3. Consider a game where player 1 chooses T or B, player 2 independ...

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3. Consider a game where player 1 chooses T or B, player 2 independently chooses L or R, and their utility payoffs (211,u2) depend on their choices: Player 1 \ Player 2 L R T a11,611 @12,612 B @21,621 b22 Leave the payoff x = us (B,R) unspecified in the above table, so that we can consider some different assumptions about it. (a) Fill in the players' payoffs (u1, u2) in the above table except for the payoff I = us(B,R) so that your game satisfies the following requirements: (i) Each aij and bis is an integer, and you can only use the integer once. That is, all 7 numbers must be different. (ii) Player l's payoffs satisfy @11 < @21 and @12 > 2. (iii) Player 2's payoffs satisfy b11 > b12 and b21 < b22. (b) Suppose first that I could be either 1 or 2, each with probability 1/2. That is, only player 1 knows x, and player 2 believes that I is equally likely to be 1 or 2. Find a Bayesian equilibrium of this game. (c) Now suppose that T is a random variable drawn from a Uniform distribution on the interval from 1 to 2. Player 1 knows the actual value of I when he chooses his action in this game, but player 2 knows only the distribution from which I is drawn. Find a Bayesian equilibrium of this game.

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