Solidarity induced by group contributions: the MI$$^k$$-value  for transferable utility games

Abstract

The most popular values in cooperative games with transferable utilities are perhaps the Shapley and the Shapley like values which are based on the notion of players' marginal productivity. The equal division rule on the other hand, is based on egalitarianism where resource is equally divided among players, no matter how productive they are. However none of these values explicitly discuss players' multilateral interactions with peers in deciding to form coalitions and generate worths. In this paper we study the effect of multilateral interactions of a player that accounts for her contributions with her peers not only at an individual level but also on a group level. Based on this idea, we propose a value called the MI k -value and characterize it by the axioms of linearity, anonymity, efficiency and a new axiom: the axiom of MN k -player. An MN kplayer is one whose average marginal contribution due to her multilateral interactions upto level k is zero and can be seen as a generalization of the standard null player axiom of the Shapley value. We have shown that the MI k -value on a variable player set is asymptotically close to the equal division rule. Thus our value realizes solidarity among players by incorporating both their individual and group contributions.

A new value for cooperative games based on coalition size

“…In Abe and Nakada (2019) the ED is generalized to obtain a weighted division and the corresponding axiomatization is obtained. For a comprehensive study of all these values, we refer to Béal et al (2017), Borkotokey et al (2020a, 2020b), Casajus (2011, 2012), Choudhury et al (2020), Kakoty et al (2021), and Nowak and Radzik (1994).…”