Axiomatizations of Permission Values for Games with a Hierarchical Permission Structure using Split Neutrality

Abstract

Recently, cooperative game theory has been applied to various economic allocation problems in which players are not fully anonymous but belong to some relational structure. One of the most developed models in this respect are communications situations or (symmetric) network situations in which players can only cooperate if there are sufficient communication links in the communication network. Another class of applications considers situations in which the players are hierarchically ordered, i.e. they are part of a structure of asymmetric relations. Examples are auctions, airport games, sequencing situations, the water distribution problem and hierarchically structured firms. This paper is about games with permission structure being a general game theoretic model to study situations with asymmetric relations between the players. We provide new axiomatic characterizations of the Shapley permission values and the first characterizations of the Banzhaf permission values using split properties which say something about the payoffs of players if we split certain players in two.