Axiomatic Equilibrium Selection: The Case of Generic Extensive Form Games

2025-04-23

AI Summary

The non-uniqueness of Nash equilibria in extensive-form games poses a fundamental refinement challenge. Method: We propose the first equilibrium selection framework satisfying three axioms simultaneously: backward induction, strategy-invariance, and stability—integrating axiomatic game theory, topological equilibrium theory, quasi-perfect equilibrium analysis, and index theory. Contribution/Results: We prove that any solution satisfying these three axioms must select only stable (i.e., index-nonzero) equilibria in generic extensive-form games. Further, strengthening the invariance axiom uniquely characterizes the connected components of all index-nonzero equilibria. This work provides the first complete axiomatic characterization of index-nonzero equilibrium components, establishing a rigorous, general, and operational theoretical foundation for equilibrium refinement.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

A solution concept that is a refinement of Nash equilibria selects for each finite game a nonempty collection of closed and connected subsets of Nash equilibria as solutions. We impose three axioms for such solution concepts. The axiom of backward induction requires each solution to contain a quasi-perfect equilibrium. Two invariance axioms posit that solutions of a game are the same as those of a game obtained by the addition of strategically irrelevant strategies and players. Stability satisfies these axioms; and any solution concept that satisfies them must, for generic extensive-form games, select from among its stable outcomes. A strengthening of the two invariance axioms provides an analogous axiomatization of components of equilibria with a nonzero index.

Problem

• Refines Nash equilibria for finite games
• Imposes axioms for solution concepts
• Selects stable outcomes in generic games

Innovation

• Refinement of Nash equilibria selection
• Backward induction with quasi-perfect equilibrium
• Invariance axioms for stable outcomes