Gametheory

Suppose a,b,CER and you are given symmetric game below. a, a b, c d, d c, b consider the modified utility amounts in games 2, 3, and 4, where x>0: a+x, a+x ax, ax bx, cx b+x, c+x d+x, d+x a, a* cm, b* b, c* d, d c+x, b+x cx, bx dx, dx For each of the solutions write down which of the games (2, 3, and 4) are guaranteed to have the same solutions as Game 1: a) Pareto optimal cells b) Nash equilibrium cells c) Mixed strategy Nash equilibrium probabilities d) Prove your answer in c) with respect to Game 2 (show your work on the back of this page)