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Compellingness in Nash Implementation

Author

Listed:
  • Chatterji, Shurojit

    (Singapore Management University)

  • Kunimoto, Takashi

    (Singapore Management University)

  • Ramos, Paulo

    (Singapore Management University)

Abstract

A social choice function (SCF) is said to be Nash implementable if there exists a mechanism in which every Nash equilibrium outcome coincides with that specified by the SCF. The main objective of this paper is to assess the impact of considering mixed strategy equilibria in Nash implementation. To do this, we focus on environments with two agents and restrict attention to finite mechanisms. We call a mixed strategy equilibrium “compelling” if its outcome Pareto dominates any pure strategy equilibrium outcome. We show that if the finite environment and the SCF to be implemented jointly satisfy what we call Condition P+M, we construct a finite mechanism which Nash implements the SCF in pure strategies and possesses no compelling mixed strategy equilibria. This means that the mechanism might possess mixed strategy equilibria which are “not” compelling. Our mechanism has several desirable features: transfers can be completely dispensable; only finite mechanisms are considered; integer games are not invoked; and players’ attitudes toward risk do not matter.

Suggested Citation

  • Chatterji, Shurojit & Kunimoto, Takashi & Ramos, Paulo, 2022. "Compellingness in Nash Implementation," Economics and Statistics Working Papers 10-2022, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2022_010
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    More about this item

    Keywords

    implementation; compelling equilibria; ordinality; mixed strategies[Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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