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Nash Implementation Using Undominated Strategies

Palfrey, Thomas R. and Srivastava, Sanjay (1991) Nash Implementation Using Undominated Strategies. Econometrica, 59 (2). pp. 479-501. ISSN 0012-9682.

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We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts.

Item Type:Article
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URLURL TypeDescription JSTORJSOR article
Palfrey, Thomas R.0000-0003-0769-8109
Additional Information:© 1991 The Econometric Society. Manuscript received December, 1986; final revision received February, 1990. Published as Caltech Social Science Working Paper 649 on Dec. 1, 1986. We thank the National Science Foundation for financial support. Palfrey also thanks the Exxon Educational Foundation and the Alfred P. Sloan Foundation for financial support while at the Center for Advanced Study in the Behavioral Sciences. We have benefited from participants of seminars at Caltech, Carnegie Mellon, Chicago, Michigan, Pennsylvania, Princeton, Stanford, SUNY-Buffalo, and USC. We also thank Dilip Abreu, Roger Guesnerie, Jean-Jacques Laffont, Paul Milgrom, John Moore, the referees, and especially Matthew Jackson, for helpful comments.
Group:Social Science Working Papers
Funding AgencyGrant Number
Exxon Educational FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Implementation, decentralization, social choice, equilibrium refinements
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Other Numbering System NameOther Numbering System ID
Social Science Working Paper649
Issue or Number:2
Record Number:CaltechAUTHORS:20160307-145552688
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Official Citation:Palfrey, Thomas R., and Sanjay Srivastava. 1991. “Nash Implementation Using Undominated Strategies”. Econometrica 59 (2). [Wiley, Econometric Society]: 479–501. doi:10.2307/2938266.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65147
Deposited On:01 Apr 2016 00:10
Last Modified:22 Nov 2019 09:58

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