Need help with Bayesian games. I have not learnt game theory before. Please walk me through each step.

Trading Places?Two players, 1 and 2, each own a house. Each player i values his own house at vi . The value of player i's house to the other player, i.e., to

player j= i, is 3/2*vi . Each player i knows the value vi of his own house to himself, but not the value of the other player's house. The values vi are drawn

independently from the interval [0, 1] with uniform distribution.

a. Suppose players announce simultaneously whether they want to exchange their houses. If both players agree to an exchange, the exchange

takes place. Otherwise no exchange takes place. Find a Bayesian Nash equilibrium of this game in pure strategies in which each player i accepts an exchange if and only if the value vi does not exceed some

threshold ?i .

b. How would your answer to (a) change if player j 's valuation of player i's house were 5/2*vi?

Trading Places: Two players, 1 and 2, each own a house. Each player i values his own house at v;. The value of player i's house to the other player, i.e., to player j i, is =up. Each player / knows the value v; of his own house to himself, but not the value of the other player's house. The values v; are drawn independently from the interval [0, 1] with uniform distribution. a. Suppose players announce simultaneously whether they want to ex- change their houses. If both players agree to an exchange, the exchange takes place. Otherwise no exchange takes place. Find a Bayesian Nash equilibrium of this game in pure strategies in which each player i ac- cepts an exchange if and only if the value v; does not exceed some threshold of. b. How would your answer to (a) change if player j's valuation of player i's house were