Intuitive criterion

The intuitive criterion is a technique for equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by first restricting the type group to types of agents who could obtain higher utility levels by deviating to off-the-equilibrium messages and second by considering in this sub-set of types the types for which the off-the-equilibrium message is not equilibrium dominated.^[1]

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 many 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.^[2] 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 among 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 could benefit from 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.

An equilibrium strategy (m*, a*) violates the intuitive criterion if there is a type θ and a message he can send m such that:

min u_i (m,a,θ) > u_i* (θ) for some θ ∈ Θ**(m)

_{a ∈ A*(Θ**(m),m)}

Where m* is the equilibrium message, a* is the equilibrium response (action) of the receiver.^[3]

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 same 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.

Notes

References

• Mas-Colell, Whinston, Green (1995) Microeconomic Theory