A friendly computable characteristic function

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. (C) 2016 Elsevier B.V. All rights reserved.