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Axiomatic Equilibrium Selection For Generic Two-Player Games

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  • SRIHARI GOVINDAN
  • ROBERT WILSON

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).

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000203.

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Date of creation: 06 Oct 2010
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Handle: RePEc:cla:levarc:661465000000000203

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  1. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  2. Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine.
  3. Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Discussion Paper 1991-30, Tilburg University, Center for Economic Research.
  4. Damme, E.E.C. van, 2002. "Strategic equilibrium," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91439, Tilburg University.
  5. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
  6. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October.
  7. 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.
  8. 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.
  9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  10. Srihari Govindan & Tilman Klumpp, 2003. "Perfect equilibrium and lexicographic beliefs," International Journal of Game Theory, Springer, vol. 31(2), pages 229-243.
  11. Srihari Govindan & Robert Wilson, 2006. "Sufficient Conditions for Stable Equilibria," Levine's Bibliography 784828000000000267, UCLA Department of Economics.
  12. 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.
  13. Govindan, Srihari & Wilson, Robert B., 2007. "Metastable Equilibria," Research Papers 1934r, Stanford University, Graduate School of Business.
  14. Srihari Govindan & Robert Wilson, 2002. "Maximal stable sets of two-player games," International Journal of Game Theory, Springer, vol. 30(4), pages 557-566.
  15. 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.
  16. Damme, E.E.C. van, 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154427, Tilburg University.
  17. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  18. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  19. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.

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