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Iterated Strict Dominance in General Games

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  • Yi-Chun Chen
  • Ngo Van Long

    ()

  • Xiao Luo

Abstract

We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria. Nous donnons une définition de l’élimination itérative des stratégies qui sont strictement donimées (EISSD) pour les jeux avec un nombre fini (ou infini) de joueurs , des ensembles de stratégies compactes (ou non-compactes), et des fonctions de gains continues (ou non-continues). Le processus EISSD est bien défini et indépendant de l’ordre d’élimination. Nous donnons une caractérisation du processus EISSD en utilisant un critère de stabilité et offrons une condition épistémologique. Nous démontrons que le processus EISSD peut produire des équilibres faux dans la classe des jeux de meilleures réponses sécuritaires de Reny. Nous donnons des conditions nécessaires et suffisantes pour que le processus EISSD conserve l’ensemble des équilibre de Nash.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2007s-03.

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Date of creation: 01 Feb 2007
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Handle: RePEc:cir:cirwor:2007s-03

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Keywords: game theory; strict dominance; iterated elimination; Nash equilibrium; Reny's better-reply secure games.; théorie des jeux; dominance stricte; élimination itérative; équilibre de Nash; jeux de meilleures réponses sécuritaires de Reny;

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Citations

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Cited by:
  1. Robin P. Cubitt & Robert Sugden, 2010. "The reasoning-based expected utility procedure," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-04, School of Economics, University of East Anglia, Norwich, UK..
  2. repec:hal:wpaper:halshs-00587863 is not listed on IDEAS
  3. Luo, Xiao, 2009. "The foundation of stability in extensive games with perfect information," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 860-868, December.
  4. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  5. Luo, Xiao & Yang, Chih-Chun, 2009. "Bayesian coalitional rationalizability," Journal of Economic Theory, Elsevier, vol. 144(1), pages 248-263, January.
  6. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
  7. Robin P. Cubitt & Robert Sugden, 2008. "Common reasoning in games," Discussion Papers 2008-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  8. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, vol. 51(1), pages 1-12, September.
  9. Michael Trost, 2012. "An Epistemic Rationale for Order-Independence," Jena Economic Research Papers 2012-010, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.

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