Group for Research in Decision Analysis

G-2014-78

A friendly computable characteristic function

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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.

, 16 pages