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Definable and Contractible Contracts

Author

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  • Michael Peters
  • Balázs Szentes

Abstract

This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of the other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player's contract. We provide a complete characterization of the set of allocations supportable as pure strategy Bayesian equilibrium of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.
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Suggested Citation

  • Michael Peters & Balázs Szentes, 2012. "Definable and Contractible Contracts," Econometrica, Econometric Society, vol. 80(1), pages 363-411, January.
    • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:1:p:363-411
    DOI: ECTA8375
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    Cited by:

    1. Paul Duetting & Michal Feldman & Inbal Talgam-Cohen, 2024. "Algorithmic Contract Theory: A Survey," Papers 2412.16384, arXiv.org.
    2. Karl Wärneryd, 2014. "Observable Strategies, Commitments, and Contracts," CESifo Working Paper Series 5089, CESifo.
    3. Attar, Andrea & Campioni, Eloisa & Mariotti, Thomas & Pavan, Alessandro, 2021. "Keeping the Agents in the Dark: Competing Mechanisms, Private Disclosures, and the Revelation Principle," TSE Working Papers 21-1227, Toulouse School of Economics (TSE), revised Jun 2025.
    4. Andrea Attar & Eloisa Campioni & Thomas Mariotti & Alessandro Pavan, 2021. "Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms," CEIS Research Paper 519, Tor Vergata University, CEIS, revised 21 Oct 2021.
    5. Attar, Andrea & Campioni, Eloisa & Mariotti, Thomas & Piaser, Gwenaël, 2021. "Competing mechanisms and folk theorems: Two examples," Games and Economic Behavior, Elsevier, vol. 125(C), pages 79-93.
    6. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2019. "Private communication in competing mechanism games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 258-283.
    7. Arieli, Itai & Babichenko, Yakov & Tennenholtz, Moshe, 2017. "Sequential commitment games," Games and Economic Behavior, Elsevier, vol. 105(C), pages 297-315.
    8. Peters, Michael & Troncoso-Valverde, Cristián, 2013. "A folk theorem for competing mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 953-973.
    9. Forges, Françoise & Koessler, Frédéric & Salamanca, Andrés, 2024. "Interacting mechanisms: A perspective on generalized principal–agent problems," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    10. Andrea Attar & Eloisa Campioni & Gwenael Piaser, 2011. "Information Revelation in Competing Mechanism Games," CEIS Research Paper 205, Tor Vergata University, CEIS, revised 04 Jul 2011.
    11. Peters, Michael, 2015. "Reciprocal contracting," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 102-126.
    12. Han, Seungjin, 2015. "Robust competitive auctions," Economics Letters, Elsevier, vol. 136(C), pages 207-210.
    13. Seungjin Han, 2020. "Quasi Ex-Post Equilibrium in Competing Mechanisms," Department of Economics Working Papers 2020-11, McMaster University.
    14. Severinov, Sergei & Virag, Gabor, 2024. "Who wants to be an auctioneer?," Journal of Economic Theory, Elsevier, vol. 217(C).
    15. Françoise Forges & Ulrich Horst & Antoine Salomon, 2016. "Feasibility and individual rationality in two-person Bayesian games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 11-36, March.
    16. Gorkem Celik & Michael Peters, 2016. "Reciprocal relationships and mechanism design," Canadian Journal of Economics, Canadian Economics Association, vol. 49(1), pages 374-411, February.
    17. Juan I. Block & David K. Levine, 2016. "Codes of conduct, private information and repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 971-984, November.
    18. Li, Anqi & Xing, Yiqing, 2020. "Intermediated implementation," European Economic Review, Elsevier, vol. 123(C).
    19. Forges, Françoise, 2013. "A folk theorem for Bayesian games with commitment," Games and Economic Behavior, Elsevier, vol. 78(C), pages 64-71.
    20. Lavi, Ron & Shamash, Elisheva S., 2022. "Principal-agent VCG contracts," Journal of Economic Theory, Elsevier, vol. 201(C).
    21. Peck, James, 2018. "Competing mechanisms with multi-unit consumer demand," Journal of Economic Theory, Elsevier, vol. 177(C), pages 126-161.
    22. Szentes, Balázs, 2015. "Contractible contracts in common agency problems," LSE Research Online Documents on Economics 66071, London School of Economics and Political Science, LSE Library.
    23. Philippe Jehiel & Laurent Lamy, 2018. "A Mechanism Design Approach to the Tiebout Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 735-760.

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