Intuitive criterion
The intuitive criterion is a technique for 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. The definition of PBE does, however, not require anything about signals that the sender never sends, since Bayes' rule is not applicable for events that occur with probability zero. Therefore, it is possible to have a PBE with the following properties. 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. 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. Intuitively, we can eliminate a PBE if there is exists a sender type who wants to deviate, assuming that the receiver has a reasonable belief. It is reasonable to believe that the deviating sender is of a type who would benefit from the deviation in at least the best-case scenario. If a type of sender could not benefit from the deviation even if the receiver changed his belief in  the best possible way for the sender, then the receiver should reasonably put zero probability on the sender being of that type. The deviating sender type formula_1 could persuasively tell the receiver to interpret his deviating signal formula_2 favorably: Formally, given any set of types formula_5, let formula_6 denote the set of actions that are optimal for the receiver given some belief with support in formula_7 and given the signal formula_3. Let formula_9 denote the sender utility as a function of her type formula_10, her signal formula_11, and the receiver action formula_12. Given any PBE with sender strategy formula_13 and  receiver strategy formula_14, the equilibrium payoff of any type formula_10 is denoted formula_16. The set of types such that deviating to signal formula_17 can, in the best case, yield a weakly higher payoff than the equilibrium payoff is For types outside of this set, the signal formula_17 is called equilibrium dominated. A particular PBE is eliminated by the intuitive criterion if there exists a sender type formula_1 and a deviating signal formula_3 that guarantees for this type a payoff above their equilibrium payoff as long as the receiver has a reasonable belief, that is, assigns zero probability to the deviation  having been made by a type for whom formula_3 is equilibrium dominated. Formally, 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 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). Suppose the abilities of low and high types of worker are 0 and 10, with equal probability, that in equilibrium the employer will pay the worker his expected ability, and that the cost of education formula_24 is formula_24 for high-ability workers and formula_26 for low-ability workers. There would be a continuum of separating equilibria with formula_27 and  of pooling equilibria with formula_28. The intuitive criteria would rule out a separating equilibrium such as formula_29 for the high type and formula_30 for the low type because the high-ability worker could profitably deviate to, for example, formula_31. That is because if the employer still believe the worker is high-ability, his payoff is higher than with formula_32, receiving the same salary of 10 but paying less for education, while the low-ability worker does worse even if his deviation persuades employers that he has high ability, because although his wage would rise from 0 to 10, his signal  cost would rise from 0 to 2*5.1. Thus, it is reasonable for the employer to believe that only a high-ability worker would ever switch to formula_33. This argument applies to all separating equilibria with formula_34. The intuitive criterion also rules out all pooling equilibria. Consider the equilibrium in which both types choose formula_35 and receive the expected ability of 5 as their wage. If a worker deviates to formula_36 (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.