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4) (20 points) Let T = (N, S, u) be a finite strategic game. Denote by PNE (D) all pure Nash equilibria of T. a) Let T' = (N, S, u') be a finite strategy game that we obtain from I through a positive affine transformation of the utility functions, i.e., for every player i E N and every strategy profile s E S, let u'(s) = au;(s) + B for some a E R+ (strictly positive real numbers) and BE R (real numbers). Show that the set of pure Nash equilibria remains the same under this transformation, i.e., PNE(r) = PNE(I'). b) Give an example of a strategic game I = (N, S, u) showing that claim in (a) does not hold if we allow arbitrary affine transformations, i.e., when a, B E R