Answer to Question #63497 in Microeconomics for boset00

Question #63497
Consider a two player game with payoff matrix L R X Y Z 3, θ 0, 0 2, 2θ 2, θ 0, 0 3, −θ where θ ∈ {−1, 1} is a parameter known by Player 2. Player 1 believes that θ = −1 with probability 1/2 and θ = 1 with probability 1/2. Everything above is common knowledge. (a) Write this game formally as a Bayesian game. (b) Compute the Bayesian Nash equilibrium of this game. (c) What would be the Nash equilibria in pure strategies (i) if it were common knowledge that θ = −1, or (ii) if it were common knowledge that θ = 1?
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