The Potential and Consistency Property for Multi-Choice Shapley Value

Abstract

In this article, we complete the proof that the extended Shapley value has w-consistent property proposed by Hsiao, Yeh and Mo [4]. Then we suggest an axiomatization which is the parallel of Hart and Mas-Colell's [1] axiomatization of the Shapley value by applying the w-consistency property.

The size of the maximum antichains in products of linear orders

“…We then substitute r with the summation bounds, we simplify and we take the limit, keeping only the coefficients of the highest power of m (i.e. m n−1 ) and we obtain (9). The second highest power of m is m n−2 and this completes the proof of ( 9).…”

“…Since multichoice cooperative games have been generalized to heterogeneous sets of actions [9] and the analysis of Electre tri-nb also involves antichains in a heterogeneous product set [1], we need results about s(m). Let us define m I = i∈I m i and…”

“…In [9], a generalization of multichoice cooperative games is presented by considering that the set of actions available to agent i is {1, . .…”