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Implementation in Nash Equilibrium (II): Applications

  • Luis C. Corchón
Chapter
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Abstract

In the previous chapter we presented a general mechanism that implements in Nash equilibrium any social choice correspondence satisfying monotonicity and no veto power. A general criticism of the Nash equilibrium approach to the theory of implementation is that, in the case where a correspondence is implemented, this kind of equilibrium requires a good deal of coordination among agents in order to select those strategies corresponding to a particular equilibrium.1 This problem is well-known in game theory: when playing, say, The Battle of the Sexes agents may, by means of strategies that are part of different Nash equilibria of the game, achieve outcomes that are not Nash equilibria. In our case, if the mechanism is run by a real person, she can suggest what strategy agents have to use (truth-telling). This is of course cheap talk, but it makes slightly more palatable the assumption that agents know the particular Nash equilibrium that is going to be played.

Keywords

Nash Equilibrium Market Game Strong Equilibrium Walrasian Equilibrium Feasible Allocation 
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References

  1. A criticism of integer games can be found in: M.O. Jackson (1992), ‘Implementation in Undominated Strategies: A Look at Bounded Mechanisms’, Review of Economic Studies, vol. 59, pp. 757–75.CrossRefGoogle Scholar
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  3. Sections 5.2 and 5.3 rely heavily on L.C. Corchbn and S. Wilkie (1990), ‘Doubly Implementing the Ratio Correspondence by Means of a Natural Mechanism’, Mimeo, Bellcore and Universidad de AlicanteGoogle Scholar
  4. L.C. Corchbn and S. Wilkie (1989), ‘Implementation of the Walrasian Correspondence by Market Games’, Mimeo, Rochester, September, 1989. Revised November, 1994.Google Scholar
  5. The following papers present particular mechanisms for implementing the Lindahl correspondence with three or more agents: T. Groves and J. Ledyard (1977), ‘Optimal Allocation of Public Goods: A Solution to the “Free Rider” Problem’, Econometrica, 45, pp. 783–809CrossRefGoogle Scholar
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  11. Implementation of the Walrasian correspondence by means of market games has been considered by: J.P. Benassy (1986), ‘On Competitive Market Mechanisms’, Econometrica, 1986 no. 54, pp. 95–108CrossRefGoogle Scholar
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  25. Implementation of matching rules is discussed in T. Kara, and T. Sönmez: ‘Nash Implementation of Matching Rules’ Journal of Economic Theory, (forthcoming) and T. Sönmez, ‘Implementation in Generalized Matching Problems’, Journal of Mathematical Economics (forthcoming).Google Scholar
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Copyright information

© Luis C. Corchón 1996

Authors and Affiliations

  • Luis C. Corchón
    • 1
  1. 1.Universidad de AlicanteAlicanteSpain

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