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 unique and satisfies all the axioms of a $\Theta$-symmetric axiomatic value operator. It is shown that for the uncountably large invariant probability measurable group $\left(\breve\Theta,\breve{\cal B},\breve\Gamma\right)$ of Lebesgue measure preserving automorphisms constructed in Raut [1996], $\breve\Theta$-symmetric random order value exists for most games in BV and it coincides with the fully symmetric Aumann-Shapley axiomatic value on pNA. Thus by restricting the set of admissible orders suitably the paper provides a possibility result to the Aumann-Shapley Impossibility Principle for the random order approach to values of non-atomic games.
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Length: 33 pages Date of creation: 19 Mar 1996 Date of revision: Handle: RePEc:wpa:wuwpga:9603001
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