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Consider the following simultaneous game between two players. Player 1 and Player 2.
Player 2
Player 1
X Y
K (9,2) (1,0)
L (1,0) (6,1)
M (3,3) (4,2)
Answer the following question:
Show that M is a dominated strategy for Player 1, by considering the expected payoff to
Player 1 from the mixed strategy for Player 1, σ1 = (⅙, ⅓, ½).
Hint: The mixed strategy σ1 = (⅙, ⅓, ½) means that Player 1 plays K with probability ⅙, L
with probability ⅓ and M with probability ½. Note that ⅙ + ⅓ + ½ = 1, i.e., the probabilities
over all of Player 1’s actions add up to 1.
