Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose in alternative front a finite set and agents may or may not become users of the chosen alternative. All allocation is a pair given by the chosen alternative and the set Of its users. Agents have gregarious Preferences over allocations: given all allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent call be forced to be a User and no agent who wants to be it User call be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium Outcome is all efficient and stable allocation which also satisfies a maximal participation property.