A reformulation of Aumann-Shapley random order values of non- atomic games using invariant measures

Lakshmi Raut ()

Game Theory and Information from University Library of Munich, Germany

Abstract: 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.

Keywords: Non-atomic games; invariant measure; Shaply value; Random orders (search for similar items in EconPapers)
JEL-codes: C00 C71 (search for similar items in EconPapers)
Pages: 33 pages
Date: 1996-03-19
Note: Type of Document - Postscript; prepared on IBM PC - PC-TEX; to print on PostScript; pages: 33 ; figures: included. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.
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