On the characterizations of viable proposals

Abstract

Sengupta and Sengupta (Int Econ Rev 35:347–359, 1994) consider a payoff configuration of a TU game as a viable proposal if it challenges each legitimate contender. Lauwers (Int Econ Rev 43:1369–1371, 2002) prove that the set of viable proposals is nonempty for every game. In the present paper, we prove that the set of viable proposals coincides with the coalition structure core if there exists an undominated proposal; otherwise, it coincides with the set of accessible proposals. This characterization result implies that a proposal is a viable proposal if and only if it is undominated or accessible. Moreover, we prove that the set of viable proposals includes the minimal dominant set, which is another nonempty extension of the coalition structure core introduced by Koczy and Lauwers (Games Econ Behav 61:277–298, 2007). In particular, we prove that the set of viable proposals of a cohesive game coincides with the minimal dominant set.