Firms A and B are the only firms in the market for widgets. Each firm can choose between cooperating and fighting. If both firms choose to cooperate, each gets a profit of 10. If both firms choose to fight, each gets a profit of 5. If one chooses to cooperate and the other chooses to fight, the firm that chooses to cooperate gets a profit of 1 and the firm that chooses to fight gets a profit of 20. Each firm chooses the action that maximizes its profits.
(a) Suppose firms choose their actions simultaneously and they play this game once. Write the matrix of payoffs for this situation and find the pure strategy Nash equilibrium (or all equilibrium) of the simultaneous-move game played by firms A and B.
(b) Suppose firms choose their actions simultaneously but the game is repeated during 10 years. So, when firms make their decisions in a specific year, each firm knows the choices of the other firm in the previous years. Find the equilibrium (or all equilibrium) of this game.