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. 
@article{MGTA_2021_13_1_a0,
     author = {Valery A. Vasil'ev},
     title = {Nonadditive integration and some solutions of cooperative games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {5--27},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2021_13_1_a0/}
}
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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/