Theoretical Economics 1 (2006), 167–206

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### Sufficient conditions for stable equilibria

*Srihari Govindan, Robert B. Wilson*

#### Abstract

A refinement of the set of Nash equilibria that satisfies two assumptions is shown to select a subset that is stable in the sense defined by Kohlberg and Mertens. One assumption requires that a selected set is invariant to adjoining redundant strategies and the other is a strong version of backward induction. Backward induction is interpreted as the requirement that each player's strategy is sequentially rational and conditionally admissible at every information set in an extensive-form game with perfect recall, implemented here by requiring that the equilibrium is quasi-perfect. The strong version requires 'truly' quasi-perfection in that each strategy perturbation refines the selection to a quasi-perfect equilibrium in the set. An exact characterization of stable sets is provided for two-player games.

Keywords: Game theory, equilibrium selection, stability

JEL classification: C72

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