{{Infobox equilibrium|
name=Sequential Equilibrium|
subsetof=Subgame_perfect_equilibrium, perfect Bayesian equilibrium|
supersetof = extensive-form trembling hand perfect equilibrium,Quasi-perfect_equilibrium|
discoverer=David_M._Kreps and Robert Wilson|
usedfor=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 sequential equilibrium if its strategies are sensible given its beliefs '''and''' its beliefs are sensible given its strategies.
== 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.
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 '''fully 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. 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.
{{game theory}}
Category:Game_theory