4. Tony and Larry are managers of baseball teams that currently playing a game. It's late in the ballgame and Tony's team is currently winning and in the field. Tony's strategies are to bring in a right-handed pitcher (RHP) or to bring in a left-handed pitcher (LHP). Larry's strategies are to bring in a right-handed pinch hitter (RPH) or to bring in a left-handed pinch hitter (LPH). The payoff matrix is in terms of winning (W) or losing (L) the game. (10 pts.)

a. Does either player have a dominant strategy? Explain your answer. (5 pts.)

b. Does the game have a Nash equilibrium? Explain your answer. (5 pts.)

\begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{} & \multicolumn{2}{|c|}{ Larry } \\ \cline { 3 - 4 } \multicolumn{2}{|c|}{} & LPH & RPH \\ \hline & LHP & W, L & \\ T & & & L, W \\ 0 & & & \\ n & & L, W & W, L \\ y & RHP & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{} & \multicolumn{2}{|c|}{ Larry } \\ \cline { 3 - 4 } \multicolumn{2}{|c|}{} & LPH & RPH \\ \hline & LHP & W, L & \\ T & & & L, W \\ 0 & & & \\ n & & L, W & W, L \\ y & RHP & & \\ \hline \end{tabular}