Search, Heterogeneity, and Noisy Observable Types
This paper analyzes a model with search frictions, heterogeneous agents, and nontransferable utility, in which each individual observes only a noisy signal of the type of a potential partner. We show that an agent's optimal strategy must take into account not only the realization of the noisy signal observed, but also the information contained in the event that the agent is accepted. We show that there exists an equilibrium in strategies that are increasing in types; the proof is based on the analysis of a Bayesian game embedded in the model. This equilibrium exhibits a stochastic form of positive sorting of agents by types: since agents with higher types are accepted more often, and being accepted is 'better news' for them than for agents with lower types, they tend to be more selective in their acceptance decision, and, therefore, they tend to marry agents with higher types. We also shed light on whether equilibria in strategies that are not increasing in types could exist.
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