Spoilers, blocking coalitions, and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions.