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Truthfulness with value-maximizing bidders: On the limits of approximation in combinatorial markets

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  • Fadaei, Salman
  • Bichler, Martin

Abstract

In some markets bidders want to maximize value subject to a budget constraint rather than payoff. This is different to the quasilinear utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to bidders who maximize value as value bidders. While simple single-object auction formats are truthful, standard multi-object auction formats allow for manipulation. It is straightforward to show that there cannot be a truthful and revenue-maximizing deterministic auction mechanism with value bidders and general valuations. Approximation has been used as remedy to achieve truthfulness on other mechanism design problems, and we study which approximation ratios we can get from truthful mechanisms. We show that the approximation ratio that can be achieved with a deterministic and truthful approximation mechanism with n bidders cannot be higher than 1/n for general valuations. For randomized approximation mechanisms there is a framework with a ratio that is tight.

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  • Fadaei, Salman & Bichler, Martin, 2017. "Truthfulness with value-maximizing bidders: On the limits of approximation in combinatorial markets," European Journal of Operational Research, Elsevier, vol. 260(2), pages 767-777.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:2:p:767-777
    DOI: 10.1016/j.ejor.2016.12.031
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    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 413-438.
    3. Chaturvedi, Aadhaar, 2015. "Procurement auctions with capacity constrained suppliers," European Journal of Operational Research, Elsevier, vol. 247(3), pages 987-995.
    4. Klemperer, Paul, 2002. "How (not) to run auctions: The European 3G telecom auctions," European Economic Review, Elsevier, vol. 46(4-5), pages 829-845, May.
    5. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    6. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    7. Tae-Young Paik & Pradyot K. Sen, 1995. "Project Evaluation and Control in Decentralized Firms: Is Capital Rationing Always Optimal?," Management Science, INFORMS, vol. 41(8), pages 1404-1414, August.
    8. Mansouri, Bahareh & Hassini, Elkafi, 2015. "A Lagrangian approach to the winner determination problem in iterative combinatorial reverse auctions," European Journal of Operational Research, Elsevier, vol. 244(2), pages 565-575.
    9. Bichler, Martin & Schneider, Stefan & Guler, Kemal & Sayal, Mehmet, 2011. "Compact bidding languages and supplier selection for markets with economies of scale and scope," European Journal of Operational Research, Elsevier, vol. 214(1), pages 67-77, October.
    10. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    11. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    12. Holzman, Ron & Kfir-Dahav, Noa & Monderer, Dov & Tennenholtz, Moshe, 2004. "Bundling equilibrium in combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 47(1), pages 104-123, April.
    13. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    14. Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    15. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    16. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
    17. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    18. Dobzinski, Shahar & Lavi, Ron & Nisan, Noam, 2012. "Multi-unit auctions with budget limits," Games and Economic Behavior, Elsevier, vol. 74(2), pages 486-503.
    19. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
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