Stable sets of contracts in two-sided markets

TL;DR

This paper investigates the existence of stable contract systems in two-sided markets, demonstrating that stability is guaranteed under path-independent agent choices and introducing a dynamic process akin to Gale-Shapley for finding such stable sets.

Contribution

It establishes the existence of stable contract sets under path-independence, introduces a dynamic process for finding them, and links Plott functions with Lehmann hyper-orders.

Findings

Stable sets exist if agents' choices are path-independent.

A dynamic process converges to stable sets, generalizing Gale-Shapley.

A bijection between Lehmann hyper-orders and Plott functions is established.

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.