1. Player 1 and Player 2 are involved in a dispute. Player 2 is either Weak or Strong. Player 2's strength is private information. 2 knows his strength; 1 knows that 2 is Strong with probability p and that he is Weak with probability (1 - p). Both players will decide to either Fight or Yield simultaneously. The payoffs in this game are as follows:

• If they both choose Yield each earns 0 regardless of 2's type.
• If one chooses Fight and the other chooses Yield, the player who chooses Fight earns 100 and the other player earns 0 regardless of 2's type.
• If they both choose Fight
• If Player 2 is Strong then Player 1 earns a payoff of -100 and Player 2 earns a payoff of 100.
• If Player 2 is Weak then Player 1 earns a payoff of 100 and Player 2 earns a payoff of -100.

(a) Draw the game tree.

(b) Suppose p =0.3. Find the Bayes-Nash equilibrium of this game. Defend your answer carefully.

(c) Suppose p =0.7. Find the Bayes-Nash equilibrium of this game. Defend your answer carefully.