Hidden Coordination in Matching : The Role of Sequentiality

This paper explores sequential mechanisms for two-sided matching problems: The agents belonging to a side of the market (individuals or institutions) determine an eligibility restriction; and the agents on the other side (institutions or individuals, resp.) select their preferred mates, constrained by the above eligibility.We find out some asymmetries, as well as some coincidences, related to the cases where the first decision is made either by the individuals or the institutions. In particular, for the two mechanisms, stable allocations are decentralized. This can be interpreted as if the sequentiality in which agents decide takes the place of the coordination among the whole society. An 'extra' (hidden) coordination among individuals is exercised only when these agents determine the eligibility restriction. A consequence of such an 'over-coordination' is that the unique allocation supported by any equilibrium is the optimal stable matching from the individuals' point of view. A dual result, implementing the institutions' optimal stable allocation, is not obtained when eligibility is imposed by institutions