Owen coalitional value without additivity axiom

Abstract

Abstract. We show that the Owen value for TU games with coalition structure can be characterized without additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen's one by replacement of the additivity and null-player axioms via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well.

Another characterization of the Owen value without the additivity axiom

“…The Khmelnitskaya and Yanovskaya (2007) characterization replaces A and N by the axiom M below. Note that both characterizations work for fixed (N , P) .…”

A Coalitional Value for Multichoice Games with a Coalition Structure

“…As Young [25] pointed, strongly monotonicity can be replaced by independence condition, namely, a player's value depends only on the vector of his marginal contributions. Khmelnitskaya and Yanovskaya [18] …”

“…Different to Aumann and Drze [11], Owen [12] gave another model for games with a coalition structure, where the probability of cooperation among coalitions is considered, and provided the Owen value, which is an extension of the Shapley value. Later, many experts and scholars have studied deeply [13,14,15,16,17,18,19].…”

Cooperative Fuzzy Games with a Coalition Structure and Interval Payoffs

“…By extending the Shapley value for traditional games, Owen [15] proposed the Owen value for games with a coalition structure. The axiomatic systems of the Owen value are considered in [16][17][18][19]. Later, Owen [20] gave another payoff index for games with a coalition structure, which is called the Banzhaf-Owen value, and discussed its axiomatic system.…”