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| Sequential equilibrium | |
|---|---|
| Solution concept ingame 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 andRobert Wilson |
| Used for | Extensive form games |
Sequential equilibrium is a refinement ofNash equilibrium forextensive form games due toDavid M. Kreps andRobert Wilson. A sequential equilibrium specifies not only a strategy for eachof the players but also abelief for each of the players. A belief gives, for eachinformation set of the game belonging to the player, a probability distribution on the nodes in theinformation set. A profile of strategies and beliefs is called anassessment for the game. Informally speaking, an assessment is aperfect Bayesian equilibrium if its strategies are sensible given its beliefsand 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.
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 alimit point of a sequence oftotally mixed strategy profiles and associated sensible beliefs, in the above straightforward sense.
Sequential equilibrium is a further refinement ofsubgame perfect equilibrium and evenperfect Bayesian equilibrium. It is itself refined by extensive-formtrembling hand perfect equilibrium andproper equilibrium. Strategies of sequential equilibria (or even extensive-formtrembling hand perfect equilibria) are not necessarilyadmissible. A refinement of sequential equilibrium that guarantees admissibility isquasi-perfect equilibrium.
