Group for Research in Decision Analysis

# A friendly computable characteristic function

## Puduru Viswanadha Reddy and Georges Zaccour

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