Eco514--Game Theory gnawing game Marciano siniscalchi January 10, 2000 Introduction Signaling games are used to model the following situation: Player 1, the Sender, receives some private information 0 ee and sends a message m E M to Player 2, the Receiver. The latter, in turn, observes m but not 0, and chooses a response E R Players' payoffs depend on 6, m and r What could be simpler? Yet, there is a huge number of economically interesting games that fit nicely within this framework: Spence's job market signaling model is the leading example, but applications abound in IO(limit pricing, disclo finance(security design) and political economics Also, the analysis of signaling games is not entirely straightforward. The point is in general all (reasonable) Nash equilibria are also sequential, trembling-hand perfect etc; that is, they satisfy all sorts of backward-induction criteria However, many equilibria appear to be intuitively unreasonable. Moreover, tI to the particularly simple dynamic and informational structure, it is not hard to generalize intuitions concerning specific models to the whole class of signaling games As a result, a sizable literature on refinements for these games has developed. W shall only look at the most important(and most successful) notions: the intuitive criterion of Cho and Kreps, and divinity-like ideas a la Banks and Sobel Beer-Quiche and the Intuitive Criterion Consider the game of Figure 1 I told you the story behind this game in class, so I'm not going to bother you with it again. Let me just point out the essential features: either type of the Sender prefers to avoid a fight, even if this requires not enjoying her favorite breakfast(the incremental payoff from avoiding a fight is 2, whereas the preferred breakfast yields anEco514—Game Theory Signaling Games Marciano Siniscalchi January 10, 2000 Introduction Signaling games are used to model the following situation: Player 1, the Sender, receives some private information θ ∈ Θ and sends a message m ∈ M to Player 2, the Receiver. The latter, in turn, observes m but not θ, and chooses a response r ∈ R. Players’ payoffs depend on θ, m and r. What could be simpler? Yet, there is a huge number of economically interesting games that fit nicely within this framework: Spence’s job market signaling model is the leading example, but applications abound in IO (limit pricing, disclosure...), finance (security design) and political economics. Also, the analysis of signaling games is not entirely straightforward. The point is, in general all (reasonable) Nash equilibria are also sequential, trembling-hand perfect, etc.; that is, they satisfy all sorts of backward-induction criteria. However, many equilibria appear to be intuitively unreasonable. Moreover, thanks to the particularly simple dynamic and informational structure, it is not hard to generalize intuitions concerning specific models to the whole class of signaling games. As a result, a sizable literature on refinements for these games has developed. We shall only look at the most important (and most successful) notions: the intuitive criterion of Cho and Kreps, and divinity-like ideas `a la Banks and Sobel. Beer-Quiche and the Intuitive Criterion Consider the game of Figure 1. I told you the story behind this game in class, so I’m not going to bother you with it again. Let me just point out the essential features: either type of the Sender prefers to avoid a fight, even if this requires not enjoying her favorite breakfast (the incremental payoff from avoiding a fight is 2, whereas the preferred breakfast yields an 1