In this paper the random order approach to values of non-atomic games is reformulated by generating random orders from a fixed subgroup of automorphisms, $\Theta$ that admits an invariant probability measurable group structure. The resulting $\Theta$-symmetric random order value operator is...

Using techniques from the non-standard analysis, a non-standard analogue of the Aumann-Shapley random order value of non-atomic games is provided. The paper introduces the notion of effectively ergodic family of automorphism groups. It is shown that for a wide class of games, the non-standard...