Question 1

**(Bayesian Game)** Consider a two-player game in which the payoffs, which depend on $\theta$, and actions are as in the following table: $\theta = 0$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, -1$ | $-1, 1$ | | $D$ | $-1, 1$ | $1, -1$ | $\theta = 1$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, 1$ | $-1, -1$ | | $D$ | $-1, 1$ | $1, -1$ | Where $\Pr(\theta = 0) = \Pr(\theta = 1) = \frac{1}{2}$. Player 2 knows exactly what value $\theta$ has, whereas player 1 doesn't know. Based on the above data, answer the given subquestions. Under Bayesian Nash Eq., player 1 will play **(Bayesian Game)** Consider a two-player game in which the payoffs, which depend on $\theta$, and actions are as in the following table: $\theta = 0$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, -1$ | $-1, 1$ | | $D$ | $-1, 1$ | $1, -1$ | $\theta = 1$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, 1$ | $-1, -1$ | | $D$ | $-1, 1$ | $1, -1$ | Where $\Pr(\theta = 0) = \Pr(\theta = 1) = \frac{1}{2}$. Player 2 knows exactly what value $\theta$ has, whereas player 1 doesn't know. Based on the above data, answer the given subquestions. Under Bayesian Nash Eq., player 2, who knows that *θ* = 0 will play **(Bayesian Game)** Consider a two-player game in which the payoffs, which depend on $\theta$, and actions are as in the following table: $\theta = 0$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, -1$ | $-1, 1$ | | $D$ | $-1, 1$ | $1, -1$ | $\theta = 1$ | | $L$ | $R$ | |---|---|---| | $U$ | $1, 1$ | $-1, -1$ | | $D$ | $-1, 1$ | $1, -1$ | Where $\Pr(\theta = 0) = \Pr(\theta = 1) = \frac{1}{2}$. Player 2 knows exactly what value $\theta$ has, whereas player 1 doesn't know. Based on the above data, answer the given subquestions. Under Bayesian Nash Eq., player 2, who knows that *θ* = 1 will play