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Stability and Implementation via Simple Mechanisms in the Complete Information Environments

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

This paper investigates implementation of social choice functions in the complete information environments. We construct particularly simple mechanisms named local direct mechanisms, which require each agent to make a single announcement about her own and neighbors' utility indices. We assume that each agent is boundedly rational in that she may announce any best reply, including disequilibrium messages, even if the others play a Nash equilibrium. We require that the honest message profile be stable in the global sense that it is reachable from every message profile and no other message profile is reachable from it. It is shown that with a minor restriction, every social choice function is virtually implementable. We provide naive models of adaptive dynamics whose convergence characterizes the static definition of stability. We also investigate several variants of the stability notion such as BR-stability, weak stability, and weak BR-stability.

Suggested Citation

  • Hitoshi Matsushima, 2002. "Stability and Implementation via Simple Mechanisms in the Complete Information Environments," CIRJE F-Series CIRJE-F-147, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2002cf147
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2002/2002cf147.pdf
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    3. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    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. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    7. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
    8. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    9. Hitoshi Matsushima, 2001. "Stable Implementation," CIRJE F-Series CIRJE-F-128, CIRJE, Faculty of Economics, University of Tokyo.
    10. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    11. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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    Cited by:

    1. Hitoshi Matsushima, 2002. "Honesty-Proof Implementation," CIRJE F-Series CIRJE-F-178, CIRJE, Faculty of Economics, University of Tokyo.
    2. Hitoshi Matsushima, 2002. "Direct Mechanisms, Virtual Implementation, and Majority-Proofness," CIRJE F-Series CIRJE-F-149, CIRJE, Faculty of Economics, University of Tokyo.
    3. Hitoshi Matsushima, 2002. "Plurality Mechanisms, Virtual Implementation, and Condorcet-Decisiveness," CIRJE F-Series CIRJE-F-148, CIRJE, Faculty of Economics, University of Tokyo.

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