A Reformulation of the Aumann-Shapley Random Order Values of Non-Atomic Games Using Invariant Measures

Abstract

In this paper the Aumann-Shapley random order approach to values of non-atomic games is reformulated by restricting the set of random orders and the symmetry group to any subgroup of automorphisms that admits an invariant probability measurable group structure. It is shown that with respect to the uncountably large invariant probability measurable group of Lebesgue measure preserving automorphisms that is constructed in Raut [1997], the random order value exists for most games in BV, and it coincides with the fully symmetric Aumann-Shapley axiomatic value on pNA(\mu). Thus by restricting the set of admissible orders suitably, the paper provides a possibility result to the Aumann-Shapley Impossibility Principle.