Geodesic
Nonadditive integration and some solutions of cooperative games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 1, pp. 5-27.

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In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.
Keywords: nonadditive integration, polynomial cooperative game, Shapley functional, generalized Owen extension, support function of the core. 
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Valery A. Vasil'ev. Nonadditive integration and some solutions of cooperative games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 1, pp. 5-27. http://geodesic.mathdoc.fr/item/MGTA_2021_13_1_a0/

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