Stable sets of contracts in two-sided markets

Abstract: We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions. Our proof is based on application of Zorn lemma to a special poset of semi-stable pairs. Moreover, we construct a dynamic process on the poset (generalizing algorithm Gale and Shapley) steady states of which are stable sets. In Appendix we discuss Lehmann hyper-orders and establish a bijection between the set of Lehmann hyper-orders and the set of Plott functions.