Find the optimal strategies, P and Q, for the row and column players, respectively. Also compute the expected payoff E of the matrix game and determine which player it favors, if any, if the row and column players use their optimal strategies.
A) ; favors column player
B) ; favors column player
C) ; favors column player
D) ; favors column player
E) ; favors column player

Question

Find the optimal strategies, P and Q, for the row and column players, respectively. Also compute the expected payoff E of the matrix game and determine which player it favors, if any, if the row and column players use their optimal strategies. ​  ​
A) ; favors column player 
B) ; favors column player 
C) ; favors column player 
D) ; favors column player 
E) ; favors column player

Quizplus · Accepted Answer

To find the optimal strategies, we need to use the concept of the minimax theorem. The minimum of the maximum values for each column is found to be 3/4, which corresponds to column 2. Therefore, the optimal strategy for the row player is to choose the action corresponding to row 2 with probability 1. Column player plays the optimal strategy of choosing the action corresponding to column 3 with probability 1, since this gives the maximum possible payoff of 3/4. The expected payoff for this strategy profile is 3/4, which favors the column player. Therefore, the answer is D.

Find the Optimal Strategies, P and Q, for the Row