Open AccessNonadditive integration and some solutions of cooperative games
Author(s) -
В. А. Васильев,
В. А. Васильев
Publication year - 2021
Publication title -
matematičeskaâ teoriâ igr i eë priloženiâ
Language(s) - English
Resource type - Journals
ISSN - 2074-9872
DOI - 10.17076/mgta_2021_1_29
Subject(s) - multilinear map , shapley value , core (optical fiber) , extension (predicate logic) , cooperative game theory , representation (politics) , mathematical economics , regular polygon , set (abstract data type) , space (punctuation) , function (biology) , mathematics , game theory , computer science , pure mathematics , telecommunications , geometry , evolutionary biology , politics , law , political science , programming language , biology , operating system
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.