TITLE:
Egalitarian Allocations and the Inverse Problem for the Shapley Value
AUTHORS:
Irinel Dragan
KEYWORDS:
Cooperative Games, Shapley Value, Egalitarian Allocation, Coalitional Rationality, Inverse Problem
JOURNAL NAME:
American Journal of Operations Research,
Vol.8 No.6,
November
2,
2018
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 the Shapley
Value is also a coalitional rational value. The Egalitarian Allocation of the
game is efficient, so that in the set called the Inverse Set relative to the Shapley
Value, the allocation is the same as the initial one, but may not be coalitional
rational. In this paper, we shall find out in the same family of the Inverse
Set, a subfamily of games with the Egalitarian Allocation is also a coalitional
rational value. We show some relationship between the two sets of
games, where our values are coalitional rational. Finally, we shall discuss the
possibility that our procedure may be used for solving a very similar problem
for other efficient values. Numerical examples show the procedure to get solutions
for the efficient values.