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The dynamical aspect of the solution of classical cooperative games. (English. Russian original) Zbl 0814.90139

Russ. Acad. Sci., Dokl., Math. 47, No. 3, 629-632 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 6, 707-709 (1993).
Summary: In the classical theory of cooperative games the solution of an imputation problem is usually interpreted as a single-action mechanism. Below, however, this solution is treated as the result of the multistep process of achieving a final compromise in accordance with some selected optimality principle. Precisely here resides the dynamical aspect of the solution of classical cooperative games. We lay out an approach to the construction of a dynamical cooperative theory based on the one hand on the possibility of identifying an imputation in a classical cooperative game with some additive game, and on the other hand on the possibility of interpreting an operator \(\mathcal A\) in the space of classical cooperative games under an optimality principle. In this connection, the process of restriction the region of compromises (the sets of imputations) in a game \(v^{(0)}\) is modeled by the sequence of games \(v(k)= {\mathcal A}\cdot v^{(k-1)}\), \(k\in \mathbb{N}\), which under the given conditions converges to an additive game providing an imputation for the original game \(v^{(0)}\).

MSC:

91A12 Cooperative games
91A06 \(n\)-person games, \(n>2\)
91A35 Decision theory for games
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