Design of Combinatorial Auctions for Allocation and Procurement Processes Michael Schwind

1. Design of Combinatorial Auctions for Allocation and Procurement Processes Michael Schwind JWG-University Frankfurt CEC-2005 21.7.2005 Technical University of Munich

2. Basics of the Combinatorial Auction Design of an Auction Framework Economic Validation of Auction Design Summary and Outlook Literature

3. 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.

4. 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

5. 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)

6. 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.

7. Basics of the Combinatorial Auction Design of an Auction Framework Economic Validation of Auction Design Summary and Outlook Literature

8. Combinatorial Auction Decision Support • 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

9. 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

10. Basics of the Combinatorial Auction Design of an Auction Framework Economic Validation of Auction Design Summary and Outlook Literature

11. 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

12. Basics of the Combinatorial Auction Design of an Auction Framework Economic Validation of Auction Design Summary and Outlook Literature

13. 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

14. Basics of the Combinatorial Auction Design of an Auction Framework Economic Validation of Auction Design Summary and Outlook Literature

15. 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.

16. 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.