Coalitional Stability in Matching Problems with Externalities and Random Preferences:

We study the existence of stable solutions to coalitions' deviations in matching models with externalities, including marriage markets, roommate problems and housing markets as particular cases. Assuming that preferences are randomly determined, we show that the probability of having a stable solution is positively affected by three factors: the prudence of coalitions in evaluating a deviation, the social connectedness of those who can react to it, and the incidence of externalities on preferences. At the same time, we show that this probability is negatively affected by the number of agreements that agents can implement to block a matching. In this context, assuming that agents have a limited ability to organize themselves into large coalitions, we show that the probability of having stable solutions converges to one as the population grows.