Union-wise egalitarian solutions in cooperative games with a coalition structure

The egalitarian principle has been widely adopted in designing solution concepts for cooperative games. In light of egalitarianism, we introduce two egalitarian values satisfying union efficiency for cooperative games with a priori unions. The first is the union-wise egalitarian value that divides the worth of each union equally among its members. The second is the union-wise egalitarian surplus value that first assigns individual payoffs to each player and subsequently divides the remaining amount of the union containing the player equally among its members. We provide axiomatic characterizations of the egalitarian values by introducing the property of fairness for survivors within unions. Also, we propose the efficient extensions of the union efficient egalitarian values and give axiomatizations of these efficient values.