. Two countries, 1 and 2, are involved in a serious dispute. The game starts with country 1's decision of whether to avoid any action and disregard the situation (), resulting in payoffs (0, 0), or to heighten the matter (). If country 1 heightens the matter, country 2 will have two actions to choose from: either acquiesce (), which results in losing reputation and a payoff of (1, 1), or initiate a battle (). Upon the latter choice, the players will have to play a simultaneous move game where they can either withdraw ( for country 1, for country 2) or choose a nuclear war ( for country 1, for player 2) in which the world is destroyed leaving a payoff (100, 100). If both call things off, they each suffer a small loss due to the process and their payoffs will be (0.5, 0.5).

(i) Draw an extensive form representation of the game where a matrix form representation can be used for the simultaneous move game that is played in the final stage. [15 marks]

(ii) Determine the subgame perfect Nash equilibria and their outcomes. Provide an interpretation of the equilibria. [15 marks]

(iii) Find the Nash equilibria of the game. For each of the Nash equilibria, explain why no player has a profitable deviation. Determine which parts of the Nash equilibrium strategies involve uncredible threats.