Axiomatic Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs

41 Pages Posted: 23 Feb 2009

See all articles by Srihari Govindan

Srihari Govindan

University of Rochester

Robert Wilson

Stanford Graduate School of Business

Date Written: February 1, 2009

Abstract

Three 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 subsets 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.

Keywords: economic theory

Suggested Citation

Govindan, Srihari and Wilson, Robert B., Axiomatic Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs (February 1, 2009). Stanford University Graduate School of Business Research Paper No. 2008, Available at SSRN: https://ssrn.com/abstract=1345371 or http://dx.doi.org/10.2139/ssrn.1345371

Srihari Govindan (Contact Author)

University of Rochester ( email )

Department of Economics
Rochester, NY NY 14627
United States
5852757214 (Phone)

Robert B. Wilson

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States
650-723-8620 (Phone)
650-725-7979 (Fax)

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