The Intuitive Criterion
Encyclopedia
The Intuitive Criterion in Game Theory
is a technique for equilibrium refinement in signaling games. In economics, signaling games are games in which a player with private information moves first. Private information generally refers to the player's hidden or unobservable type. Signaling games typically have lots of perfect Bayesian equilibria. Equilibrium refinement techniques are ways of reducing the set of equilibria. Most refinement techniques are broadly based on restricting beliefs off the equilibrium path. Off equilibrium actions or outcomes are those that are different from what is predicted in a Nash equilibrium. The intuitive criterion was presented by In-Koo Cho and David M. Kreps
in a 1987 article. Their idea was to try to reduce the set of equilibria by requiring off-equilibrium beliefs to be reasonable in some sense. This refinement of the solution concept
allows the modeller to choose between multiple perfect Bayesian equilibria.
Formally, we can eliminate a particular perfect Bayesian equilibrium by using the Intuitive Criterion if there is some type θ who has a deviation that is assured of yielding him a payoff above his equilibrium payoff as long as other players do not assign a positive probability to the deviation having been made by any type θ for whom this action is equilibrium dominated.
Intuitively, we can eliminate a PBE if there is a type of player who wants to deviate even though he is not sure what the beliefs of other players are. The player is only sure that the other players will not think that he is a player who would find the deviation to be an equilibrium-dominated action.
In the game, there is also a continuum of separating equilibria, but the Intuitive Criterion eliminates all the separating equilibria except for the most efficient one - i.e. the one where low-ability types are just about indifferent between acquiring the amount of education that high-ability types do, and not acquiring any education at all.
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
is a technique for equilibrium refinement in signaling games. In economics, signaling games are games in which a player with private information moves first. Private information generally refers to the player's hidden or unobservable type. Signaling games typically have lots of perfect Bayesian equilibria. Equilibrium refinement techniques are ways of reducing the set of equilibria. Most refinement techniques are broadly based on restricting beliefs off the equilibrium path. Off equilibrium actions or outcomes are those that are different from what is predicted in a Nash equilibrium. The intuitive criterion was presented by In-Koo Cho and David M. Kreps
David M. Kreps
David Marc "Dave" Kreps is a game theorist and economist and professor at the Graduate School of Business at Stanford University. He is known for his analysis of dynamic choice models and non-cooperative game theory, particularly the idea of sequential equilibrium, which he developed with Stanford...
in a 1987 article. Their idea was to try to reduce the set of equilibria by requiring off-equilibrium beliefs to be reasonable in some sense. This refinement of the solution concept
Solution concept
In game theory, a solution concept is a formal rule for predicting how the game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players, therefore predicting the result of the game...
allows the modeller to choose between multiple perfect Bayesian equilibria.
Formally, we can eliminate a particular perfect Bayesian equilibrium by using the Intuitive Criterion if there is some type θ who has a deviation that is assured of yielding him a payoff above his equilibrium payoff as long as other players do not assign a positive probability to the deviation having been made by any type θ for whom this action is equilibrium dominated.
Intuitively, we can eliminate a PBE if there is a type of player who wants to deviate even though he is not sure what the beliefs of other players are. The player is only sure that the other players will not think that he is a player who would find the deviation to be an equilibrium-dominated action.
Criticisms
Other game theorists have criticized the Intuitive Criterion and suggested alternative refinements such as Universal Divinity.Example
In the standard Spence signaling game, with two types of senders, a continuum of pooling equilibrium persist under solution concepts such as Sequential equilibrium and PBE. But the Cho-Kreps Intuitive Criterion eliminates all pooling equilibria.In the game, there is also a continuum of separating equilibria, but the Intuitive Criterion eliminates all the separating equilibria except for the most efficient one - i.e. the one where low-ability types are just about indifferent between acquiring the amount of education that high-ability types do, and not acquiring any education at all.