The structure of individual payo®s in superadditive coalitional games

n-player coalitional games with transferable payo® o®er a promising framework for analyzing value appropriation under competition. But making progress necessitates understanding how the force of a player's value-producing alternatives a®ects the upper and lower bounds of his set of equilibrium (core) payo®s. Unfortunately, there are virtually no results of this kind. We explore the determinants of the equilibrium payo®s of an individual player in such a game and, among other things, provide conditions necessary and su±cient for the lower bound on a player's equilibrium payo® to coincide with his reservation payo®. We also provide a parallel set of results on the upper bound. ¤We thank Adam Brandenburger, Leslie Marx, Joe Ostroy, Ariel Rubinstein and Phil Reny for thoughtful input.