Strategy-Proofness in the Stable Matching Problem with Couples

Stable matching problems (SMPs) arising in real-world markets often have extra complementarities in the participants' preferences. These complementarities break many of the theoretical properties of SMP and make it computationally hard to find a stable matching. A common complementarity is the introduction of couples in labor markets, which gives rise to the stable matching problem with couples (SMP-C). A major concern in markets is strategy-proofness since markets that are easily manipulated often unravel. In this paper we provide some key insights into the issue of strategyproofness in SMP-C. We provide theoretical results that relate the set of resident Pareto optimal stable matchings (RPopt) admitted by an SMP-C instance to the ability of the residents to manipulate. We show that a mechanism returning an RPopt matching is, in certain cases, strategyproof against residents attempting to manipulate by truncating their preference lists. We provide an algorithm for finding an RPopt matching when one exists. And finally, we study empirically the frequency of multiple stable and multiple RPopt matchings as the market sizes grows, and under different proportions of couples in the market. Our empirical results indicate that SMP-C becomes less susceptible to manipulation as both the size of the market grows and the fraction of couples in the market shrinks.