Consider a society with a finite number of individuals. A coalition structure is a partition of the set of individuals. Each individual has personal preferences over the set of all coalition structures. We study the strategy proof core and von Neumann and Morgenstern (vN&M) solutions. A roommate problem is a problem in which each coalition in each coalition structure contains at most two members. We show that as long as the core is single-valued, the core is coalitionally strategy proof. Moreover the core mechanism is completely characterized by three properties: strategy proofness, Pareto optimality and individual rationality, in the domain with single-valued core. The single-valued core defines the largest domain one may obtain such a mechanism. We show in an example that the single-valued core is manipulable if coalition structures allow more than two members. Nevertheless we show that the single-valued vN&M solution is coalitionally stratey proof and it is individually rational and Pareto optimal. In fact the vN&M solution is the only mechanism with the three properties in the domain with single-valued vN&M solution.
