In game theory, the intuitive criterion is a type of equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by restricting the possible sender types to types who could obtain higher utility levels by deviating to off-the-equilibrium messages, and to types for which the off-the-equilibrium message is not equilibrium dominated.

Background

A signaling game is a game in which one player ("sender") has private information regarding his type. He sends a signal ("message") to the other player ("receiver") to indicate his type. The receiver then takes an action. Both the signal and the receiver action can affect both players' utilities. A perfect Bayesian equilibrium (PBE) in such a game consists of three elements.

• A sender strategy - a function from the sender type to a signal that maximizes this type's utility given the receiver strategy.

• A receiver belief - a function from the signal to a probability distribution over sender types; the belief must be consistent with the sender strategy in the sense of Bayes' rule.

• A receiver strategy - a function from the signal to an action which maximizes the receiver's utility given his belief.

The definition of PBE does, however, not impose any restrictions on the beliefs about signals that the sender never sends in equilibrium, since Bayes' rule is not applicable for events that occur with probability zero. Therefore, signaling games typically have a large number of equilibria that can be supported by an off-equilibrium belief. For example, it is possible to have a PBE with the following properties.

• The sender of all types only sends the same signal.

• The receiver believes that, if the sender did send a different signal, then the receiver would take an action that effectively "punishes" the sender by giving low utility to all types.

• There exists a belief such that the punishing action is optimal for the receiver.

While this satisfies the definition of PBE, the receiver belief might be "unreasonable". The intuitive criterion, like most refinement techniques, is based on restricting the beliefs off the equilibrium path.

Explanation

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 receiver beliefs to be reasonable in some sense.

favorably:

1. .

Formal definition

can, in the best case, yield a weakly higher payoff than the equilibrium payoff is

is called equilibrium dominated.

is equilibrium dominated. Formally,

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 perfect bayesian equilibrium. 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 -- 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.

A sketch of a typical model shows why (this model is worked out more fully in signalling games.

(for example), the intuitive criterion says that employers must believe he is the high type. That is because if they do believe, and he really is the high type, his payoff will rise from 5 - 0 = 5 to 10 - 4 = 6, but if he were the low type, his payoff would fall from 5 - 0 = 5 to 10 - 2*4 = 2. This argument can be applied to any of the pooling equilibria.

Notes

References

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

See also

• Divine equilibrium