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A Note on Purification Theorem

The purification Theorem of Harsanyi (1973) argues that one can understand the mixed strategy Nash equilibrium of a simultaneous move complete information game as the limit of a particular Bayesian Nash equilibrium of the incomplete information version of the same game where the players choose pure strategies and the incompleteness of information almost vanishes. This paper analyzes an incomplete information coordination game and the purification of the pure strategy Bayesian Nash equilibrium (as stipulated by Harsanyi (1973)). Through comparative static analysis, the paper shows that besides inheriting the problematic feature of the mixed strategy equilibrium of the complete information game, the incomplete information game also has new problematic feature of its own.