Egalitarian Allocations and the Inverse Problem for the Shapley Value

Abstract

In a cooperative transferable utilities game, the allocation of the win of the grand coalition is an Egalitarian Allocation if this win is divided into equal parts among all players. The Inverse Set relative to the Shapley Value of a game is a set of games in which the Shapley Value is the same as the initial one. In the Inverse Set we determined a family of games for which this Shapley Value is a coalitional rational value. The Egalitarian Allocation of the game is efficient, so that in the Inverse Set relative to the Shapley Value, the allocation is the same as the initial one, but may not be coalitional rational.