Design of Combinatorial Auctions for Allocation and Procurement Processes Michael Schwind

Dipl. Wirtsch. Ing. Michael Schwind, Projekt PREMIUM Internetökonomie

Design of Combinatorial Auctions for Allocation and Procurement

Processes

Michael SchwindJWG-University Frankfurt

CEC-200521.7.2005 Technical University of Munich


Basics of the Combinatorial Auction

Design of an Auction Framework

Economic Validation of Auction Design

Summary and Outlook

Literature


Combinatorial Auction Basics

• Bidders` Valuations for Bundles of Goods:– Substitutionalities Subadditivity– Complementarities Superadditivity

• Winner Determination Problem (WDP):– Allocation Auction Weighted Set Packing Problem– Procurement Auction Weighted Set Covering Problem

• Procurement Auction:

s.t.c.

jSxjSBS i

i

i

1)(,

Sisxi ,1;0)(

ii BS

ii

iSx

SpSx )()(min)(


Combinatorial Auction Variants

• Multidimensional Auction:– Exchange of complex preference information– Various dimensions: e.g. quality, delivery time

• Multi-attributive Auction:– Impact of attributes on W2P is determined by valuation

functions

• Multi-item Auction:– Single items of different goods are bundled in bids

• Multi-unit Auction:– Multiple items of a good type are bundled in bids


Combinatorial Auction Advantages / Problems

• Advantages:– Higher efficiency in final allocation– Lower transaction costs– Higher transparency

• Problems:– NP-hardness of WDP:

• Exact solutions: Integer programming, branch-and-bound• Heuristics: Simulated annealing, genetic algorithms

– Pricing Problem:• Linear prices / Non-linear prices (anonymous / personalized)

– Preference Elicitation Problem:• 2j-1 combinations of bids in worst case

– Incentive Compatibility / Stability of Mechanism:• Vickrey-Clarke-Groves (n+1 * NP-hard)


Combinatorial Auction Process Design

• Modeling of the pre and post auction phase:– Organization of the auction preparation and post processing

phase– E.g. publication of auction rules, transaction management

• Design of the main auction phase:– Major impact on the auction outcome– Design of the allocation mechanism

• Modeling of the auction process flow control:– Timing of bidding sequence, closing, clearing time

• Legal, security and system stability issues:– Transaction management protocol, etc.





Summary and Outlook

Literature


Combinatorial Auction Decision Support

Quality

Winner-DeterminationConstraints

GA / SA / Greedy SolverInteger-Programming

Solver

exact resultcalculationrequiredfast result

calculationrequired

allocationresult

constraintsrequired

CA WinnerDetermination

approximateresult

calculationallowed

One-ShotAuction

Vickrey-Clarke-Groves

OR-of-XOR

OR

AND

AND-OR

Quantity

min. Provider

other

Turnover

CA BidFormation

bid-withdrawal

allowed

manualvaluationallowed

multi-attributivevaluationrequired

leveledcommitment

alllowed

automatedbid-

generationrequired

Bidding LanguageConstraints

IterativeAuction

Sealed-Bidding

Bid-ValuationModule

only bidacceptancenotification

requiredindividualnon-linear

pricingallowed

anonymouslinearpricing

required

CA PriceFeedback

anonymousnon-linear

pricingallowed

Ascending /Descending

Auction

Open-OutcryClock-Auction

Proxy-AgentSealed-Bidding

other

Time

Quantity

• Fundamental Decisions: Price feedback– One-shot: sealed-bid

VCG usable, only acceptance

– Iterative: price feedback, anonymous pricing, usage of sealed bid proxy agents, clock auction

Bid formation– Bid valuation: multi-

attributive, manual / automated bid construction (logistics), preference elicitation by questions, bid withdrawal (leveled-commitment) allowed in connection with proxy agents


Combinatorial Auction Decision Support

• Fundamental Decisions:Bid formation (contd.)

– Bidding language constraints: Logic (AND / OR, XOR, OR-of XOR), expressiveness vs. simplicity

Winner determination: – Integer programming:

small problem size, exact, slow, VCG

– GA / SA / Greedy: big problem size, approximate, fast computational speed vs. economic efficiency

– Winner determination constraints: quantity / turnover share, no. provider

Quality

Winner-DeterminationConstraints

GA / SA / Greedy SolverInteger-Programming

Solver

exact resultcalculationrequiredfast result

calculationrequired

allocationresult

constraintsrequired

CA WinnerDetermination

approximateresult

calculationallowed

One-ShotAuction

Vickrey-Clarke-Groves

OR-of-XOR

OR

AND

AND-OR

Quantity

min. Provider

other

Turnover

CA BidFormation

bid-withdrawal

allowed

manualvaluationallowed

multi-attributivevaluationrequired

leveledcommitment

alllowed

automatedbid-

generationrequired

Bidding LanguageConstraints

IterativeAuction

Sealed-Bidding

Bid-ValuationModule

only bidacceptancenotification

requiredindividualnon-linear

pricingallowed

anonymouslinearpricing

required

CA PriceFeedback

anonymousnon-linear

pricingallowed

Ascending /Descending

Auction

Open-OutcryClock-Auction

Proxy-AgentSealed-Bidding

other

Time

Quantity





Summary and Outlook

Literature


Combinatorial Auction Economic Validation

• Analysis and Prototype Design:– Properties of procurement / allocation

process

• Experimental Game Theory:– Field implementation of prototype– Small scale experimental field evaluation– Iterative redesign

• Automated Mechanism Design:– Simulation implementation– Evaluation using benchmark– Iterative parameter optimization

• Evaluation:– Mechanism evaluation using benchmark

• Meta language description:– Auction description using XML-based

CAMeL

yes

Analysis of procurement and allocation processproperties and design of auction prototype

according to process properties

Evaluation of mechanism using benchmark

Description in auction meta language

yes

Implementation of auction prototype inmechanism design optimizer

Simulative evaluation of auction usingbenchmark

Optimalallocation quality

reached ?

auction parameteroptimization

no

Small scale experimental field evaluation

Sufficientallocation quality

reached ?

Field implementation of auction prototype

auction redesign

no





Summary and Outlook

Literature


Combinatorial Auction Summary & Outlook

• Advantages of the approach:– Enables trade off in practical environments– Two-step validation of economic properties

• Development of a Combinatorial Auction Meta Language (CAMeL):– Enables description of auction in all phases of design

process– CAMeL integrates:

• Bidding Language description• Auction constraints and admission rules• Auction process control





Summary and Outlook

Literature


Literatur

– Ausubel, L. M., Cramton, P. and Milgrom, P. (2005) The Clock-Proxy Auction: A Practical Combinatorial Auction Design. In Combinatorial Auctions.(Eds, Cramton, P., Shoham, Y. and Steinberg, R.) MIT Press.

– Bichler, M., Pikovsky, A., Setzer T. (2005) Kombinatorische Auktionen in der betrieblichen Beschaffung - Eine Analyse grundlegender Entwurfsprobleme. Wirtschaftsinformatik.

– Hohner, G., Rich, J., Ng, E., Reid, G., Davenport, A. J., Kalagnanam, J., Lee, H. S. and Chae, A. (2003) Combinatorial and Quantity-Discount Procurement Auctions Benefit Mars, Incorporated and its Suppliers. Interfaces, 33, 23-35.

– Kalagnanam, J. and Parkes, D. C. (2003) Auctions, Bidding and Exchange Design. In Supply Chain Analysis in the eBusiness Area.(Eds, Simchi-Levi, D., Wu, S. D. and Shen, M. Z.) Kluwer Academic Publishers.

– Kameshwaran, S. and Narahari, Y. (2001) Auction Algorithms for Achieving Efficiencies in Logistics Marketplaces. Proceedings of the International Conference on Energy, Automation and Information Technology.

– McAfee, P. and McMillan, J. (1987) Auctions and Bidding. Journal of Economic Literature, 25, 699-738.


Literatur

– McMillan, J. (1995) Why Auction the Spectrum? Telecommunications Policy, 19, 191-199.

– Nisan, N. (2005) Bidding Languages. In Combinatorial Auctions.(Eds, Cramton, P., Shoham, Y. and Steinberg, R.) MIT Press.

– Porter, D., Rassenti, S. J., Smith, V. L. and Roopnarine, A. (2003) Combinatorial Auction Design. Interdisciplinary Center for Economic Science, George Mason University.

– Sandholm, T. (2002a) Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence, 135, 1-54.

– Schwind, M., Stockheim, T. and Rothlauf, F. (2003) Optimization Heuristics for the Combinatorial Auction Problem. Proceedings of the Congress on Evolutionary Computation CEC 2003, Canberra, Australia, pp. 1588-1595.

– Schwind, M., Weiss, K. and Stockheim, T. (2004) CAMeL - Eine Meta-Sprache für Kombinatorische Auktionen. 2004-111, Institut für Wirtschaftsinformatik, Johann Wolfgang Goethe-Universität.

– Smith, V. L. (1994) Economics in Laboratory. The Journal of Economic Perspectives, 8, 113-131.

– Vickrey, W. (1963) Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance, 16, 8-37.

Design of Combinatorial Auctions for Allocation and Procurement Processes Michael Schwind

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