On the Strategic Stability of Equilibria

1986/09/01 by Elon Kohlberg, Jean-Francois Mertens, Jean‐François Mertens · 1,429 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Computer science #Economic theories and models #Economics #Game Theory and Applications #Game Theory and Voting Systems #Mathematical economics #Mathematics #Stability (learning theory)

paper · doi:10.2307/1912320

published in Econometrica 54(5), 1003 (Wiley)

openalex publication_date 1986/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

A basic problem in the theory of noncooperative games is the following: which Nash equilibria are strategically stable, i.e. self-enforcing, and does every game have a strategically stable equilibrium?We list three conditions which seem necessary for strategic stabilitybackwards induction, iterated dominance, and invariance-and define a set-valued equilibrium concept that satisfies all three of them.We prove that every game has at least one such equilibrium set.Also, we show that the departure from the usual notion of single-valued equilibrium is relatively minor, because the sets reduce to points in all generic games.

Cited by

• Global Games and Equilibrium Selection
• Monitoring and Reputation: The Choice between Bank Loans and Directly Placed Debt
• Refining cheap-talk equilibria
• Silver Signals: Twenty-Five Years of Screening and Signaling
• Signaling Games and Stable Equilibria
• Loss-Avoidance and Forward Induction in Experimental Coordination Games
• Deep Incentive Design with Differentiable Equilibrium Blocks
• Robust equilibria in continuous games: From strategic to dynamic robustness
• Virtual Observability in Sequential Play
• Choosing What Game to Play without Selecting Equilibria: Inferring Safe (Pareto) Improvements in Binary Constraint Structures
• Equilibrium Tracing in Bimatrix Games
• Evolution of Communication with Partial Common Interest
• A Category for Extensive-Form Games
• Gradient play in stochastic games: stationary points, convergence, and sample complexity
• Sunspot Equilibrium in General Quitting Games
• Strategically Robust Game Theory via Optimal Transport
• Compactification of Extensive Game Structures and Backward Dominance Procedure
• Rank-1 Bi-matrix Games: A Homeomorphism and a Polynomial Time Algorithm
• On the Implications of Lookahead Search in Game Playing
• Nash equilibria in semidefinite games and Lemke-Howson paths
• Note on the size of a stable matching
• Credible assignments in coordination games
• Order of play in strategically equivalent games in extensive form
• Ordinality in non cooperative games
• Mind-reading in strategic interaction: The impact of perceived similarity on projection and stereotyping
• Equilibrium Selection in Signaling Games
• Promises Made, Promises Kept: Safe Pareto Improvements via Ex Post Verifiable Commitments
• The Folk Theorem in Repeated Games with Discounting or with Incomplete Information
• Virtual bargaining: a theory of social decision-making. [europepmc]
• Some further results on the stability of Ky Fan's points. [europepmc]
• Conflicting intentions: rectifying the consistency requirements. [europepmc]
• Strategic manipulation in Bayesian dialogues. [europepmc]

Related

• Axiomatic Equilibrium Selection: The Case of Generic Extensive Form Games
• A Robust Characterization of Nash Equilibrium
• On the Characterization of Local Nash Equilibria in Continuous Games
• Discrete Nondeterminism and Nash Equilibria for Strategy-Based Games
• Learnable Mixed Nash Equilibria are Collectively Rational