Riedel and Sass (2013) study complete information normal form

games in which ambiguity averse players use ambiguous randomization strategies, in addition to pure and mixed strategies. The solution concept they propose, the Ellsberg equilibrium, is a coarsening of the

classical Nash equilibrium. We provide a foundation of the new equilibrium concept in the spirit of Harsanyi. We prove an extension of the Purification Theorem for 2x2 normal form games. Our result implies that any Ellsberg equilibrium of such game is the limit case of a mixed strategy equilibrium in a disturbed version of the game for

which payoffs are ambiguously disturbed.