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Axiomatic Equilibrium Selection for Generic Two-Player Games

  • Govindan, Srihari

    (University of Iowa)

  • Wilson, Robert

    (Stanford University)

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).

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Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 2021.

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Date of creation: May 2009
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Handle: RePEc:ecl:stabus:2021
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  1. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  2. MERTENS, Jean-François, 1990. "The "small worlds" axiom for stable equilibria," CORE Discussion Papers 1990007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
  4. Srihari Govindan & Tilman Klumpp, 2003. "Perfect equilibrium and lexicographic beliefs," International Journal of Game Theory, Springer, vol. 31(2), pages 229-243.
  5. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Working papers 90-13, Wisconsin Madison - Social Systems.
  6. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
  7. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, 01.
  8. Srihari Govindan & Robert Wilson, 2006. "Metastable Equilibria," Levine's Bibliography 122247000000001211, UCLA Department of Economics.
  9. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Srihari Govindan & Robert Wilson, 2006. "Sufficient Conditions for Stable Equilibria," Levine's Bibliography 784828000000000267, UCLA Department of Economics.
  11. Van Damme, Eric, 2002. "Strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 41, pages 1521-1596 Elsevier.
  12. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  13. Srihari Govindan & Robert Wilson, 2002. "Maximal stable sets of two-player games," International Journal of Game Theory, Springer, vol. 30(4), pages 557-566.
  14. Srihari Govindan & Robert Wilson, 2009. "Axiomatic Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs," Levine's Working Paper Archive 814577000000000125, David K. Levine.
  15. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  16. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  17. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
  18. Srihari Govindan & Jean-François Mertens, 2004. "An equivalent definition of stable Equilibria," International Journal of Game Theory, Springer, vol. 32(3), pages 339-357, 06.
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