Limited farsightedness in priority-based matching

Abstract

We introduce the horizon- vNM stable set to study one-to-one priority-based matching problems with limited farsightedness. We show that, once agents are sufficiently farsighted, the matching obtained from the Top Trading Cycles (TTC) algorithm becomes stable: a singleton set consisting of the TTC matching is a horizon- vNM stable set if the degree of farsightedness is greater than three times the number of agents in the largest cycle of the TTC. Our main results do not hold per se for many-to-one priority-based matching problems: more coordination and cooperation on behalf of the agents are required. In the presence of couples, farsightedness may improve both efficiency and stability. When each agent owns an object, a singleton set consisting of the TTC matching is the unique horizon- vNM stable set.