In Bolger an efficient value was obtained for a class of games called games with n players and r alternatives. In these games, each of the n players must choose one and only one of the r alternatives. This value can be used to determine a player's ‘a priori’ value in such a game. In this paper, we show that the value has a consistency property similar to the ‘consistency’ for TU games in Hart–Mas-Colell and we present a set of axioms (including consistency) which characterizes this value. The games considered in this paper differ from the multi-choice games considered by Hsiao and Raghavan. They consider games in which the actions of the players are ordered in the sense that, if i > j, then action i carries more ‘weight’ than action j. These games also differ from partition function games in that the worth of a coalition depends not only on the partitioning of the players but also on the action chosen by each subset of the partition.
