Tops responsiveness, Strategy-Proofness and Coalition Formation Problems

This paper introduces a property over agents’ preferences, called Tops Responsiveness condition. Such a property guarantees that the core in Hedonic Coalition Formation games is not empty. It is also shown that a mechanism exists that selects a stable allocation. It turns out that this mechanism, to be called tops covering, is strangely-proof even if the core is not a singleton. Furthermore, we also find out that the tops covering mechanism is the only strategy-proof mechanism that always selects stable allocations.