# Purification and disambiguation of Ellsberg equilibria

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## Abstract

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.

## Keywords

Knightian uncertainty Ellsberg games Ambiguity aversion Purification Disambiguation## JEL Classification

C72 D81## Notes

### Acknowledgements

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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