The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games

Original Article

Abstract

In 1951, Dvoretzky, Wald and Wolfowitz (henceforth DWW) showed that corresponding to any mixed strategy into a finite action space, there exists a pure-strategy with an identical integral with respect to a finite set of atomless measures. DWW used their theorem for purification: the elimination of randomness in statistical decision procedures and in zero-sum two-person games. In this short essay, we apply a consequence of their theorem to a finite-action setting of finite games with incomplete and private information, as well as to that of large games. In addition to simplified proofs and conceptual clarifications, the unification of results offered here re-emphasizes the close connection between statistical decision theory and the theory of games.

Keywords

DWW theorem Atomless Mixed and pure strategies equilibria Randomization Purification 

JEL Classification Numbers

C07 DO5 

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Copyright information

© Springer Verlag 2005

Authors and Affiliations

  1. 1.Department of EconomicsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Department of Economics and EconometricsUniversity of Notre DameNotre DameUSA
  3. 3.Department of MathematicsNational University of SingaporeSingaporeSingapore
  4. 4.Department of EconomicsNational University of SingaporeSingaporeSingapore

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