Two-sided search and perfect segregation with fixed search costs

This paper studies a two-sided search model with the following characteristics: there is a continuum of agents with different types in each population, match utility is nontransferable, and agents incur a fixed search cost in each period. When utility functions are additively separable in types and strictly increasing in the partner's type, there is a unique matching equilibrium. It exhibits perfect segregation as in Smith [Smith, The marriage model with search frictions, Working paper (1997) Department of Economics, MIT] and Burdett and Coles [Quarterly Journal of Economics, 112 (1997) 141]; i.e. agents form clusters and mate only within them. A simple sufficient condition on the match utility function and the density of types characterizes the duration of the search for each type of agent. The sufficiency of additive separability in the fixed search cost case is explained and contrasted with the discounted case; moreover, the results are generalized to a broader class of search cost functions that subsumes discounting and fixed search costs as special cases.