Sequential equilibrium
Sequential equilibrium | |
---|---|
A solution concept in game theory | |
Relationship | |
Subset of | Subgame perfect equilibrium, perfect Bayesian equilibrium |
Superset of | extensive-form trembling hand perfect equilibrium, Quasi-perfect equilibrium |
Significance | |
Proposed by | David M. Kreps and Robert Wilson |
Used for | Extensive form games |
Sequential equilibrium is a refinement of Nash equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies not only a strategy for each of the players but also a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. A profile of strategies and beliefs is called an assessment for the game. Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs and its beliefs are confirmed on the outcome path given by its strategies. The definition of sequential equilibrium further requires that there be arbitrarily small perturbations of beliefs and associated strategies with the same property.
Consistent assessments
The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expected payoff in every information set. It is also straightforward to define what a sensible belief should be for those information sets that are reached with positive probability given the strategies; the beliefs should be the conditional probability distribution on the nodes of the information set, given that it is reached. This entails the application of Bayes' rule.
It is far from straightforward to define what a sensible belief should be for those information sets that are reached with probability zero, given the strategies. Indeed, this is the main conceptual contribution of Kreps and Wilson. Their consistency requirement is the following: The assessment should be a limit point of a sequence of totally mixed strategy profiles and associated sensible beliefs, in the above straightforward sense.
Relationship to other equilibrium refinements
Sequential equilibrium is a further refinement of subgame perfect equilibrium and even perfect Bayesian equilibrium. It is itself refined by extensive-form trembling hand perfect equilibrium and proper equilibrium. Strategies of sequential equilibria (or even extensive-form trembling hand perfect equilibria) are not necessarily admissible. A refinement of sequential equilibrium that guarantees admissibility is quasi-perfect equilibrium.
References
David M. Kreps and Robert Wilson. "Sequential Equilibria", Econometrica 50:863-894, 1982.
Roger B. Myerson. Game Theory: Analysis of Conflict, 1991.
- v
- t
- e
- Congestion game
- Cooperative game
- Determinacy
- Escalation of commitment
- Extensive-form game
- First-player and second-player win
- Game complexity
- Graphical game
- Hierarchy of beliefs
- Information set
- Normal-form game
- Preference
- Sequential game
- Simultaneous game
- Simultaneous action selection
- Solved game
- Succinct game
concepts
- Bayes correlated equilibrium
- Bayesian Nash equilibrium
- Berge equilibrium
- Core
- Correlated equilibrium
- Epsilon-equilibrium
- Evolutionarily stable strategy
- Gibbs equilibrium
- Mertens-stable equilibrium
- Markov perfect equilibrium
- Nash equilibrium
- Pareto efficiency
- Perfect Bayesian equilibrium
- Proper equilibrium
- Quantal response equilibrium
- Quasi-perfect equilibrium
- Risk dominance
- Satisfaction equilibrium
- Self-confirming equilibrium
- Sequential equilibrium
- Shapley value
- Strong Nash equilibrium
- Subgame perfection
- Trembling hand
of games
- Go
- Chess
- Infinite chess
- Checkers
- Tic-tac-toe
- Prisoner's dilemma
- Gift-exchange game
- Optional prisoner's dilemma
- Traveler's dilemma
- Coordination game
- Chicken
- Centipede game
- Lewis signaling 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 game
- War of attrition
- El Farol Bar problem
- Fair division
- Fair cake-cutting
- Cournot game
- Deadlock
- Diner's dilemma
- Guess 2/3 of the average
- Kuhn poker
- Nash bargaining game
- Induction puzzles
- Trust game
- Princess and monster game
- Rendezvous problem
figures
- Albert W. Tucker
- Amos Tversky
- Antoine Augustin Cournot
- Ariel Rubinstein
- Claude Shannon
- Daniel Kahneman
- David K. Levine
- David M. Kreps
- Donald B. Gillies
- Drew Fudenberg
- Eric Maskin
- Harold W. Kuhn
- Herbert Simon
- Hervé Moulin
- John Conway
- Jean Tirole
- Jean-François Mertens
- Jennifer Tour Chayes
- John Harsanyi
- John Maynard Smith
- John Nash
- John von Neumann
- Kenneth Arrow
- Kenneth Binmore
- Leonid Hurwicz
- Lloyd Shapley
- Melvin Dresher
- Merrill M. Flood
- Olga Bondareva
- Oskar Morgenstern
- Paul Milgrom
- Peyton Young
- Reinhard Selten
- Robert Axelrod
- Robert Aumann
- Robert B. Wilson
- Roger Myerson
- Samuel Bowles
- Suzanne Scotchmer
- Thomas Schelling
- William Vickrey
- All-pay auction
- Alpha–beta pruning
- Bertrand paradox
- Bounded rationality
- Combinatorial game theory
- Confrontation analysis
- Coopetition
- Evolutionary game theory
- First-move advantage in chess
- Glossary of game theory
- List of game theorists
- List of games in game theory
- No-win situation
- Paradox of tolerance
- Solving chess
- Topological game
- Tragedy of the commons
- Tyranny of small decisions