The Shapley value on convex geometries

The Shapley value on convex geometries

A game on a convex geometry is a real-valued function de0ned on the family L of the closed sets of a closure operator which satis0es the 0nite Minkowski–Krein–Milman property. If L is the boolean algebra 2 then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axiom...

The Shapley value in totally convex multichoice games

-In this paper, we introduce a class of totally convex multichoice cooperative games a.nd prove that the Shapley value of such games is always in the core. @ 2000 Elsevier Science I~td. All rights reserved. K e y w o r d s M u l t i c h o i c e game, Shapley value, Total convexity, Core, Coalition. 1. I N T R O D U C T I O N Hsiao and R a g h a v a n [1] i n t roduced a class of mul t ichoice c...

A Minimal Test for Convex Games and the Shapley Value

A set of necessary and sufficient conditions for convexity of a transferable utility game in terms of its decomposition into unanimity games is shown to be minimal: none of the conditions is redundant. The result is used to provide an axiomatization of the Shapley value on the set of convex games.

The Shapley group value

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic charact...

64 The Shapley Value