2. (3 marks) Recall that the set of pure strategy Bayesian Nash equilibria of a Bayesian game are the set of pure strategy Nash equilibria of the associated ex-ante normal form game. Based on this information, consider the following claim: " Every Bayesian game has a pure strategy Bayesian Nash equilibrium." Is this claim true or false? If true, prove it; if false illustrate an example which has no pure strategy Bayesian Nash equilibrium. [Hint: Note that every normal form game is a special Bayesian game.]