A friendly computable characteristic function

• We highlight the properties of the easy-to-compute δδ characteristic function (CF).
• For games with negative externalities, the δδ CF is superadditive.
• The δδ CF has a nonempty core.
• The δδ-core is a subset of the γγ-core.

We consider an nn-player game in coalitional form. We use the so-called δδ characteristic function to determine the strength of all possible coalitions. The value of a coalition is obtained under the behavioral assumption that left-out players do not react strategically to the formation of that coalition, but stick to their Nash equilibrium actions in the nn-player noncooperative game. This assumption has huge computational merit, especially in games where each player is described by a large-scale mathematical program. For the class of games with multilateral externalities discussed in Chander and Tulkens, we show that the δδ characteristic function is superadditive and has a nonempty core, and that the δδ-core is a subset of the γγ-core.