Purification and disambiguation of Ellsberg equilibria

  • Benoit DecerfEmail author
  • Frank Riedel
Research Article


Recently, the use of Knightian (uncertain) strategies in normal form games has received increasing attention. The use of uncertain acts in games leads to new (Ellsberg) equilibria. We provide a foundation of the new equilibrium concept in the spirit of Harsanyi by proving an extension of the Purification Theorem for \(2\times 2\) normal form games. Our result implies that Ellsberg equilibria are limits of equilibria in slightly perturbed games with private information. In such equilibria, players use pure or maxmin strategies only.


Knightian uncertainty Ellsberg games Ambiguity aversion Purification Disambiguation 

JEL Classification

C72 D81 



We are grateful to Claude d’Aspremont, Jan-Henrik Steg, Francois Maniquet, John Weymark, Igor Muraviev, Nikoleta Ŝćekić and Martin Van der Linden for the comments provided on previous versions of this document.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DEFIPPUniversity of NamurNamurBelgium
  2. 2.Center for Mathematical EconomicsBielefeld UniversityBielefeldGermany
  3. 3.Faculty of Economic and Financial SciencesUniversity of JohannesburgJohannesburgSouth Africa

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