Efficient and stable collective choices under crowding preferences

We consider a set of agents who have to choose one alternative among a finite set of social alternatives. A final allocation is a pair given by the selected alternative and the group of its users. Agents have crowding preferences over allocations: between any pair of allocations with the same alternative, they prefer the allocation with the largest number of users. We require that a decision be efficient and stable (which guarantees free participation in the group of users and free exit from it). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property. The social choice function implemented by the proposed mechanism is also anonymous and group stable.