Strategic Formation of Coalitions

Consider a society with a finite number of players. Each player has personal preferences over coalitions in which he joints. A social outcome is a coalition structure that is defined by a partition of the set of players. We study the strategy proof core and von Neumann and Morgenstern (vN&M) solutions. The roommate problem is a problem in which each coalition contains at most two members. We show that if the core is a singleton, then the core mechanism is coalitionally strategy proof. Since a singleton core defines the largest domain of preferences to admit a mechanism that is strategy proof, individually rational (IR) and Pareto optimal (PO), our result shows that this largest domain is achieved in the roommate problem. We show in an example that a singleton core is manipulable if coalitions contain more than two members (three, say). We show that if a vN&M solution is a singleton, then it is the unique vN&M solution and coincides with the core. Moreover the vN&M solution mechanism is coalitionally strategy proof in the domain with a singleton vN&M solution. In fact the vN&M solution is the only mechanism that is strategy proof, IR and PO in the domain.