# The Core of Aggregative Cooperative Games with Externalities

Giorgos Stamatopoulos ()

The B.E. Journal of Theoretical Economics, 2016, vol. 16, issue 1, 389-410

Abstract: This paper analyzes cooperative games with externalities generated by aggregative normal form games. We construct the characteristic function of a coalition S for various coalition formation rules and we examine the corresponding cores. We first show that the γ$$\gamma$$-core is non-empty provided each player’s payoff decreases in the sum of all players’ strategies. We generalize this result by showing that if S believes that the outside players form at least l(s)=n−s−(s−1)$$l(s) = n - s - (s - 1)$$ coalitions, then S has no incentive to deviate from the grand coalition and the corresponding core is non-empty (where n is the number of players in the game and s the number of members of S). We finally consider the class of linear aggregative games (Martimort and Stole 2010). In this case, if S believes that the outsiders form at least lˆ(s)=ns−1$$\widehat l(s) = {n \over s} - 1$$ coalitions [where lˆ(s)≤l(s)$$\widehat l(s) \le l(s)$$] a core non-emptiness result holds again.

Date: 2016
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