On the γ-Core of Asymmetric Aggregative Games

This paper analyzes the core of cooperative games generated by asymmetric aggregative normal-form games, i.e., games where the payoff of each player depends on his strategy and the sum of the strategies of all players. We assume that each coalition calculates its worth presuming that the outside players stand alone and select individually optimal strategies (Chander & Tulkens 1997). We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced, i.e. it has a non-empty gamma-core. Our paper thus offers an existence result for a core notion that is considered quite often in the theory and applications of cooperative games with externalities.