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Egalitarian Allocations and the Inverse Problem for the Shapley Value

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Document pages: 9 pages

Abstract: In a cooperative transferable utilities game, the allocation of the win of thegrand coalition is an Egalitarian Allocation, if this win is divided into equalparts among all players. The Inverse Set relative to the Shapley Value of agame is a set of games in which the Shapley Value is the same as the initialone. In the Inverse Set, we determined a family of games for which the ShapleyValue is also a coalitional rational value. The Egalitarian Allocation of thegame is efficient, so that in the set called the Inverse Set relative to the ShapleyValue, the allocation is the same as the initial one, but may not be coalitionalrational. In this paper, we shall find out in the same family of the InverseSet, a subfamily of games with the Egalitarian Allocation is also a coalitionalrational value. We show some relationship between the two sets ofgames, where our values are coalitional rational. Finally, we shall discuss thepossibility that our procedure may be used for solving a very similar problemfor other efficient values. Numerical examples show the procedure to get solutionsfor the efficient values.

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