Consider a two-player game with payoff matrix X L (3, 0) (2, 20) (0,0) R (0,0) (2, 0) (3,-0) Y Z where 0 E{-1,1} is a pa

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Consider A Two Player Game With Payoff Matrix X L 3 0 2 20 0 0 R 0 0 2 0 3 0 Y Z Where 0 E 1 1 Is A Pa 1 (73.96 KiB) Viewed 24 times

Consider a two-player game with payoff matrix X L (3, 0) (2, 20) (0,0) R (0,0) (2, 0) (3,-0) Y Z where 0 E{-1,1} is a parameter known only by player 2. Player 1 believes that 0 = 1 with probability and 8 = -1 with probability. Everything above is common knowledge. a) Write this game formally as a Bayesian game (strategies, types, prior distributions (beliefs), utilities (payoffs)). b) Compute all Bayesian Nash equilibria of this game. (You can use any method of your preference e.g., you can use possible normal form representations that can arise or draw the extensive form respresentation as a game of imperfect information à la Harsanyi). c) What would be the Nash equilibria in pure strategies (1) if it were common knowledge that a = -1, or (ii) if it were common knowledge that 0 = 1? =