Sharing values for multi-choice games: an axiomatic approach

A Sharing value for transferable utility games distributes the Harsanyi dividend of each coalition among the players in the coalition's support. Such distribution is done according to a certain sharing system that determines the Sharing value. In this paper, we extend Sharing values to multi-choice games. Multi-choice games are a generalization of transferable utility games in which players have several activity levels. Unlike in transferable utility games, there is no straightforward way to interpret the support of a coalition in a multi-choice game. This makes it more tedious to distribute the Harsanyi dividend of a multi-choice coalition. We consider three possible interpretations of the support of a multi-choice coalition. Based on these interpretations, we derive three families of Sharing values for multi-choice games. To conduct this study, we discuss novel and classical axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these families of values.