Stability in Matching Markets with Peer Effects

Abstract The paper investigates conditions which guarantee the existence of a stable outcome in a school matching in the presence of peer effects. We consider an economy where students are characterized by their type and schools are characterized by their quality and capacity. We divide students and schools into groups, so that going to a school outside of one's group is associated with additional costs or prohibited. A student receives utility from a school per se and from one's classmates. We find that sufficient condition for a stable matching to exist is that a directed graph, which governs the possibility to go from one group to another, should not have (undirected) cycles. We construct a polynomial time algorithm, which produces a stable matching. Furthermore, we show that if the graph has a cycle, then there exist other economy parameters (types, costs and so on), so that no stable matching exists.