FSS-ECON Seminar: Multi-period Matching: Stability, and Non-cooperative Foundations

Speaker: Prof. Sambuddha GHOSH, Associate Professor, Department of Economics, Shanghai University of Finance & Economics

Date:22 May 2024 (Wed)

Time:14:00 – 15:15

Venue: E21B-G002

Language: English

Abstract: We study a multi-period version of the classic “marriage problem”. Specifically, two fixed and disjoint sets of agents live for T periods, and match in every period with exactly one partner from the other set or oneself. No monetary transfers are involved. Preferences over continuation matches may depend on past matches.
We first introduce two notions of stability for the above multi-period marriage problem — prudent stability, and instantaneous stability. Agents in both definitions compare the equilibrium to their worst-case scenario when they contemplate blocking. We then pursue the “Nash programme” for multi-period marriage problems by linking our notions of stability to equilibria of two non-cooperative matching games, each lasting for T periods. The first of these games has one-sided sequential proposals; any pure SPNE of this produces a prudently stable matching. This readily implies the existence of a prudently stable matching. The second game involves two-sided simultaneous proposals. A pure pairwise SPNE (i.e. no mutually profitable pairwise deviations exist) produces an instantaneously stable matching. Thus, both cooperative notions emerge in two natural non-cooperative games.