(b) Two players, 1 and 2, must each choose to move left (L) or right (R). If they both

choose L they both get a payoff of 100. If they both choose R they both get a payoff of

60. If 1 chooses L and 2 chooses R, payoffs for 1 and 2 are respectively 0 and 60. If 1

chooses R and 2 chooses L, payoffs for 1 and 2 are respectively 60 and 0.

(i) Describe all pure-strategy Nash equilibria for this game.

(ii) Suppose that each of the two players believes that with probability 1/2 her

opponent is a rational player whose strategies are chosen as best responses to her

opponent's choices, but with probability 1/2 her opponent is a machine that selects

L or R by tossing a coin, L and R being selected with equal probabilities. What are

the pure-strategy equilibria in this scenario? Explain.