A sequential approach to the characteristic function and the core in games with externalities

This paper proposes a formulation of coalitional payoff possibilities in games with externalities, based on the assumption that forming coalitions can exploit a "first mover advantage". We derive a characteristic function and show that when outside players play their best response noncooperatively, the core is always nonempty when the game has strategic complementarities. We apply this result to cartel formation in Bertrand oligopoly and in Shapley-Shubik (1977) strategic market games.