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Nash Implementation and Uncertain Renegotiation

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Abstract

This paper studies Nash implementation when the outcomes of the mechanism can be renegotiated among the agents but the planner does not know the renegotiation function that they will use. We characterize the social objectives that can be implemented in Nash equilibrium when the same mechanism must work for every admissible renegotiation function. The constrained Walrasian correspondence, the core correspondence, and the Pareto-efficient and envy-free correspondence satisfy the necessary and sufficient conditions for this form of implementation if and only if freedisposal of the commodities is allowed. The uniform rule, on the other hand, is not Nash implementable for some admissible renegotiations functions.

Suggested Citation

  • Pablo Amorós, 2003. "Nash Implementation and Uncertain Renegotiation," Economic Working Papers at Centro de Estudios Andaluces E2003/27, Centro de Estudios Andaluces.
  • Handle: RePEc:cea:doctra:e2003_27
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    References listed on IDEAS

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    1. Ma, Ching-to & Moore, John & Turnbull, Stephen, 1988. "Stopping agents from "cheating"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 355-372, December.
    2. Chakravorty, Bhaskar & Corchon, Luis C. & Wilkie, Simon, 2006. "Credible implementation," Games and Economic Behavior, Elsevier, vol. 57(1), pages 18-36, October.
    3. Jackson, Matthew O. & Palfrey, Thomas R., 2001. "Voluntary Implementation," Journal of Economic Theory, Elsevier, vol. 98(1), pages 1-25, May.
    4. Eric Maskin & John Moore, 1999. "Implementation and Renegotiation," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 39-56.
    5. Arya, Anil & Glover, Jonathan & Hughes, John S., 1997. "Implementing Coordinated Team Play," Journal of Economic Theory, Elsevier, vol. 74(1), pages 218-232, May.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    7. Matthew O. Jackson & Thomas R. Palfrey, 1998. "Efficiency and Voluntary Implementation in Markets with Repeated Pairwise Bargaining," Econometrica, Econometric Society, vol. 66(6), pages 1353-1388, November.
    8. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
    9. Baliga, Sandeep & Corchon, Luis C. & Sjostrom, Tomas, 1997. "The Theory of Implementation When the Planner Is a Player," Journal of Economic Theory, Elsevier, vol. 77(1), pages 15-33, November.
    10. Pablo AmorÕs & Bernardo Moreno, 2001. "original papers : Implementation of optimal contracts under adverse selection," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 41-61.
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    Cited by:

    1. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Zvika Neeman & Gregory Pavlov, 2010. "Renegotiation-proof Mechanism Design," UWO Department of Economics Working Papers 20101, University of Western Ontario, Department of Economics.
    3. Triossi, Matteo & Corchón Díaz, Luis Carlos, 2005. "Implementation with state dependent feasible sets and preferences: a renegotiation approach," UC3M Working papers. Economics we057136, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Yi, Jianxin, 2011. "Implementation via mechanisms with transfers," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 65-70, January.
    5. Neeman, Zvika & Pavlov, Gregory, 2013. "Ex post renegotiation-proof mechanism design," Journal of Economic Theory, Elsevier, vol. 148(2), pages 473-501.

    More about this item

    Keywords

    Implementation theory; Nash equilibrium; renegotiation function.;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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