Banzhaf Permission Values for Games with Permission Structure

Abstract

**Please note that the full text is embargoed** ABSTRACT: A game with a permission structure describes a situation in which cooperation possibilities in a cooperative game with transferable utility are limited because there are players that need permission from other players before they are allowed to cooperate. In the conjunctive approach it is assumed that every player needs permission from all its direct superiors. In the disjunctive approach it is assumed that each player only needs permission from at least one of its direct superiors. Both approaches yield different modified games which take account of the limited cooperation possibilities. Applying the Banzhaf value to these modified games yields allocation rules that distribute the payoffs in games with a permission structure over the individual players. In this paper we provide axiomatic characterizations of these Banzhaf permission values.