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Next, consider the following static incomplete-information game, called Game C . It is played between Player 1 and Player 2. Player 1 chooses an action
Next, consider the following static incomplete-information game, called "Game C" . It is played between Player 1 and Player 2. Player 1 chooses an action x1 E R, trying to maximize the following payoff function: u1 (21, 202) = 0121 + 721202 -701 where 1 is a parameter. Similarly, Player 2 chooses an action .2 E R, trying to maximize the following payoff function: U2($1, X2) = 02 2 +,2102 -,23, where 02 is a parameter. The value of 0i (i = 1, 2) is private information to Player i, but it is common knowledge that 01 and 02 are independently drawn from a uniform distribution on the interval [0, 1]. The two players choose their actions x1 and x2 simultaneously with each other. (c) Solve for a Bayesian Nash equilibrium of Game C. . Hint: Guess that there is an equilibrium in which the players use linear strategies of the following form: x1 = A1 + B101, x2 = A2 + B202, respectively, where A1, A2, B1, and B2 are constants that you must determine the values of
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