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Rationalizable Implementation of Correspondences

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  • Takashi Kunimoto
  • Roberto Serrano

Abstract

We come close to characterizing the class of social choice correspondences that are implementable in rationalizable strategies. We identify a new condition, which we call set-monotonicity, and show that it is necessary and almost sufficient for rationalizable implementation. Set-monotonicity is much weaker than Maskin monotonicity, which is the key condition for Nash implementation and which also had been shown to be necessary for rationalizable implementation of social choice functions. Set-monotonicity reduces to Maskin monotonicity in the case of functions. We conclude that the conditions for rationalizable implementation are not only starkly different from, but also much weaker than those for Nash implementation, when we consider social choice correspondences.

Suggested Citation

  • Takashi Kunimoto & Roberto Serrano, 2016. "Rationalizable Implementation of Correspondences," Working Papers 2016-4, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2016-4
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    References listed on IDEAS

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    2. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
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    4. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
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    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    7. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    8. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
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    10. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
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    Cited by:

    1. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    2. Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-16, Brown University, Department of Economics.
    3. Ritesh Jain & Michele Lombardi, 2019. "Virtual implementation by bounded mechanisms: Complete information," IEAS Working Paper : academic research 19-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.

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