Answer Happy

Consider the following situation faced by two players. There are two possible simultaneous games they might be playing, G1 and G2. The payoff matrices for the two games are: L L U 0,22 D 21,0 R 22,0 0,01 U 12,0 D 0,02 R 0,01 41,0 where ( < 01 <02. 1. Suppose that both players share a common prior 7 € (0,1) that the actual game being played is Gy. If neither player knows which game is played, what is the equilibrium of this new game as a function of ? 2. Suppose again that both players share a common prior T € (0,1) that the actual game being played is G]. In addition, suppose that the Row player is told which game is actually being played before taking an action but that the Column player is not told (and that these facts are common knowledge). (a) Specify this new game as a game of incomplete information by writing down the types, beliefs, and payoff functions of both players (b) Write down the extensive form of the resulting game of incomplete information (C) Is there a pooling equilibrium in this game? If so, fully describe it as a function of a (d) Is there a separating equilibrium in this game? If so, fully describe it as a function of a (Hint #1: Notice that, since it is a simultaneous game, both players move at the same time, and they cannot update their beliefs.) (Hint #2: Let pı and p2 denote the probabilities that Row plays U for type G1 and type G2 respectively. Let also q denote the probability that Column plays L. You need look for triples (P1, P2, and q) that are the Bayesian equilibria.)