A solution concept for cooperative games, the extended core, is introduced. This concept is always nonempty yet coincides with the core whenever it is nonempty. Moreover, a non-cooperative framework can generate the extended core. Every transferable utility game is associated with a two-player zero-sum non-cooperative game. The min-max values of the associated zerosum games characterize when cooperative games have nonempty cores. If the core is empty, the min-max value determines how an exogenous regulator can impose costs on proper coalition formation so that there are no incentives to deviate from extended core imputations, which are necessarily feasible in the original game. In order to choose among the imputations belonging to the extended core, a proportional version of the nucleolus is proposed as a selection device.
