Q4. Consider the following two-player simultaneous-move game, called the rock- paper-scissors-lizard game. Player 1 is the row player; player 2 is the column player. R stands for rock, P for paper, 3 for scissors, and L for lizard. R beats S but loses against P and L; P beats R but loses against S and L; 5 beats P but loses against R and L; L beats R, P and S. The payoff for winning is l 33,-, with 3' = R, P, S, L, and the payoff for losing is 1; when both players choose the same strategy they each get 0. Assume that :1: R : mp : 11:3 : U and that 113' L 2 U (this implies that the payoff for winning with R, P, or S is equal to 1, and the payoff from winning wit L is equal to l :1: L). Moreover, assume that Player Row chooses R with probability 7', P with probability p, and S with probability .3 (similarly for Player Column). a) Write down the normal form representation of the game. b) Assume that 33;, : (J. Find all the Nash equilibria (pure and mixed strategies) of the game. Comment. (3) Next, assume that 33;, : 1. Find all the Nash equilibria (pure and mixed strategies) of the game. Comment. (1) Finally, assume that :1: L : 2. Find all the Nash equilibria (pure and mixed strategies) of the game. Comment