midterm question

Q3. Consider the following situation: Player 1 and 2, both male goats, have to cross a narrow bridge every morning. Suppose that player I's barn is closer to the bridge than player 2's, thus we may assume that player 1 moves first. Suppose that player 1 (moving first) can choose to cross or to wait. Player 2 observes player I's action and based on that can choose to cross the bridge or to wait. If player one chooses "cross" and player 2 "cross" they will meet in the middle of the bridge, and they would have to stay there a long time. This will result in a payoff of 1 for player 1 and 1 for player 2. However, if a player crosses the bridge while the other waits then the crossing agent gets a payoff of 5, and the waiting agent gets a payoff of 2. Finally if they both wait, they get a return of 0 each. a. Formulate this situation as an extensive form game by drawing a game tree. b. Find the set of (pure strategy) Nash equilibria of this extensive form game. c. Find the subgame perfect Nash equilibrium of this game. For Nash equilibria which are not subgame perfect, if any, indicate the non-credible threat