On the $$\gamma $$-core of asymmetric aggregative games

Abstract

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 best strategies (Hart and Kurz Econometrica 51:1047–1064, 1983; Chander and Tulkens Int J Game Theory 26:379–401, 1997). We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced and has a non-empty core (which is the $$\gamma $$-core). Our paper thus offers an existence result for a core notion which is frequently encountered in the theory and applications of cooperative games with externalities.