I study the limit rule for bilateral bargaining when agents recognize that the aggregate economy (influencing the match surplus) follows a dynamic process that randomly switches back and forth between a finite number of possible states. The rule derived in this paper is of special importance for decentralized exchange economies with bargaining. Two simple applications are presented to illustrate this fact. The first example is a model of wage bargaining and trade externalities. I show that in those situations sophisticated bargaining tends to increase the volatility (due to extrinsic uncertainty) of the wage bill. The second example is based on the Kiyotaki-Wright model of money. I explain how equilibrium prices depend in a fundamental way on the dynamic bargaining solution.
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