1. Criticisms

2. Example

3. Notes

4. References

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 them a payoff above their 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, assuming that other players are reasonable. What does it mean to be unreasonable? It is unreasonable to believe the deviating player is of a type for whom the deviating action is a bad idea (for that type, it is definitely worse than some alternative action).

An equilibrium strategy violates the intuitive criterion if there is a type and a message they can send such that:

for some

where is the equilibrium message, is the equilibrium response (action) of the receiver,

and is the set of types for which that message cannot be equilibrium dominated.^[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 exactly 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

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