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Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance

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  • Martin Dufwenberg

    () (Stockholm University, Sweden)

  • Mark Stegeman

    () (Virginia Polytechnic Institute, U.S.A.)

Abstract

Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well-defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better-reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator. Copyright The Econometric Society 2002.

Suggested Citation

  • Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:5:p:2007-2023
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    Cited by:

    1. Herings, P.J.J. & Predtetchinski, A., 2015. "Best response cycles in perfect information games," Research Memorandum 017, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    3. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    4. 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.
    5. Cubitt, Robin P. & Sugden, Robert, 2011. "The reasoning-based expected utility procedure," Games and Economic Behavior, Elsevier, vol. 71(2), pages 328-338, March.
    6. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    7. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
    8. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economic Research Papers 2014-032, Friedrich-Schiller-University Jena.
    9. Luo, Xiao & Yang, Chih-Chun, 2009. "Bayesian coalitional rationalizability," Journal of Economic Theory, Elsevier, vol. 144(1), pages 248-263, January.
    10. 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.
    11. Christian Bach & Jérémie Cabessa, 2012. "Common knowledge and limit knowledge," Theory and Decision, Springer, vol. 73(3), pages 423-440, September.
    12. Pedro Jara-Moroni, 2008. "Rationalizability in games with a continuum of players," Working Papers halshs-00587863, HAL.
    13. Shimoji, Makoto, 2004. "On the equivalence of weak dominance and sequential best response," Games and Economic Behavior, Elsevier, vol. 48(2), pages 385-402, August.
    14. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    15. Yukio KORIYAMA & Matias Nunez, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    16. repec:eee:mateco:v:72:y:2017:i:c:p:82-87 is not listed on IDEAS
    17. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    18. Amanda Friedenberg & Martin Meier, 2017. "The context of the game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 347-386, February.
    19. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    20. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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