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Optimal Mechanisms with Finite Agent Types

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  • William S. Lovejoy

    (Ross School of Business, University of Michigan, 701 Tappan, Ann Arbor, Michigan 48109-1234)

Abstract

In some mechanism design problems, finite-type spaces may be natural ones to consider, yet the current literature is dominated by analyses of continuous-type spaces. This probably derives from the intellectual dominance of the early work in this area. Here we present an analysis of the finite-state case that unifies and generalizes current understanding of these problems. We analyze general quasi-linear utility functions among asymmetric agents with an arbitrary number of finite types, in the context of incentive-compatible direct revelation games. A key part of the analysis is the relationship between expected benefit functions that feature alternative forms of supermodularity that translate into relaxations or restrictions of the original problem. The required features can be attained with a range of assumptions on the model primitives, each of which can support the results. This unified approach can suggest a range of alternative assumption combinations, often more general than their counterparts in the continuous-space literature, and each of which can reduce the problem to a more tractable form. Also, mechanism design problems with finite-type spaces can require conscious attention to how the principal handles ties, which are probability-zero events, and hence innocuous in continuous spaces.

Suggested Citation

  • William S. Lovejoy, 2006. "Optimal Mechanisms with Finite Agent Types," Management Science, INFORMS, vol. 52(5), pages 788-803, May.
  • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:5:p:788-803
    DOI: 10.1287/mnsc.1050.0502
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    Cited by:

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    4. Andrzej Baranski & Sumit Goel, 2024. "Contest design with a finite type-space: A unifying approach," Papers 2410.04970, arXiv.org, revised Oct 2024.
    5. Vasiliki Skreta, 2007. "Optimal Auctions with General Distributions," Levine's Bibliography 843644000000000227, UCLA Department of Economics.
    6. Dimitris Zissis & George Ioannou & Apostolos Burnetas, 2020. "Coordinating Lot Sizing Decisions Under Bilateral Information Asymmetry," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 371-387, February.
    7. Zissis, Dimitris & Ioannou, George & Burnetas, Apostolos, 2015. "Supply chain coordination under discrete information asymmetries and quantity discounts," Omega, Elsevier, vol. 53(C), pages 21-29.
    8. Takashi Kunimoto & Cuiling Zhang, 2021. "On incentive compatible, individually rational public good provision mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 431-468, August.
    9. Mobini, Zahra & van den Heuvel, Wilco & Wagelmans, Albert, 2019. "Designing multi-period supply contracts in a two-echelon supply chain with asymmetric information," European Journal of Operational Research, Elsevier, vol. 277(2), pages 542-560.
    10. Zhibin (Ben) Yang & Göker Ayd{i}n & Volodymyr Babich & Damian R. Beil, 2009. "Supply Disruptions, Asymmetric Information, and a Backup Production Option," Management Science, INFORMS, vol. 55(2), pages 192-209, February.
    11. Li, Ying & Gupta, Sudheer, 2011. "Strategic capability investments and competition for supply contracts," European Journal of Operational Research, Elsevier, vol. 214(2), pages 273-283, October.
    12. Manea, Mihai & Maskin, Eric, 2023. "Withholding and damage in Bayesian trade mechanisms," Games and Economic Behavior, Elsevier, vol. 142(C), pages 243-265.
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