Existence and Computation of Matching Equilibria

In this paper we give a constructive proof of existence of competitive equilibrium in two-sided matching markets. The same approach shows that the set of equilibrium prices is pathwise connected. We then extract from these results an algorithm for finding equilibria which can be further specified to compute the minimum price equilibrium that is optimal for all buyers individually. The two-sided matching markets we consider consist of indivisible objects on one side and buyers on the other. The indivisibles can be goods or bads, such as houses or tasks, and it is assumed that buyers are not interested in acquiring more than one object each. An allocation in such a market is given by a matching between the two sides and associated transfers of money. This model has been shown to have remarkable properties. Notably among these, all core allocations can be achieved by price taking behaviour [Quinzii (1984)], and core payoffs have lattice structure so that there is in particular an outcome best for the buyers/worst for the sellers and a polar opposite one best for the sellers/worst for the buyers [Demange and Gale (1985)]. In fact, buyers canot gain by falsifying their preferences for any procedure selecting the buyers-optimal outcome, a generalized Vickreyauction property raising hopes for mechanisms which could elicit truthful revelation [Demange and Gale (1985)]. The latter two properties hold also