This paper endogenizes the market structure of an economy with heterogeneous agents who want to form bilateral matches in the presence of search frictions and when utility is non-transferable. We depart from standard matching models where all agents are assumed to be in a unique meeting place by assuming the existence of infinitely many meeting places and allowing each agent to choose which meeting place to be in. The market is thus allowed to be segmented into dierent meeting places, and agents not only get to choose who to match with, but also who they meet with. We show that in equilibrium all market structures feature perfect segmentation where agents match with the rst person they meet. All these market structures have the same matching pattern, implying that the value of search to each agent is the same. Although perfect assortative matching cannot be obtained in equilibrium, the degree of assortativeness is nevertheless greater than in standard models.
