Outline A . Signaling Games 1 . The Intuitive

1. The Intuitive Criterion (Cho & Kreps, 1987) This paper analyzes a simple signaling model that has applications throughout information economics. There are two players: a Sender of information (S) and a Receiver of information (R). The timing of the game is: (1) nature draws a type for S, denoted t ∈ T, according to the probability distribution p(t); (2) S privately observes the type t and then sends the message m ∈ M to R; and (3) R observes m and then takes the action a ∈ A. The three sets T, M, and A are all finite. The payoffs are U(t,m,a) and U(t,m,a). Everything about the game except nature's choice of t is common knowledge. The paper proposes a test for identifying unreasonable sequential equilibria of this game. Part of the paper concerns the use of this test as an intuitive implication of the not-so-intuitive equilibrium concept designed by Kohlberg and Mertens [1986]. But the test is of substantial interest in its own right as a way to refine the set of sequential equilibria. To explain the test Cho & Kreps propose, consider a simple version of the game: T={t,t'} and M={m,m'}. Suppose that in a particular equilibrium both types send the message m with probability one. Then the message m' is off the equilibrium path, so R's beliefs after observing m' cannot be derived from Bayes' rule. Instead, these beliefs need only satisfy Kreps and Wilson's definition of consistency in order to be part of a sequential equilibrium. (It is left as an exercise to show that in a signaling game any beliefs off the equilibrium path satisfy consistency.) Sequential rationality dictates that the action R taken after observing m' must be optimal given R's beliefs. That is,