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Uniqueness of the index for Nash equilibria of two-player games

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Author Info
Robert Wilson (Business School, Stanford University, Stanford, CA 94305-5015, USA)
Srihari Govindan (Economics Department, University of Western Ontario, London, Ontario N6A 5C2, CANADA)

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Abstract

Given a map whose roots are the Nash equilibria of a game, each component of the equilibrium set has an associated index, defined as the local degree of the map. This note shows that for a two-player game, every map with the same roots induces the same index. Moreover, this index agrees with the Shapley index constructed from the Lemke-Howson algorithm.

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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 10 (1997)
Issue (Month): 3 ()
Pages: 541-549
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Handle: RePEc:spr:joecth:v:10:y:1997:i:3:p:541-549

Note: Received: May 30, 1996; revised version June 25, 1996
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  1. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On the indices of zeros of nash fields," CORE Discussion Papers 2000017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  2. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On knots and dynamics in games," CORE Discussion Papers 2000010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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