Coalitional desirability and the equal division value

Abstract

The views expressed are those of the authors and do not necessarily reflect those of CRESE.

Necessary versus equal players in axiomatic studies

“…We propose two similar axioms in which necessary coalitions replace equal coalitions: equal treatment of necessary coalitions and average equal treatment of necessary coalitions. We confirm two results in Béal et al (2019) by showing that there is no sharing rule satisfying equal treatment of necessary coalitions and efficiency while the Equal Division value is the unique sharing rule that satisfies efficiency, linearity and average equal treatment of necessary coalitions.…”

“…Another approach investigated by Béal et al (2019) and Hu (2019) is based on coalitional variants of equal treatment of equals 3 . Instead of equal players, these articles consider equal coalitions.…”

“…The answer of question 3 relies on two coalitional variant of equal treatment of necessary players that are similar to those studied in Béal et al (2019). In that article, equal coalitions are considered instead of equal players and two axioms are introduced: one requiring the same total payoff for two equal coalitions, one requiring the same average payoff within two equal coalitions.…”

Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism

“…Experimental evidence also backs egalitarian outcomes (Bolton and Ockenfels, 2000). It is worthy to note that usual characterizations of the egalitarian solution heavily rely on the properties of either additivity (Béal et al, 2016(Béal et al, , 2019Bergantiños and Vidal-Puga, 2004;Casajus and Huettner, 2014a;Hougaard and Moulin, 2018;van den Brink, 2007;van den Brink et al, 2015) or monotonicity (Bergantiños and Vidal-Puga, 2009;Huettner, 2013, 2014b), which are not required here.…”

On egalitarian values for cooperative games with a priori unions

“…For instance, van den Brink (2007) provides a comparison of the equal division value and the Shapley value, and Casajus and Hüttner (2014) compare those two solutions with the equal surplus division value (studied first in Driessen and Funaki 1991). In van den Brink and Funaki (2009), Park (2012), van den Brink et al (2016), Ferrières (2017) and Béal et al (2019) several axiomatic characterizations of the equal division and equal surplus division values are provided. Ju et al (2007) introduce and characterize the consensus value, a new solution that somewhat combines the Shapley value and the equal division rule.…”