Consider a kicker (K) and a goalie (G) in a soccer game. Suppose that if K kicks to the right and G jumps to the right, the probability of a goal is 0.3. If K kicks to the right and G jumps to the left, the probability of a goal is 0.9. If K kicks to the left, the probability of a goal is 0.8 if G jumps to the right and 0.5 if G jumps to the left. The optimal strategies of K and G are
A. (L,L) and (R,R) only
B. There is no equilibrium in pure strategies, and the Nash equilibrium in mixed strategies is K plays L with probability 1/2 and R with probability 1/2, and G plays L with probability 4/5 and R with probability 1/5.
C. There is no equilibrium in pure strategies, and the Nash equilibrium in mixed strategies is K plays L with probability 2/3 and R with probability 1/3, and G plays L with probability 5/9 and R with probability 4/9.
D. (L,L) in pure strategies and there is no equilibrium in mixed strategies