Competitive search with two-sided risk aversion

Search theory is widely used in economics to study markets where trading frictions are prevalent. However, all existing theoretical models assume that either buyers or sellers (or both) are risk neutral, and the case where both parties are risk averse remains unexplored. This paper is a first step to fill this gap. I analyze a static competitive search model where risk-averse agents with different wealth seek to exchange an indivisible good. The housing market is an important application since a home typically represents a large part of a person's wealth. I prove that a competitive search equilibrium is constrained efficient, and derive a generalized Hosios condition that relates the gains of the two parties in each transaction. Under risk aversion, wealthier buyers are more concerned with increasing their trading probability than with getting the best price. The opposite is true for sellers when the coefficient of absolute risk aversion is non-increasing. This results in positive sorting in equilibrium, that is, wealthier (poorer) buyers and sellers trading with each other at higher (lower) prices. This sorting mechanism offers a novel explanation for why the separation between rich and poor neighborhoods can be persistent.