Coalitional desirability and the equal division value
- 59 Downloads
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.
KeywordsDesirability Coalitional desirability Average coalitional desirability Uniform coalitional desirability Equal division value Shapley value
- Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.Google Scholar
- Lapidot, E. (1968). Weighted majority games and symmetry group of games. MSc Thesis in hebrew, Technion, Haifa.Google Scholar
- Levínský, R., & Silársky, P. (2004). Global monotonicity of values of cooperative games: An argument supporting the explanatory power of Shapley’s approach. Homo Oeconomicus, 20, 473–492.Google Scholar
- Shapley, L. S. (1953). A value for \(n\)-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contribution to the theory of games vol. II. Annals of mathematics studies 28. Princeton: Princeton University Press.Google Scholar