Priority relations and cooperation with multiple activity levels

This paper analyzes cooperation situations between heterogeneous players. It considers two types of heterogeneity. First, the players are differentiated with respect to a priority structure. This structure captures asymmetries between players, which may reflect exogenous rights, different needs, merit, or hierarchical constraints. Second, each player may have different cooperation possibilities represented by a set of activity levels. To analyze these situations, we enrich the model of multi-choice games, which is a natural extension of transferable utility games, with a priority structure. A new value on the class of multi-choice games with a priority structure is introduced. To accommodate the different activity levels and the asymmetries between players, this value follows an allocation process based on a lexicographic procedure. New axioms for multi-choice games with a priority structure are introduced. These axioms endogenously determine the lexicographic procedure used to define the value. Two axiomatic characterizations of this value are provided.