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Search models of monetary exchange have typically relied on Nash [1950. The bargaining problem. Econometrica 18, 155–162] bargaining, or strategic games that yield an equivalent outcome, to determine the terms of trade. By considering alternative axiomatic bargaining solutions in a search model with divisible money, we show that the properties of the bargaining solutions do matter both qualitatively and quantitatively for questions of first-degree importance in monetary economics such as: (i) the efficiency of monetary equilibrium; (ii) the optimality of the Friedman rule and (iii) the welfare cost of inflation.

In the last decade search-theoretic models of money have become the dominant framework for studying monetary theory. Contrary to traditional monetary models, trade is decentralized and carried out bilaterally. Since Shi (1995) and Trejos and Wright (1995), the standard approach for determining the terms of trade in bilateral matches is to impose the generalized Nash solution, or to use a strategic bargaining game that yields a similar outcome.1 Recent extensions to allow for policy analysis by Shi (1997) and Lagos and Wright (2005) (LW) produce new results regarding the optimality of the Friedman rule and the welfare cost of inflation. It is unclear, however, whether these new results are robust predictions of models with search and bargaining or if they are driven by the choice of a particular bargaining solution.

Bargaining is an integral part of models of decentralized trading. Yet very little work has been done to understand how various bargaining solutions affect the qualitative and quantitative predictions of these models. In this paper we examined two standard bargaining solutions to do just that in the context of a monetary search model. Our analysis provided qualitative and quantitative insights as to which properties of the bargaining solution matter for the efficiency of equilibrium, the optimal policy and the welfare cost of inflation.