Restricted component additive games

Curiel, Potters, Prasad, Tijs and Veltman introduced component additive games which are cooperative TU games that arise by imposing an order on the player set. Further, they introduced the β-rule which allocates a core element to each component additive game. In this paper we consider the class of restricted component additive games that arise by restricting the attention to head–tail coalitions. The extreme points of the corresponding restricted core are characterized. Further, it is shown that the β-rule is the barycenter of the corresponding restricted core and that the β-rule coincides with the nucleolus of this restricted game.