We consider an $n$-player game in coalitional form. We use the so-called $\delta$ 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 $n$-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 $\delta$ characteristic function is superadditive and has a nonempty core, and that the $\delta$-core is a subset of the $\gamma$-core.