Self-confirming equilibrium

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Self-confirming equilibrium
A solution concept in game theory
Relationships
Subset of	Rationalizability
Superset of	Nash equilibrium
Significance
Proposed by	Drew Fudenberg and David K. Levine
Used for	Extensive-form games

In game theory, self-confirming equilibrium is a generalization of Nash equilibrium for extensive form games, in which players correctly predict the moves their opponents actually make, but may have misconceptions about what their opponents would do at information sets that are never reached when the equilibrium is played. Informally, self-confirming equilibrium is motivated by the idea that if a game is played repeatedly, the players will revise their beliefs about their opponents' play if and only if they observe these beliefs to be wrong.

Consistent self-confirming equilibrium is a refinement of self-confirming equilibrium that further requires that each player correctly predicts play at all information sets that can be reached when the player's opponents, but not the player herself, deviate from their equilibrium strategies. Consistent self-confirming equilibrium is motivated by learning models in which players are occasionally matched with "crazy" opponents, so that even if they stick to their equilibrium strategy themselves, they eventually learn the distribution of play at all information sets that can be reached if their opponents deviate.

References

Drew Fudenberg and David K. Levine: "Self-confirming Equilibrium", Econometrica 61:523-545, 1993.

v t e Topics in game theory

Definitions	Normal-form game Extensive-form game Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game Large Poisson game Nontransitive game Global games

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Cake cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Screening game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Kenneth Arrow Robert Aumann Kenneth Binmore Samuel Bowles Melvin Dresher Merrill M. Flood Drew Fudenberg Donald B. Gillies John Harsanyi Leonid Hurwicz David K. Levine Daniel Kahneman Harold W. Kuhn Eric Maskin Jean-François Mertens Paul Milgrom Oskar Morgenstern Roger Myerson John Nash John von Neumann Ariel Rubinstein Thomas Schelling Reinhard Selten Herbert Simon Lloyd Shapley John Maynard Smith Jean Tirole Albert W. Tucker William Vickrey Robert B. Wilson Peyton Young

See also	Tragedy of the commons Tyranny of small decisions All-pay auction List of games in game theory Confrontation analysis List of game theorists Combinatorial game theory

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