Population monotonic allocation schemes on externality games

This paper introduces a new class of cooperative games called externality games. In these games each player contributes with their specific endowment and also with their presence to the total worth of the coalition he or she belongs to. We prove that for these games there exists a unique efficient, anonymous and population monotonic rule: the proportional rule. A subclass of externality games is also analyzed. Games in this subclass are not necessarily convex although we show that the Shapley value is in the core of these games, but it is not a population monotonic rule.