Consider a sequential game in which Player 1 first chooses between A and B and Player...

 

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Consider a sequential game in which Player 1 first chooses between A and B and Player 2 then chooses between a and b. Player 1's type is either t or t, and each type occurs with a probability of 0.5. Player 1 knows their type, but Player 2 does not know Player 1's type. If Player 2 chooses a, both players receive a payoff of 1. If Player 2 chooses b, both players receive a payoff of 0 when Player 1's type is t, and both players receive a payoff of 3 when Player 1's type is tp, A. Show the game in extensive form. (Be careful to label information sets correctly.) B. Find one perfect Bayesian equilibrium of this game. Show your work. Consider a sequential game in which Player 1 first chooses between A and B and Player 2 then chooses between a and b. Player 1's type is either t or t, and each type occurs with a probability of 0.5. Player 1 knows their type, but Player 2 does not know Player 1's type. If Player 2 chooses a, both players receive a payoff of 1. If Player 2 chooses b, both players receive a payoff of 0 when Player 1's type is t, and both players receive a payoff of 3 when Player 1's type is tp, A. Show the game in extensive form. (Be careful to label information sets correctly.) B. Find one perfect Bayesian equilibrium of this game. Show your work.