The Structure of Equilibrium Payoffs in Superadditive Coalitional Games

We explore the determinants of the payoffs an individual player may obtain in the equilibria of superadditive n-player coalitional games with transferable payoff. We provide conditions necessary and sufficient for the lower bound on a player's equilibrium payoff to coincide with his reservation payoff, and show that if this lower bound is strictly larger than the reservation payoff, then there is an implied condition whose obvious interpretation is in terms of competing groups of players. We also provide a parallel set of results on the upper bound