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Worst-case optimal redistribution of VCG payments in multi-unit auctions

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  • Guo, Mingyu
  • Conitzer, Vincent

Abstract

For allocation problems with one or more items, the well-known Vickrey-Clarke-Groves (VCG) mechanism (aka Clarke mechanism, Generalized Vickrey Auction) is efficient, strategy-proof, individually rational, and does not incur a deficit. However, it is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. We study mechanisms that redistribute some of the VCG payments back to the agents, while maintaining the desirable properties of the VCG mechanism. Our objective is to come as close to budget balance as possible in the worst case. For auctions with multiple indistinguishable units in which marginal values are nonincreasing, we derive a mechanism that is optimal in this sense. We also derive an optimal mechanism for the case where we drop the non-deficit requirement. Finally, we show that if marginal values are not required to be nonincreasing, then the original VCG mechanism is worst-case optimal.

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  • Guo, Mingyu & Conitzer, Vincent, 2009. "Worst-case optimal redistribution of VCG payments in multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 67(1), pages 69-98, September.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:69-98
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    3. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
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    14. Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    15. Thirumulanathan, D. & Vinay, H. & Bhashyam, Srikrishna & Sundaresan, Rajesh, 2017. "Almost budget balanced mechanisms with scalar bids for allocation of a divisible good," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1196-1207.
    16. Yi, Jianxin & Wang, Hefei & Li, Yong, 2018. "Designing efficient and incentive compatible mechanisms is almost impossible in quasi-linear environments," Economics Letters, Elsevier, vol. 173(C), pages 113-117.
    17. Naroditskiy, Victor & Steinberg, Richard, 2015. "Maximizing social welfare in congestion games via redistribution," LSE Research Online Documents on Economics 62771, London School of Economics and Political Science, LSE Library.
    18. de Clippel, Geoffroy & Naroditskiy, Victor & Polukarov, Maria & Greenwald, Amy & Jennings, Nicholas R., 2014. "Destroy to save," Games and Economic Behavior, Elsevier, vol. 86(C), pages 392-404.
      • Geoffroy de Clippel & Louis Putterman & Victor Naroditskiy & Maria Polukarov & Amy Greenwald & Nicholas R. Jennings, 2012. "Destroy to Save," Working Papers 2012-9, Brown University, Department of Economics.
    19. Ruben Juarez & Jung S. You, 2019. "Optimality of the uniform rule under single-peaked preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 27-36, May.
    20. Kazuhiko Hashimoto, 2015. "Strategy-Proof Rule in Probabilistic Allocation Problem of an Indivisible Good and Money," ISER Discussion Paper 0931, Institute of Social and Economic Research, Osaka University.
    21. Naroditskiy, Victor & Steinberg, Richard, 2015. "Maximizing social welfare in congestion games via redistribution," Games and Economic Behavior, Elsevier, vol. 93(C), pages 24-41.
    22. Drexl, Moritz & Kleiner, Andreas, 2015. "Optimal private good allocation: The case for a balanced budget," Games and Economic Behavior, Elsevier, vol. 94(C), pages 169-181.
    23. Athanasiou, Efthymios, 2013. "A Solomonic solution to the problem of assigning a private indivisible good," Games and Economic Behavior, Elsevier, vol. 82(C), pages 369-387.
    24. Yi, Jianxin & Li, Yong, 2016. "A general impossibility theorem and its application to individual rights," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 79-86.
    25. You, Jung S., 2015. "Optimal VCG mechanisms to assign multiple bads," Games and Economic Behavior, Elsevier, vol. 92(C), pages 166-190.

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