Potentials and Solutions of Cooperative Games

Takaaki Abe () and Satoshi Nakada ()
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Takaaki Abe: : School of Political Science and Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan.
Satoshi Nakada: School of Management, Department of Business Economics, Tokyo University of Science, 1-11-2, Fujimi, Chiyoda-ku, Tokyo, 102-0071, Japan

No 2114, Working Papers from Waseda University, Faculty of Political Science and Economics

Abstract: This paper considers the solution concepts of cooperative games that admit a potential function. We say that a solution admits a potential function if the solution is given as the gradient vector of the potential function at the player set. Hart and Mas-Collel (1989) show that the Shapley value is the only solution that is efficient and admits the potential function for games with variable player sets. In this paper, first, we argue that if we remove efficiency, various solutions admit a potential function. Second, we characterize the class of the solutions that admit a potential function and provide their general functional form. Third, we define a potential function for games with a fixed player set and associate a potential function with the axioms that the Shapley value obeys. Finally, we discuss how the efficiency requirement induces the uniqueness of the Shapley value through a potential function.

Keywords: Cooperative games; Efficiency; Potential function; Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2021-07
New Economics Papers: this item is included in nep-gth, nep-isf and nep-ore
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