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Encyclopedia > Sequential equilibrium
Sequential Equilibrium
Part of the equilibrium refinement series
Relationships
Subset of: Subgame perfect equilibrium, perfect Bayesian equilibrium
Superset of: extensive-form trembling hand perfect equilibrium,Quasi-perfect equilibrium
Significance
Discoverer: 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 sequential equilibrium if its strategies are sensible given its beliefs and its beliefs are sensible given its strategies. In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ... Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ... David M. Kreps is a game theory economist and professor at the Graduate School of Business at Stanford University. ... It has been suggested that Game tree be merged into this article or section. ... In game theory, the Nash equilibrium (named after John Nash, who proposed it) is a kind of solution concepts of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ... It has been suggested that Game tree be merged into this article or section. ... David M. Kreps is a game theory economist and professor at the Graduate School of Business at Stanford University. ... In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ... In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ...


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. Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... In classical (frequentist) decision theory, an admissible decision rule is a rule for making a decision that is better in some sense than any other rule that may compete with it. ... Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ...


References

David M. Kreps and Robert Wilson. "Sequential Equilibria", Econometrica 50:863--894, 1982. David M. Kreps is a game theory economist and professor at the Graduate School of Business at Stanford University. ...

Topics in game theory
Definitions Normal form game - Extensive form game - Cooperative game - Information set - Strategy - Mixed strategy - Preference
Equilibrium concepts Dominant strategy equilibrium - Nash equilibrium - Subgame-perfect Nash equilibrium - Bayes-Nash equilibrium - Perfect Bayes-Nash equilibrium - Sequential equilibrium - Quasi-perfect equilibrium - Evolutionarily stable strategy - Other equilibria
Classes of games Symmetric game - Perfect information - Dynamic game - Repeated game - Signaling game - Cheap talk - Zero-sum game - Mechanism design - Win-win game
Games Prisoner's dilemma - Chicken - Stag hunt - Ultimatum game - Matching pennies - Minority Game - Rock, Paper, Scissors - Dictator game -...
Theorems Revelation principle - Minimax theorem - Purification theorems - Folk theorem of repeated games - Bishop-Cannings theorem
Related topics Mathematics - Economics - Behavioral economics - Evolutionary biology - Evolutionary game theory - Population genetics - Behavioral ecology - List of game theorists
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