Exercise 3. Consider a game in the following figure. Player I chooses from three actions, L,...

  

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Exercise 3. Consider a game in the following figure. Player I chooses from three actions, L, M, and R. Player II chooses from two actions, 1 and r. The decision nodes are zo, zz, and ZM. In the following figure, the top payoff in the pair of payoffs at the end of each branch of the game tree is player I's, the bottom player II's. || 21 1 Zo L 00 1 01 R M Z 0 1 Write down the normal form of the game in a matrix. (ii) Find all the pure-strategy and mixed-strategy Nash equilibria. (iii) Find all the weak perfect Bayesian equilibria. Exercise 3. Consider a game in the following figure. Player I chooses from three actions, L, M, and R. Player II chooses from two actions, 1 and r. The decision nodes are zo, zz, and ZM. In the following figure, the top payoff in the pair of payoffs at the end of each branch of the game tree is player I's, the bottom player II's. || 21 1 Zo L 00 1 01 R M Z 0 1 Write down the normal form of the game in a matrix. (ii) Find all the pure-strategy and mixed-strategy Nash equilibria. (iii) Find all the weak perfect Bayesian equilibria.