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Implementation in Minimax Regret Equilibrium

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  • Ludovic Renou
  • Karl H. Schlag

Abstract

This note studies the problem of implementing social choice correspondences in environments where individuals have doubts about the rationality of their opponents. We postulate the concept of "-minimax regret as our solution concept and show that social choice correspondences that are Maskin monotonic and satisfy the no-veto power condition are implementable in "-minimax regret equilibrium for all " ? [0, 1).

Suggested Citation

  • Ludovic Renou & Karl H. Schlag, 2009. "Implementation in Minimax Regret Equilibrium," Discussion Papers in Economics 09/24, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:09/24
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp09-24.pdf
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    References listed on IDEAS

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    1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    2. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    3. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    4. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    5. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    6. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    7. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    8. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    9. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    10. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    11. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    12. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    13. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
    14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
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    Citations

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    Cited by:

    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Bernhard Kasberger & Karl H. Schlag, 2024. "Robust Bidding in First-Price Auctions: How to Bid Without Knowing What Others Are Doing," Management Science, INFORMS, vol. 70(7), pages 4219-4235, July.
    3. Bernhard Kasberger & Karl H. Schlag, 2017. "Robust Bidding in First-Price Auctions: How to Bid without Knowing what Otheres are Doing," Vienna Economics Papers 1707, University of Vienna, Department of Economics.
    4. Bierbrauer, Felix & Netzer, Nick, 2016. "Mechanism design and intentions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 557-603.
    5. Yao, Koffi Serge William & Lavaine, Emmanuelle & Willinger, Marc, 2024. "Effectiveness of the approval mechanism in a three-player common pool resource dilemma," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 109(C).
    6. Masuda, Takehito & Okano, Yoshitaka & Saijo, Tatsuyoshi, 2014. "The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally," Games and Economic Behavior, Elsevier, vol. 83(C), pages 73-85.
    7. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    8. George F. N. Shoukry, 2019. "Outcome-robust mechanisms for Nash implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 497-526, March.
    9. repec:dpr:wpaper:0874 is not listed on IDEAS
    10. Koffi Serge William Yao & Emmanuelle Lavaine & Marc Willinger, 2021. "Effectiveness of the approval mechanism for CPR dilemmas: unanimity versus majority rule," CEE-M Working Papers hal-03234786, CEE-M, Universtiy of Montpellier, CNRS, INRA, Montpellier SupAgro.
    11. Yingni Guo & Eran Shmaya, 2019. "Robust Monopoly Regulation," Papers 1910.04260, arXiv.org.
    12. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    13. Schlag, Karl, 2018. "How to Play Out of Equilibrium: Beating the Average," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181525, Verein für Socialpolitik / German Economic Association.
    14. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    15. repec:dpr:wpaper:0874r is not listed on IDEAS
    16. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    17. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    18. Xiaochuan Huang & Takehito Masuda & Yoshitaka Okano & Tatsuyoshi Saijo, 2014. "Cooperation among behaviorally heterogeneous players in social dilemma with stay or leave decisions," Working Papers SDES-2014-7, Kochi University of Technology, School of Economics and Management, revised Feb 2015.

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    More about this item

    Keywords

    Implementation; minimax regret; Maskin monotonicity.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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