Consider the following game of incomplete information Player

Consider the following game of incomplete information. Player S is unable to observe the type of player T (type T_1 or T_2). The probability distribution over types is common knowledge. Note that payoffs in this game are ordered player S followed by player T : (pi_s, pi_T). What is a separating equilibrium in a Bayesian game? What is a Pooling equilibrium in a Bayesian game. What are the beliefs of a player in a Bayesian game? What is the relation between beliefs of a player and the type of equilibrium (Pooling vs. Separating)? Consider a Bayesian perfect Nash equilibrium involving mixed strategies. Player S plays L with probability beta and M with probability 1 - beta. Type T_1 plays E with probability a and G with probability 1 - alpha. There is no other mixing in the game. Find the mixed strategy of player 5 and the strategy of type T_2. Complete the description of the Bayesian perfect Nash equilibrium from by finding the equilibrium strategy of type T_1 and the beliefs of player S. Describe a pooling equilibrium to this game if one exists. If there is no pooling equilibrium clearly demonstrate that no pooling equilibrium exists.

Solution

(a) Separating equilibrium

L for T₁ and M for T₂

L for T₂ and M for T₁

pooling equilibrium

Both for L,   Both for M