An efficient solidarity value for interval cooperative games

Abstract

This paper proposes an efficient interval solidarity value that operates well for interval cooperative games. In addition to the axioms of symmetry, efficiency, and additivity, this value also satisfies two new axioms, namely, interval-egalitarian A-null player and interval differential marginality. The interval-egalitarian A-null player axiom equally divides the result of the difference between the grand coalition value and the sum of the solidarity value of players in the degenerate interval game among A-null players. The interval differential marginality axiom is an interval version of the Casajus differential marginality axiom. This property states that the difference in the interval solidarity value of two players is determined by the difference between their average marginal contributions in the degenerate interval game. Eventually, the efficiency results and applicability of the proposed approach are compared with those of the other methods.