Characterization of the Myerson value for cooperative games on union stable structures

Clinton Gassi (University of Evry Paris-Saclay) & Aurelien Mekuko Yonta (Department of Mathematics, University of Yaounde I)

 

This paper is dedicated to an axiomatic study of the Myerson value for cooperative

games in which the set of feasible coalitions is a union-stable system. This type of partial

cooperation structure generalizes well-known communication graph games and contains the

widely studied union-closed and voting structures. In this framework, we provide a simple

and intuitive characterization of the Myerson value using five appealing and independent

axioms. We show that the Myerson value is the only allocation rule on the set of union-stable

structures that satisfies component-efficiency, additivity, modularity, the extra-null player

property, and equal treatment of veto players. We also show that this characterization is

valid for the restricted class of union-closed structures.

Key words: TU-game, Union-stable structure, Harsanyi dividends, Harsanyi power

solution, Myerson value.