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Minimarg and maximarg operators

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Abstract

Two operators on the set ofn-person cooperative games are introduced, the minimarg operator and the maximarg operator. These operators can be seen as dual to each other. Some nice properties of these operators are given, and classes of games for which these operators yield convex (respectively, concave) games are considered. It is shown that, if these operators are applied iteratively on a game, in the limit one will yield a convex game and the other a concave game, and these two games will be dual to each other. Furthermore, it is proved that the convex games are precisely the fixed points of the minimarg operator and that the concave games are precisely the fixed points of the maximarg operator.

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Communicated by P. L. Yu

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Curiel, I., Tijs, S. Minimarg and maximarg operators. J Optim Theory Appl 71, 277–287 (1991). https://doi.org/10.1007/BF00939921

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Key Words

  • Convex games
  • marginal contributions
  • duality
  • symmetric games