CONICET | Buscador de Institutos y Recursos Humanos

We study the problem of convergence to stability in coalition formation games inwhich the strategies of each agent are coalitions in which she can participate and outcomesare coalition structures. Given a natural blocking dynamic, an absorbing setis a minimum set of coalition structures that once reached is never abandoned. Thecoexistence of trivial (singleton) and non-trivial absorbing sets is what causes lack ofconvergence to stability. To characterize games in which both types of set are present,we first relate circularity among coalitions in preferences (rings) with circularity amongcoalition structures (cycles) and show that there is a ring in preferences if and only ifthere is a cycle in coalition structures. Then we identify a special configuration of overlappingrings in preferences characterizing games that lack convergence to stability.Finally, we apply our findings to the study of games induced by sharing rules.