Axiomatization and implementation of a class of solidarity values for TU-games

Coalitional desirability and the equal division value

“…This desirability relation among the players originates from Isbell (1958) and has been studied extensively in order to evaluate the influence of voters on the class of simple games (see also Courtin and Tchantcho, 2015;Molinero et al, 2015, among others). The axiom of Desirability is often invoked in the characterization of classes of values such as the two classes of equal sharing values (van den Brink and Funaki, 2009;van den Brink et al, 2016), the procedural values (Malawski, 2013), the egalitarian Shapley values (Casajus and Huettner, 2013), a class of solidarity values (Béal et al, 2017) or to delimit subclasses of the linear, efficient and symmetric values (Levínský and Silársky, 2004;Radzik and Driessen, 2013).…”

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

“…Several values are introduced in the literature through which solidarity among players is achieved. Examples include the Solidarity value (Nowak and Radzik, 1994), The Egalitarian Shapley value (Joosten, 1996), the Generalized Egalitarian Shapley value (Choudhury et al, 2020), the Solidarity value due to (Béal et al, 2017), the discounted Shapley value (Joosten, 1996) and their respective characterizations, (Casajus and Huettner, 2013;Béal et al, 2017;Kamijo and Kongo, 2012;Radzik, 2013;Casajus and Huettner, 2014;van den Brink, 2007;van den Brink et al, 2013;van den Brink and Funaki, 2015;Weber, 1988;Yokote and Funaki, 2017;Young, 1985) etc., just to name a few. We assume here that players form groups within coalitions to indulge in interactions which we call multilateral interactions.…”

“…The null player axiom of the Shapley value (Shapley, 1953) blocks all sorts of egalitarianism in the distribution of the wealth. Thus, combining the axioms of efficiency, symmetry and linearity 4 with a property that replaces the null player axiom has been accepted as essential for ensuring solidarity, take for example the Average null-player property for the Solidarity value, (Nowak and Radzik, 1994), the Null player in a productive environment for the Egalitarian Shapley value, (Casajus and Huettner, 2013), the null player in a null environment for positive game for the Solidarity value (Béal et al, 2017), the null player in a non-negative environment for the Generalized Egalitarian Shapley value (Choudhury et al, 2020), the Invariance from proportional and quasi proportional deletion for the Equal Division and Solidarity value (Kamijo and Kongo, 2012), the δ-reducing property for the discounted Shapley value (van den Brink and Funaki, 2015) etc., to name just a few.…”

The Egalitarian Efficient Extension of the Aumann–Drèze Value

“…Assume that every player has equal right on the surplus, then a null player should get the average of the surplus, which is exactly NEAS requires a null player to get. Moreover, NEAS belongs to the growing set of variants of the classical null player axiom (see [24][25][26] and the references therein).…”