Duality and anti-duality in TU games applied to solutions,axioms, and axiomatizations |
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Institution: | 1. IMUS-Departamento de Geometría y Topología, Facultad de Matemáticas, Sevilla, Spain;2. Departamento de Estadística, Universidad Carlos III de Madrid, Spain;3. Instituto de Matemática Interdisciplinar (IMI), Departamento de Estadística e Investigación Operativa, Universidad Complutense de Madrid, Spain |
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Abstract: | In this paper, for each solution for TU games, we define its “dual” and “anti-dual”. Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta–Ray solution. |
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Keywords: | Duality Anti-duality Core Shapley value Dutta–Ray solution |
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