Is this analysis correct? 

(3) For the following game, find all (including mixed) Nash Equilibrium. Player 2 Player 1 Player 1 Up Down Up Down We have 4 pure Nash Equilibrium A. (Up; Left) B. (Up; Right) C. (Down; Left} D. (Down; Right} Left -2,-2 -2,-2 Left Player 2 -2, -2 -2, -2 Right -2,-2 -2,-2 Right -2,-2 -2, -2 For mixed Nash equilibrium, the strategies would be the same. Introducing probabilities would not change the pay off and the strategies. For examples, if the probability of playing up for player 1 is P, the probability for playing down is (1-p). -2 (p) +-2 (1-P) -2p-2 +2p