Relation between the Shapley value and null group cohomology

Abstract

The purpose of this paper is to give an application of homological methods to game theory. The main theorems give conditions of a homological nature for the existence and uniqueness of the Shapley value for games with continuum players.

Relation between the Shapley value and null group cohomology

“…The Shapley value for n-person games was introduced in [ 3 ] . In [/] Aumann and Shapley have given the following definition of the Shapley value for games of continuum players; Let I = [0, l ] be the set of players, let BV denote the space of all bounded variation set functions defined on Borel sets 8 of I , and l e t FA denote the set of a l l bounded finitely additive set functions on ( I , 8) .…”