Max-convex decompositions for cooperative TU games
We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with nonnegative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition.
|Date of creation:||2004|
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- Einy, Ezra, 1988. "The shapley value on some lattices of monotonic games," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 1-10, February.
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