Axiomatic Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs
AbstractThree axioms from decision theory are applied to refinements that select connected subsets of the Nash equilibria of games with perfect recall. The first axiom requires all equilibria in a selected subset to be admissible, i.e. each player's strategy is an admissible optimal reply to other players' strategies. The second axiom invokes backward induction by requiring a selected subset to contain a sequential equilibrium. The third axiom requires a refinement to be immune to embedding a game in a larger game with additional strategies and players, provided the original players' strategies and payoffs are preserved, viz., selected subsets must be the same as those induced by the selected sub- sets of any larger game in which it is embedded. These axioms are satisfied by refinements that select subsets that are stable as defined by Mertens (1989). For a game with two players, perfect information, and generic payoffs, we prove the converse that the axioms require a selected set to be stable. In the space of mixed strategies of minimal dimension, the stable set is unique and consists of the admissible equilibria with the same outcome as the unique subgame-perfect equilibrium obtained by backward induction. Each other admissible equilibrium with this outcome is the profile of players' strategies in an admissible sequential equilibrium of a larger game in which the original game is embedded, so the third axiom requires it to be included.
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Date of creation: 15 Feb 2009
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Other versions of this item:
- Govindan, Srihari & Wilson, Robert, 2009. "Axiomativ Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs," Research Papers 2008, Stanford University, Graduate School of Business.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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- 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.
- Srihari Govindan & Robert Wilson, 2009.
"Axiomatic Equilibrium Selection for Generic two-player games,"
Levine's Working Paper Archive
814577000000000231, David K. Levine.
- Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, 07.
- Srihari Govindan & Robert Wilson, 2010. "Axiomatic Equilibrium Selection For Generic Two-Player Games," Levine's Working Paper Archive 661465000000000203, David K. Levine.
- Govindan, Srihari & Wilson, Robert, 2009. "Axiomatic Equilibrium Selection for Generic Two-Player Games," Research Papers 2021, Stanford University, Graduate School of Business.
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