Technology Category
Game Theory and Economic Paradigms: EquilibriumMultiagent Systems: Mechanism DesignReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
Axiomatic Equilibrium Selection: The Case of Generic Extensive Form Games
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
Refines Nash equilibria for finite games
Imposes axioms for solution concepts
Selects stable outcomes in generic games
Innovation
Methods, ideas, or system contributions that make the work stand out.
Refinement of Nash equilibria selection
Backward induction with quasi-perfect equilibrium
Invariance axioms for stable outcomes
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