Priority relations and cooperation with multiple activity levels

Abstract

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.