Coalitional desirability and the equal division value

Sylvain Béal (1) , Éric Rémila (2) , Philippe Solal (2)

1 CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190)
2 GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne

We introduce three natural collective variants of the well-known axiom of desirability (Maschler and Peleg in Pac J Math 18:289-328, 1966), which require that if the (per capita) contributions of a first coalition are at least as large as the (per capita) contributions of a second coalition, then the (average) payoff in the first coalition should be as large as the (average) payoff in the second coalition. These axioms are called coalitional desirability and average coalitional desirability. The third variant, called uniform coalitional desirability, applies only to coalitions with the same size. We show that coalitional desirability is very strong: no value satisfies simultaneously this axiom and efficiency. To the contrary, the combination of either average coalitional desirability or uniform coalitional desirability with efficiency and additivity characterizes the equal division value.

Mots clés: Desirability; Coalitional desirability; Average coalitional desirability; Uniform coalitional desirability; Equal division value; Shapley value

Domaines: Economies et finances

Sylvain Béal, Éric Rémila, Philippe Solal. Coalitional desirability and the equal division value. Theory and Decision, 2019, 86 (1), pp.95-106. ⟨10.1007/s11238-018-9672-x⟩. ⟨halshs-01951010⟩