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On the existence of pure strategy Nash equilibria in two person discrete games

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  • Mallick, Indrajit

Abstract

We construct a generalized two-person discrete strategy static game of complete information where continuity, convexity and compactness cannot be invoked to show the existence of pure strategy Nash equilibrium. We show that, when best responses are unique from both sides, a condition of Minimal Acyclicity is necessary and sufficient for the existence of pure strategy Nash equilibria.

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File URL: http://www.sciencedirect.com/science/article/B6V84-5276T18-2/2/e60969d76b5348f19b6208392259319c
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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 111 (2011)
Issue (Month): 2 (May)
Pages: 144-146

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Handle: RePEc:eee:ecolet:v:111:y:2011:i:2:p:144-146

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Web page: http://www.elsevier.com/locate/ecolet

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Keywords: Pure strategy Nash equilibrium Best response Minimal Acyclicity;

References

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  1. Guilherme Carmona, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," Game Theory and Information 0412008, EconWPA.
  2. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  3. Lu, Haishu, 2007. "On the existence of pure-strategy Nash equilibrium," Economics Letters, Elsevier, vol. 94(3), pages 459-462, March.
  4. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  5. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  6. Ziad, Abderrahmane, 1999. "Pure strategy Nash equilibria of non-zero-sum two-person games: non-convex case," Economics Letters, Elsevier, vol. 62(3), pages 307-310, March.
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