Locally stable marriage with strict preferences

Abstract

We study two-sided matching markets with locality of information and control. Each male (female) agent has an arbitrary strict preference list over all female (male) agents. In addition, each agent is a node in a fixed network. Agents learn about possible partners dynamically based on their current network neighborhood. We consider convergence of dynamics to locally stable matchings that are stable with respect to their imposed information structure in the network. While existence of such states is guaranteed, we show that reachability becomes NP-hard to decide. This holds even when the network exists only among one side. In contrast, if only one side has no network and agents remember a previous match every round, reachability is guaranteed and random dynamics converge with probability 1. We characterize this positive result in various ways. For instance, it holds for random memory and for memory with the most recent partner, but not for memory with the best partner. Also, it is crucial which partition of the agents has memory. Finally, we conclude with results on approximating maximum locally stable matchings. © 2013 Springer-Verlag.