Question

2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.

Answer 1

Strategy space of player 1 is certain ,. It's the space of player 2 that is uncertain because of incomplete information about its type being theya=1 or theta=-1 .

Pure strategy bayesian Nash can be found out by calculating the expected pay offs of the player 1 with respect to the strategies.

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