Consider a variant of Example 2 (Prisoner's Dilemma II). in this variant, only a tough player...

 

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Consider a variant of Example 2 (Prisoner's Dilemma II). in this variant, only a tough player 2 has a dominant strategy. P1 P2 (Tough) P1 P2 (Accommodating) C n n (0,0) (7,-2) (-2,0) (5,-2) n (-2,7) (5,5) n (0,5) (7,7) Now consider a sequential variant (with the same payoffs as those shown in the strategic form representation above) where player 2 plays c or n, followed by player 1 choosing c or n. (a) Draw the game in extensive form and describe the set of strategies for each player. For each of player 1's strategies, describe player 2's beliefs (or feasible set of beliefs) e [1,0] about player 1's type at each of player 2's information sets. (b) Write the set of best responses for each player. (c) Identify the set of Bayesian Nash Equilibrium in the sequential variant, for an arbitrary value of p. In what equilibria is player 1 able to identify player 2's type based on their actions. Consider a variant of Example 2 (Prisoner's Dilemma II). in this variant, only a tough player 2 has a dominant strategy. P1 P2 (Tough) P1 P2 (Accommodating) C n n (0,0) (7,-2) (-2,0) (5,-2) n (-2,7) (5,5) n (0,5) (7,7) Now consider a sequential variant (with the same payoffs as those shown in the strategic form representation above) where player 2 plays c or n, followed by player 1 choosing c or n. (a) Draw the game in extensive form and describe the set of strategies for each player. For each of player 1's strategies, describe player 2's beliefs (or feasible set of beliefs) e [1,0] about player 1's type at each of player 2's information sets. (b) Write the set of best responses for each player. (c) Identify the set of Bayesian Nash Equilibrium in the sequential variant, for an arbitrary value of p. In what equilibria is player 1 able to identify player 2's type based on their actions.