Simultaneous game between two players.

  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.