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k-Balanced games and capacities

  • Miranda, Pedro
  • Grabisch, Michel

In this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of the game. Based on the concept of k-additivity, we define the so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 200 (2010)
Issue (Month): 2 (January)
Pages: 465-472

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Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:465-472
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