4. (25 pts) 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=0.35 and that he is Weak with probability (1 - p)=0.65. 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 15 regardless of 2's type. . If one chooses Fight and the other chooses Yield, the player who chooses Fight earns 40 and the other player earns 15 regardless of 2's type. If they both choose Fight: -If Player 2 is Strong then Player 1 earns a payoff of -40 and Player 2 earns a payoff of 40. - If Player 2 is Weak then Player 1 earns a payoff of 40 and Player 2 earns a payoff of -40. (a) (5 pts) Draw the game tree. (b) (5 pts) Draw the payoff matrix for the game. (d) (15 pts) Find all pure strategy Bayes Nash equilibria. Explain your work clearly. (with sentences) 4. (25 pts) 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=0.35 and that he is Weak with probability (1 - p)=0.65. 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 15 regardless of 2's type. . If one chooses Fight and the other chooses Yield, the player who chooses Fight earns 40 and the other player earns 15 regardless of 2's type. If they both choose Fight: -If Player 2 is Strong then Player 1 earns a payoff of -40 and Player 2 earns a payoff of 40. - If Player 2 is Weak then Player 1 earns a payoff of 40 and Player 2 earns a payoff of -40. (a) (5 pts) Draw the game tree. (b) (5 pts) Draw the payoff matrix for the game. (d) (15 pts) Find all pure strategy Bayes Nash equilibria. Explain your work clearly. (with sentences)