Compellingness in Nash Implementation

Shurojit Chatterji (), Takashi Kunimoto and Paulo Ramos ()
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Shurojit Chatterji: Singapore Management University
Paulo Ramos: Singapore Management University

No 10-2022, Economics and Statistics Working Papers from Singapore Management University, School of Economics

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.

Keywords: implementation; compelling equilibria; ordinality; mixed strategies[Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C72 D78 D82 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2022-07-01
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-sea
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Working Paper: Compellingness in Nash Implementation (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:ris:smuesw:2022_010

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