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“Consider the following variant of a war of attrition. In each period, first firm A decides whether to fight or quit. Then, after observing firm A’s choice, firm B decides whether to fight or to quit. If both firms quit, both firms get 0 payoff that period and the game ends. If firm A fights and firm B quits, then firm A gets 5 and firm B gets 0 that period, and the game ends. If firm A quits and firm B fights, then firm A gets 0 and firm B gets 5 that period, and the game ends. If both firms fight, then firm A gets a payoff of ?2 that period, and firm B gets a payoff of ?1 that periods, and the game continues to the next period. The game continues until at least one firm quits or until the end of period 3.

There are two differences to the war of attrition we discussed in class. First, in each period reached, firm B observes firm A’s move before deciding its own move. Second, the costs of fighting are asymmetric: ?2 per period for firm A and ?1 per period for firm B.

Assume that both firms are rational. For your answers, you can restrict attention to pure strategies. 

Describe the equilibrium path of play in this game. What are the firms’ equilibrium payoffs? “

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