third section formulatesthe research problem, the developed model isdepicted in the fourth section. Consequently, experi-ments conducted for verifying the model validityand usability is described. The sixth sectionoutlines further research directions and possiblemodel extensions. Finally, the discussed issuesare concluded in the last section of the paper.

COMPLEX AGENT-BASED MODELS:APPLICATION OF A CONSTRUCTIVISM INTHE ECONOMIC RESEARCHVladimír Bure‰, Petr Tuãník

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1. Literature ReviewAgent-based modelling is a quite popularmodelling approach which is widely used inmany disciplines. This approach is characterisedby three main tenets [2]:(i) there is a multitude of objects that interact

with each other and with the environment;(ii) objects are autonomous (hence, they are

called agents), no central or “top down”control over their behaviour is admitted;and

(iii) the outcome of their interaction is numericallycomputed.

Up to date, current scientific papers indexedin recognised scientific databases (ISI Web ofScience or Scopus) are classified to tens ofresearch areas. Whereas the majority ofresearch papers belong to the field of computerscience or engineering (approximately one thirdof them); plethora of other application areassuch as toxicology, entomology, oceanography,crystallography, management of biologicalincidents, mobile applications and enterprise,or tourism can be identified [7], [23], [24], [29].

In the economics domain ACE representsrelatively new field of study. It is primary basedon using of computational power for researchand scientific purposes. Thus, the first studies,which were tied with agent-based simulations,were published in the scientific literature in themid of 1990’s [4], [15], [19]. Since then, it hasbeen possible to undertake the first compu-tationally demanding experiments required tomodel the interactions of a large number ofheterogeneous agents with bounded rationalityin an economy characterised by non-equilibriumdynamics and information asymmetries [2]. Inhis study Giaglis [17] concluded that complexityof economic modelling requires applicationa single, ‘holistic’ technique that could effectivelyrepresent various perspectives in a rigorousand concise fashion, and hence be applicablein all modelling situations. In general, theagent-based modelling enables to developmodels with a large number of heterogeneouscomponents, where the emerging dynamics isnot known a priori, and outcomes are not trivialand immediately deducible from individualbehaviour [8], [37].

In the business and economy realm, theagent-based modelling is applied from theearliest stages of development of this research

paradigm. For instance, Janssen and Vries [21]develop a simple dynamic model of theeconomy-energy-climate system and provethat the adaptive behaviour can be included inglobal change modelling. Vidal and Durfee [38]use an economic multi-agent system to deter-mine when agent should behave strategically(i.e. learn and use models of other agents), andwhen it should act as a simple price-taker. Theirresults show how savvy buyers can avoid beingcheated by sellers, how price volatility can beused to quantitatively predict the benefits ofdeeper models, and how specific types of agentpopulations influence system behaviour. Tradingbetween buyers and sellers representsa segment of economics which was oftenselected for application of multi-agent modellingand simulation principles. Systems such asKasbah [9] or Magma [35] can serve asexamples.

Since the first pioneering studies had beenpublished, the application area in the businessand economy field was extended. For instance,Babita, Rao and Shukla [1] investigate generalpossibilities of multi-agent systems in the e-business realm, Guessoum et al. [18] proposea new adaptive multi-agent model that includesthe organisational forms into the economicmodels, or Wilkinson and Young [39] applyagent-based simulation models for identifyingand modelling underlying mechanisms andprocesses in the marketing realm. Damaceanuand Capraru [10] focus their attention onbanking market. In their study, they conduct 11computer experiments and study the evolutionof various banking market indicators such astotal amount of money, savings, wallets, or bankreserves. Due to its complexity, Sinha et al. [33]studied and created model of petroleum supplychain. Dosi et al. [14] develop an evolutionarymodel of output and investment dynamicsyielding endogenous business cycles. Themodel describes an economy composed ofparticular organisations and consumers. Whereasfirms belong to two industries, consumers selltheir labour and consume their income.Simulation results show that the model is ableto deliver self-sustaining patterns of growthcharacterised by the presence of endogenousbusiness cycles. Desmarchelier et al. [13](re)assess the relationship between knowledgeintensive business services (KIBS) and theeconomic growth with the help of a multi agent-

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based system involving industrial firms,consumer-services firms, consumers, KIBSfirms and a banking system. This model helpsthem to conclude that that KIBS can beregarded as an engine for the economic growthand that they operate as a substitute for thematerial capital accumulation.

In the field of economics, latest researchdirections aim at simulating and synthesizingemergent phenomena and collective behaviourin order to understand economic and socialsystems. Particular topics addressed in scientificjournals include artificial markets with hetero-geneous agents, multi-agents in economics,experimental economics [36], financial marketswith heterogeneous agents [26], non-linear eco-nomic dynamics [25], interacting particle systemsin economics, markets as complex adaptivesystems, or theory and simulation of agent-based models. According to Bargigli & Tedeshi[2], these models have been able to:� Drop the unrealistic assumptions prevailed

in general equilibrium theory.� Obtain the macroeconomic level through

the interaction of agents at the micro level,without imposing either unrealistic repre-sentative agents or simple aggregationprocesses, which only provide a rough,inefficient approximation.

� Allow the existence of an intermediatemeso-scale, which also plays a role indescribing the economic and financialsystem.

� Offer a realistic environment that is wellsuited for studying the out-of-equilibrium tran-sitory dynamics of the economy, as causedby changes in the policy parameters.

Considering all these advantages, it is notsurprising that Delli Gatti et al. [12] discussissues and challenges facing modern macro-economics and state that there is the necessityto replace the reductionist approach at the heartof mainstream a dynamic-stochastic-general-equilibrium (DSGE) model with an approachrooted on the science of complexity and agent-based modelling. For instance, Lengnick andWohltmann [27] combine a simple agent-basedmodel of financial markets and a New Key-nesian macroeconomic model with boundedrationality via two straightforward channels. Theybring a macroeconomic model which enablesthe endogenous development of business

cycles and stock price bubbles. They show thatmarket sentiments exert important influence onthe macro-economy, i.e. impulse-responsefunctions [20] of macroeconomic variablesbecome more volatile which makes the effect ofa given shock hard to predict. Furthermore,Pegoretti et al. [31] analyse how the structure ofsocial networks affects innovation diffusion andcompetition under different information regimes.Diffusion is modelled as the consequence ofidiosyncratic adoption thresholds, local networkeffects and information diffusion. The experi-ments reveal that for example a high socialcohesion decreases the probability of oneinnovation cornering the market, while a lowsocial cohesion also increases the probabilityof falling into traps of under-adoption.

However, the ACE movement has to copewith issues related to this research paradigm.For instance, ACE modelling requires theconstruction of dynamically complete economicmodels. It means that a modeller has to startfrom initial conditions and the model mustpermit and fully support the playing out of agentinteractions over time without further interven-tion from the modeller. This completenessrequires detailed initial specifications for agentdata and methods determining structural attributes,institutional arrangements, and behaviouraldispositions. Consequently, there is the difficultywith validating ACE model outcomes againstempirical data. ACE experiments provideoutcome distributions for theoretical economicsystems with explicitly articulated micro-foundations. Mostly these outcome distributionshave a multi-peaked form suggesting multipleequilibria rather than a central-tendency formpermitting simple point predictions [34]. Then,intensive experimentation must often beconducted over a wide array of plausible initialspecifications for ACE models if robustprediction is to be achieved [22].

2. Model Description

2.1 General CharacterisationAlthough slight extension of application domainsand development of more complex models isapparent, the literature review reveals thatseveral main areas can be identified in thebusiness and economics modelling. However,these areas are mostly problem-based focusingon particular issues and their solutions. Thus,

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they are inevitably independent from theresearch perspective and do not allow simulationand analysis of mutual interrelationship thatrepresents typical feature of the real economicsystems. Moreover, even though the systemicnature of conducted research is obvious insome cases, several models are still based onthe “ceteris paribus” assumption when modelanalysis and simulations are run. Therefore,effort needs to be focused on mutualconnection of the following economic segmentsand related issues, which individually representa challenge from both the modelling andbusiness perspective [36]:1. Logistics – path finding and application of

the graph theory; mechanisms of grouptransport coordination; dynamical routechanges.

2. Consumer behaviour – accordance withexisting theories in economics; content ofthe consumer basket and its determinantssuch as taxing, education, or social level.

3. Production processes (manufacturing) –production chain management; standardi-sation; achieving a certain quality level withexisting technological limitations.

4. Supplying processes – supply chainmanagement; continuity of processes withminimisation of delays; relationship ofvolume to number of transportation agents.

5. Managerial decision-making and planning –level of autonomy; pricing; decisionsrelated to organisational development.

6. Labour market – education and qualificationissues; accordance with existing theories;structural differentiation in an economy.

7. Services – composition of services; influenceof consumer utility function; (dis)similarity totangible products.

8. Representation of environment – mapsutilisation; infrastructure; mobility of agents.

The model described below aims at simula-tion of economic principles and behaviour ofsubjects, e.g. effective price and quantitysetting under specific demand and capacityconstraints [32]. Hence, the focus is on tradingproducts and services, and demanding work ona labour market. Virtual economy simulation issimilar to the work of Deguchi et al. [11],however, in that representation the entitiesconsidered are more specific, producing morecomplicated net of relations than necessary. On

the other hand, trust issues as discussed forexample in [16] and similar concerns are not ofprimary attention in the presented virtualeconomy. Due to the simplicity and clarity ofrelations and transparency of design, severalservice sectors such as banking or govern-mental sector are not included in the model.Thus, the model represents structured two-sector model of economy described in themacroeconomics.

2.2 Formal Model StructureThe created model comprises four types ofagents: a) consumer agent, b) factory agent, c)mining agent and d) transportation agent. Ingeneral an agent is described as a vector ofeight observed parameters

AGENT = (pos, w, k, s, con, e, pro, mob, a)(1)

where � pos represents the agent’s position in the

2-D Cartesian coordinates during thesimulation;

� w means wealth with the assumption wagent >= 0, i.e. no debts are allowed;

� s represents storage capacity, which is anytype of container in which material can besaved;

� con gives an agent’s consumption, in caseof consumer agents it represents combina-tion of production manufactured by factoryagents, in case of mining and transportationagents it represents consumption of capitalrequired for production, and in case offactory agent it expresses combination ofproducts on inputs and labour;

� e stands for efficiency (i.e. technologicallevel in case of factor, mining andtransportation agents, and qualification ofconsumer agents);

� pro represents a production function, whichrepresents combination of inputs used byfactory and mining agents;

� mob gives mobility, i.e. working efficacy ofa transport agent; and

� a stands for agent’s affiliation to a colony(defined below), whereas agent → COLthat express that each agent belongs to justone colony in the model;

Thus, particular agents are formally descri-bed by the following vectors of parameters:

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� consumer agent: C = (pos, a, w, s, con, eC),� factory agent: F = (pos, a, w, s, con, eF,

pro),� mining agent: M = (pos, w, s, con, eM, pro),� transportation agent: T = (pos, a, s, con, eT,

mob).

Moreover, a colony is added as the fifthtype of agent (meta-agent) and has thefollowing parameters

COLmetaagent = (pos, s, w, cw, CP) (2)

where� cw reports the creditworthiness of a colony;

and� CP indicates the colony population, i.e. size

of the colony in terms of number of agents.

2.3 Detailed Agent DescriptionConsumer agent embodies the economic entitythat consumes products and services (i.e.goods) and offers work. Consumer agents canbuy goods based on the wealth they possess.The wealth of a consumer agent is a product ofwork and qualification (higher qualification resultsin faster accumulation of wealth). A consumeragent makes a trade-off between investmentinto higher qualification (ec) and consumption.The combination of products consumed and thespeed of consumption is given by the consumptionfunction. The combination of products formsa pattern of consumption that can be used todivide consumers into three categories. The threecategories are low income, middle income andhigh income consumers. The pattern determi-nes the ratio of goods that the consumer agentis buying. There three types of goods:necessity, normal, luxurious. For example theproportion of goods bought by a low incomeclass consumer might be 70% of necessitygoods such as food and basic householdservices; 20% of normal goods and 10% ofluxury goods. The willingness to buy a certainproduct depends on the stock. The lower thestock of that particular product the higher priceis consumer agent willing to pay). In otherwords, the scarcity increases acceptable price.This principle is corresponding with standardprice and demand relationship. The price pmaxis the amount a consumer is willing to pay whenthe stock of that product is empty. Conversely,as the stock is close to 100% of the capacity

the price approaches zero i.e. the consumer iswilling to buy only if the price is very low.

The second type of agent, a factory agent,corresponds with a company in a real economy.Factory agent is responsible for transforminginput to output i.e. material and other productsto final product that is bought by consumeragent for consumption or serves as a sub-product that is used by another factory agent inits manufacturing processes. The consumptionfunction determines types of materials and theirproportions. The production function determinesthe portfolio of goods produced. Productionrequires workforce i.e. employing consumer agents.The production depends on the technologicallevel eF and qualification of the workforce i.e.employed consumer agents eC. The productionequation is as follows:

(3)

Let kicon be the speed of consumption of

a material xi and WF is the workforce; ec isqualification level of a consumer agent and eFtechnological level factory agent; kj

pro be thespeed of production of a product yj.

Third type of agent in the model is miningagent. This is agent responsible for transformingresources, located in the environment, into rawmaterials that are used by factory agents inproduction of goods. The cost of mining isdetermined by the consumption function inwhich the energy and technology necessary formining is reflected. The function is similar toconsumption function of a factory agent. Eachmining agent supplies only one type of rawmaterial (if several types of raw materials areproduced simultaneously, each is representedby a single specialised mining agent). Rawmaterial, as transformed from resources, isstocked in order to be later sold to transportagents and distributed to processing facilities(i.e. factories) by logistic network.

Transport agents serve as intermediarybetween mining agents and factory agents. Thecost of transportation is given by the distance.There might be barriers or obstacles on the wayfrom mining agent to the factory agent; hence,it is the task of the transportation agent to finda route that is the most economical orotherwise efficient. Different strategies may beused for solving path-finding and distributionproblems, e.g. transport agents may co-ordinate

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transportation effort with each other in order toachieve maximum efficiency. The performanceof a transportation agent is determined by thespeed (or mobility), capacity and technologicallevel. Transport agent is a proxy for a particularfactory agent. Thus, transport agent does nothave any wealth and is buying material on

behalf of a factory agent. The technologicaladvancement of a transportation agent is alsothe same as for the factory agent. Transportationagent is always buying all available material upto the capacity of transportation. Transportedmaterial that is not used directly in production isstored in factory agent`s warehouse.

Fig. 1: Prototype of virtual economy in NetLogo

Source: own

The modelled virtual economy containsalso representation of a society of agents whichis called “colony” in this context in order toavoid possible confusion with sociologicalsemantics. The colony consists of consumer,factory and transportation agents. Miningagents do not belong to any colony, as they aredistributed throughout the environment, dependingon the location of resources they process (seeFig. 1). The colony is characterised by its positionin the environment and size of population.Colonies compete for resources that aresupposed to be scarce or at least limited. Theenvironment is important for transportation

services provided by transportation agents.The success of a colony can be measured

by several factors. The most commonefficiency metric is wealth. This metric can beused as default even in case of scenario whenno special task is assigned to the colony. Thewealth of a colony is given by the sum of wealthof all agents. Due to different colony populationsthe comparison among colonies requirescomputing wealth per agent. The formula is asfollows:

(4)

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where

(5)

Scalability and configuration options of themodel enable for various configuration and thusfor conducting specific experiments. Theseexperiments might be focused on thriving of bigcolonies with a large population of agents. Otherset of experiments might include the competitionamong colonies in case of a universal resourcethat cannot be substituted in the productionprocess. Similarly, an interesting experimentmight reveal the speed of wealth accumulationin case of one large colony as compared toa number of smaller competing colonies.

2.3 User InterfaceThe user interface is designed in order to providemaximum transparency of the model. As canbe seen at the Fig. 2, the environmentrepresentation is situated on the left side of thescreen and model output (charts) is on the rightside. Control buttons on the top allow switchingdisplay of additional information on/off. Individualagent communities are distinguished by colourcode. Additional configuration settings for basicmodel parameters (such as number of colonies,resources, or their location in environment) arealso available; however these are not shown atthe Fig. 2.

Fig. 2: User interface layout in NetLogo application

Source: own

3. Example ScenariosThe presented system is already implementedas a prototype version in NetLogo environmentand several experiments have been conducted.However, since this platform has certain limitsfor large scale experiments, full version is intendedto be implemented in a more sophisticatedenvironment. Two resource-oriented scenariosshowing model behaviour are provided in thissection of the text. In both cases the working

hypothesis about system’s ability to finda solution were tested.

3.1 Example Scenario #1 – Resource Production

In this scenario, the working hypothesis H0states that “the created model is capable tocapture dynamics of price development whenthe demand is continuously saturated”. There isan M-agent producing one type of material

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needed at four colonies of different sizes. Fig. 3shows user interface used in prototype applicationwith described scenario settings. At the beginning,each colony has certain amount of resources instockpile in order to survive the initial phasewhen the production is established. However,when the colony runs out of this stockpile, scarcity

of resources will be reflected by increased priceof the given commodity. Depending on the typeof resource, the scarcity might ultimately resultin termination of colony existence (in case ofsome sort of vital resource, e.g. food) or theproduction in the colony will be suspended untilthe supply line is established again.

Fig. 3: Scenario layout

Source: own

The price chart, shown at the Fig. 4 coversfirst 1,000 iterations of the model run. Duringfirst 500 steps, the agent was unable toproduce satisfactory amount of material tosatisfy demand of all colonies. The scarcity ofthis resource is reason why the price holds athigh levels during this time. This situation isfavourable for the M-agent and it accumulateswealth quickly. This allows it to purchase

technological upgrades after approximately 500steps, allowing it to increase level of productionand satisfy more customers. Individual agentsare more saturated, and price level dropsoccasionally (price which customers are willingto pay is derived from the size of their reserve).At this point, M-agent strategy should be adjustedto maximisation of profits, becoming efficientlya price-maker for the given commodity.

Fig. 4: Chart of “rm1” material price in 1000 iterations

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From the colony perspective, the satisfactionlevel is heavily dependent on its size (i.e.population). In this case, data related to fourconsidered colonies are labelled c-eff1, c-eff2,c-eff3, and c-eff4 respectively, with size of 100,75, 50 and 25 agents respectively. Situation isshown at the Fig. 5. Best results are achievedby colony #4, due to its small size (it is easier tosatisfy demand of smaller community of

agents) where satisfaction has quickly risen tohigh values. Colony #1 was able to fully satisfydemand of its inhabitants for first 200 steps only(probably also because of some small supply ofmaterial in reserve given at the initialisation ofthe model). This resulted in unsatisfactory saturationof C-agent population (consumers) inside of thecolony (which reached even critical levels) inthe latter phases of the simulation.

Fig. 5: Satisfaction of inhabitants (C-agents) of four colonies

Source: own

It is apparent the hypothesis H0 is confirmedbe the achieved results. There are possibleexpansions of this scenario which may beconsidered. There is a question of selection ofappropriate strategy for all participants – forexample the M-agent may maintain such levelof production which maximises its profit for aslong as possible. But a new source of materialor a competition may be introduced to themodel in later phase. New mining facility maybe purchased by colonies in order to reduce theprice. The idea is to create system able toadapt to changing conditions in the dynamicenvironment. All this is done autonomously,without intervention of human operator (user).

3.2 Example Scenario #2 – Resource Proximity

This scenario tests the working hypothesis H0that “proximity of a critical source influenceefficiency of a colony”. The production chain ismore complex in this case, consisting of fiveraw materials and three levels of productionwith eleven products in total (it will not bepresented here in detail but rather described asneeded). However, the experiment is focusedmostly on raw material number 5 (labelled as

“rm5” in charts). There are three colonies usedin this scenario. In order to allow comparison ofeffectiveness, rm5 is near one of them – “Colony#3”, see Fig. 6, where the key raw material rm5is situated in the upper right quarter. Alternativeconfiguration is shown at the Fig. 7, where rm5is situated in the middle of the screenshot.

After 1,000 iterations of the model run,there can be seen some similarities in results.The most significant is price of the rm5 com-modity. While other resources tend to lowertheir price over time, as the demand is graduallymore satisfied, price of rm5 stays high all thetime. Also, the overall efficiency of colonies isinfluenced by the proximity of rm5 resource.Being the most important resource in theenvironment, effectiveness of the given colonydepends heavily on the distance from it. Otherresources have clearly some impact too, but incomparison, it is not so intense.

Two configurations shown at Fig. 6 and 7are just examples of more extensive testing.After thirty simulation runs, behaviour of theprice of rm5 commodity remains always thesame. This leads to following conclusions. Theproximity of the critical resource is determiningeconomic dominance in the environment. The

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behaviour of the colony should be adaptable toboth environment and competition. As soon asthe economic dominance is clearly recognisedby tendency to achieve high c-efficiency scoreshown in histogram over long period of time(iterations), typically in correlation with pricechart, the colony should re-specialise its productionto other type of product. This statement is supportedby Fig. 8, where left side shows result related toenvironment configuration shown at the Fig. 6,whereas the right side is tied to the Fig. 7.Notice similarity in price development “M-agents-price” for “rm5” material. Thus, the

hypothesis H0 is confirmed. Moreover, speciali-sation should be determined by initial conditionsof the model, ideally at the beginning of thesimulation but even during its run, and thechoice regarding specialisation is influenced bythese factors:� Majority of given raw material is in close

proximity of the colony.� Other sources of this resource are insigni-

ficant in quantity or distant for competition.� Production facilities and workforce required

for its processing are available to thecolony.

Fig. 6: Model environment layout

Source: own

To conclude, colonies should specialisetheir production according to the initialconfiguration of the model, capitalizing all theadvantage over competition environment mayprovide. Described factors also allow coloniesto autonomously recognise error in judgementeven later and eventually re-specialise. Inconfigurations where all colonies use the same

production pattern it is a matter of optimisationof workforce allocation. Obtained results will befully utilised in full version of the model which isbeing implemented. Nonetheless, they mayserve as an example of information which canbe used to improve autonomous decisionmaking and effectiveness of agents in theproposed model.

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4. Further Development – CollectivePerspective

Most of the work done so far was focused onindividual agents. On the other hand, groupperspective is important as well since a colonyis a collection of agents supposed to beworking together collaboratively, not just at thesame place and in the same time. Behaviouralconcepts where agent would act simplyunselfishly are typically inconsistent withgeneral economic theory since an individual isexpected to maximise its own utility. In fact,such concepts would probably have more incommon with control mechanisms of insects orother animals, rather than humans [33].Although the task at hand is not to createa complete real-world simulation but onlya simplified model, we would not like to recedetoo far from reality of human economy.

For this reason individual approach todecision making at the level of a single agent isa requisite. It leads to more autonomousbehaviour, which makes models more credible,decentralised and agent-oriented. Moreover,real-world customers are also able to decide on

their own course of actions. However, as it wasclearly described by Batten [3] in gametheory’s classical scenario ofprisoner’s dilemma, it is more efficient tocooperate than to scam each other from thelong-term perspective. Since the range ofpossible actions for individual agents is wide,provided model is designed rationally and is runin several iterations. This leads to conclusionthat there should be rules at the communitylevel allowing this collaboration to happen onthe scale of the whole group.

In order to narrow possible actions andmanipulate agents to work for the benefit of thegroup as a whole, a set of rules should beestablished. There might be general groundrules applied in the model such as the followingstatement: it should be more profitable for theindividual agent to follow such rules than todefy them. This actually reflects laws existing inhuman communities. This does not necessarilymeans that agents could not break rules at all,but it should only be done rarely. On the otherhand, there are also other incentives other thangeneral rules or laws that can be used to

Fig. 7: Another example of model environment layout

Source: own

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stimulate appropriate behaviour, e.g. financialbonuses, price reduction for services, or moreeffective community services (such as trans-portation, infrastructure condition, education,security, etc.). Thus, it is becoming more importantto focus more attention on stimuli allowingagent to decide correctly, i.e. according toglobal (community) goals, corresponding withadopted community policy and priorities. It isnatural to expect that under given conditionsand with provided information the agent will bedoing its own decision rationally, act efficientlyand predicatively. But one may ask: what can

be considered to be an efficient or rationaldecision?

The question of “correct” or “proper”decision making is not as complicated as itmight seem at the first glance. It only requiresapproach suitable for machine processing ofinformation. In context of this paper, thisrequires definition of a global goal in a waywhich allows mathematical comparison of a newstate over previous state(s) of the environmentas the simulation develops over time in order tomonitor progress in goal pursue. This globalgoal may be defined by the user, randomly

Fig. 8: Comparison of results

Source: own

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selected from the set of goals or adoptedautonomously by the colony when circums-tances require it (like switching manufacturingpriority to food production when scarcity of foodoccurs). In all cases, it must be clearly numeri-cally represented in the form of a variablevalue.

Although very general metrics to measureefficiency of the system like “colony wealth”described in the equation (4) can be used, thegoal definition is important for measuring

efficiency of the model on a larger scale. Asthere is more information and attributes beingimplemented in the model, the wealth metric isgradually becoming insufficient to cover allimportant factors contributing to “efficiency”.Furthermore, similarly to real-world, there is notonly one goal but several goals to be pursuedat the same time. As the model becomes moredetailed and covers more factors, more goalsare to be pursued as well. Examples aredepicted in the Fig. 9.

Fig. 9: Examples of parallel goals of agents in the system

Source: own

As it can be seen from these examples,goals are to be pursued simultaneously atseveral levels. Priorities may differ for individualgoals according to actual policy. Moreover, allgoals are mutually interrelated. Thus, setting oftheir priorities (weights) and structure of relation-ships needs to be considered as a furtherresearch direction. The task at hand is how tomotivate all types of agents to work togetherefficiently. The solution is in establishing set ofconstraints which would limit agent`s decisionmaking capabilities to the form which manifestsabove mentioned parameters – predictability,efficiency, rationality – at both individual andcommunity levels. These constraints can beimplemented by two major factors, see Fig. 10.

Inevitable parallelism in goals’ pursue leadsconclusively to some form of aggregateattribute, representing overall progress and

efficiency of any singular agent. In theproposed model, this aggregate attribute ismarked as “satisfaction” – which is numericallyrepresented without units of measure. Ingeneral, an agent tries to maximise itssatisfaction. This concept also allows furtherexpansion of model with new features or inmore detail without a need to redesignefficiency measurement system with every newaddition.

The most difficult task is proper design andbalance of the environment (prices, wages,taxes). For this, we use data provided by CzechStatistical Office, up to the limited (reasonable)extent. This helps us to configure systemparameters, but we try to avoid overwhelmingcomplexity which would result from full scaleimplementation of all data available. Proposedmodel is to be modular and transparent.

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Conclusions

Modelling of economic systems is tied witheconomics as an independent discipline fromearly stages of its formulation. As investigatedphenomena had become more comprehensive,usage of various tools and methods wasnecessary. One of the most current approachesin the field of business and economics modellingis grounded in agent based approaches, whichresulted in establishment of Agent-basedComputational Economics. In this regard, thispaper provides readers with a novel model ofeconomy with two dominant attributes. Firstly, itis theoretically grounded in the ACE paradigm.Secondly, it is complex in its nature and thusnot focused merely on selected standard problemssolved in the economic research (searching forequilibrium might serve as an example). Depictedmodel serves as a platform form wide variety oftests and experiments, which can be used for betterunderstanding or verification of both basiceconomic principles and practical problems. Themodel proved its validity and reasonability withthe help of several experiments, while two resource--oriented tasks are presented in this paper. Modularityof model implementation and transparency ofthe system allows further model developmentand incorporation of new features in future.

This research has been supported by theFIM UHK Excellence Project “Agent-basedmodels and Social Simulation”.

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doc. Ing. Vladimír Bure‰, Ph.D.University of Hradec Kralove

Faculty of Informatics and ManagementDepartment of Information Technologies

[email protected]

RNDr. Petr Tuãník, Ph.D.University of Hradec Kralove

Faculty of Informatics and ManagementDepartment of Information Technologies

[email protected]

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Abstract

COMPLEX AGENT-BASED MODELS: APPLICATION OF A CONSTRUCTIVISMIN THE ECONOMIC RESEARCHVladimír Bure‰, Petr Tuãník

The current state in research of economic systems is characterised by two prevailing issues. Firstly,study of economic systems is traditionally based on analytical and econometric tools, which havebeen the main arbiters of the veracity or plausibility of assumptions and hypotheses in economics.This approach has been proved to be highly suitable for theory development. Secondly, practicalissues and necessity to support decision-making led to development of various modelling andsimulation techniques or tools. However, majority of these approaches usually fail when coping withcomplexity. Furthermore, several main areas of interest can be identified in the business andeconomics modelling. Nevertheless, these areas are mostly independent due to their problem-based focusing on particular issues and their solutions. Depicted gaps might be bridged with thehelp of new modelling paradigms that have been established only recently. Application of agent-based modelling in the realm of economic systems is labelled as Agent-based ComputationalEconomics (ACE). In particular sections of this paper results of experiments run on the novel modelare described. The model is based on agents, which are described as a vector of several observedparameters, and four types of agents are used, namely consumer agent, factory agent, miningagent, and transportation agent. In addition, a colony is added as the fifth type of meta-agent.Scalability and configuration options of the model enable for various configuration and thus forconducting specific experiments. The presented system is already implemented as a prototypeversion in the NetLogo environment. The paper depicts two example scenarios, resourceproduction and resource proximity, and offers interpretation of achieved results. Since most of thework done so far was focused on individual agents, group perspective as an important extensionof ACE modelling is suggested as the further research and development direction.

Key Words: Multi-agent modelling, agent-based computational economics, NetLogo,resource.

JEL Classification: C6, D8, M2.

DOI: 10.15240/tul/001/2014-3-012

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