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Axiomatic Equilibrium Selection for Generic Two-Player Games

Author

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  • Govindan, Srihari

    (University of Iowa)

  • Wilson, Robert

    (Stanford University)

Abstract

We apply three axioms adapted from decision theory to refinements of the Nash equilibria of games with perfect recall that select connected closed sub- sets called solutions. No player uses a weakly dominated strategy in an equilibrium in a solution. Each solution contains a quasi-perfect equilibrium and thus a sequential equilibrium in strategies that provide conditionally admissible optimal continuations from information sets. A refinement is immune to embedding a game in a larger game with additional players provided the original players' strategies and payoffs are preserved, i.e. solutions of a game are the same as those induced by the solutions of any larger game in which it is embedded. For games with two players and generic payoffs, we prove that these axioms characterize each solution as an essential component of equilibria in undominated strategies, and thus a stable set as defined by Mertens (1989).

Suggested Citation

  • Govindan, Srihari & Wilson, Robert, 2009. "Axiomatic Equilibrium Selection for Generic Two-Player Games," Research Papers 2021, Stanford University, Graduate School of Business.
  • Handle: RePEc:ecl:stabus:2021
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    Cited by:

    1. Gatti, Nicola & Gilli, Mario & Marchesi, Alberto, 2020. "A characterization of quasi-perfect equilibria," Games and Economic Behavior, Elsevier, vol. 122(C), pages 240-255.
    2. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    3. Dieter Balkenborg & Dries Vermeulen, 2016. "Where Strategic and Evolutionary Stability Depart—A Study of Minimal Diversity Games," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 278-292, February.
    4. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    5. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
    6. Nicola, Gatti & Mario, Gilli & Alberto, Marchesi, 2018. "On the characterization of quasi-perfect equilibria," Working Papers 389, University of Milano-Bicocca, Department of Economics, revised 07 Nov 2018.
    7. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    8. Sun, Lan, 2016. "Hypothesis testing equilibrium in signaling games," Center for Mathematical Economics Working Papers 557, Center for Mathematical Economics, Bielefeld University.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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