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On the symmetry relation between different characteristic functions for additively separable cooperative games

This study was partially done while E. Gromova was with St. Petersburg State University

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  • We analyze 4 characteristic functions $ V^\alpha $, $ V^\delta $, $ V^\zeta $, and $ V^\eta $, and give a necessary condition for these functions to satisfy the relation $ V^\alpha - V^\delta = V^\zeta - V^\eta $ for all coalitions $ S $. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.

    Mathematics Subject Classification: Primary: 91A12;Secondary: 91A06.


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    [5] E. GromovaE. Marova and D. Gromov, A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games, J. Dyn. Games, 7 (2020), 105-122.  doi: 10.3934/jdg.2020007.
    [6] E. Gromova and L. Petrosyan, On a approach to the construction of characteristic function for cooperative differential games, Autom. Remote Control, 78 (2017), 1680-1692.  doi: 10.1134/s0005117917090120.
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    [12] P. V. Reddy and G. Zaccour, A friendly computable characteristic function, Math. Social Sci., 82 (2016), 18-25.  doi: 10.1016/j.mathsocsci.2016.03.008.
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