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Potentials and weighted values of nonatomic games. (English) Zbl 0887.90189
Summary: The “potential approach” to value theory for finite games was introduced by S. Hart and A. Mas-Colell [Econometrica 57, No. 3, 589–614 (1989; Zbl 0675.90103)]. Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley value [R. J. Aumann and L. S. Shapley, Values of non-atomic games. Princeton, N.J.: Princeton Univ. Press (1974; Zbl 0311.90084)]. As a corollary we obtain the uniqueness of the Aumann-Shapley value on certain subspaces of games. Next, the potential approach is applied to the weighted case, leading to “weighted non-atomic values.” It is further shown that the asymptotic weighted value is well-defined, and that it coincides with the weighted value generated by the potential.

91A13 Games with infinitely many players (MSC2010)
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