Two solutions on TU games with preference relations: The core and the globally stable solution

This paper proposes a novel model of TU games with preference relations to overcome the limitations of the dominance relation, where the preference relation of each coalition is employed to select a set of superior allocations from any payoff vector set. In this framework, the core and the globally stable solution on TU games with preference relations are defined as the intersections of all coalitions’ preferable sets and superior sets, respectively. We propose new properties to characterize the stability of the core and the globally stable solution for this class of games. The core of TU games with C-monotonic preferences, which overcomes the incompleteness of the dominance relation, is shown to be a subset of the core proposed by Gillies for TU games. Addressing the issue caused by the monotonicity of the dominance relation, a necessary and sufficient condition is shown for the non-emptiness and uniqueness of the globally stable solution on TU games with C-single peaked preferences. Moreover, our finding reveals the equivalence of the globally stable solution and the core for this specified game.