Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? Solve the problem and find an optimal strategy. Clearly indicate your steps.
a b c d e
A | (-2,9) (-1, 7) (7, 10) (9, 7) (0, 10)
B | (3, 7) (2, 6) (4, -10) (5, 5) (0, 8)
C | (4, 6) (-1, 6) (5, 10) (0, -4) (0, 10)
D | (4, -1) (3, 4) (7, 3) (4, 4) (0, -2)
E | (1, 11) (-2, 2) (1, 2) (0, -3) (0, 10)
F | (3, 9) (1, 1) (0, 8) (2, 0) (0, 10)
This was midterm question that I got wrong. I think the correct answer should be
D weakly dominates C
b weakly dominates d
D weakly dominates A, B, E, and F
b weakly dominates a, c, and e
answer = (3, 4) Can anyone clarify if I'm eliminating correctly?
The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.