5. Consider the following normal-form game where the row player can choose action A, B or C and the column player could choose action D, E, or F:

D E F A 40, 40 120, 10 60, 30 B 30, 60 110, 60 90, 90 C30, 110100, 10070, 120 where the pairs give the value of the outcome for the row player followed by the value for the column player.

(a) When eliminating dominant strategies, what strategies (if any) can be eliminated?

Explain what is eliminated, and what cannot be eliminated.

(b) Specify a Nash equilibrium for this game. (For a randomized strategy, give just the actions that are randomized; you do not need to give the probabilities). Explain why it is a Nash equilibrium.

(c) Is there more than one Nash equilibrium? If so, give another one. If not explain why there is no other one.

(d) If the agents could coordinate, could they get a better outcome than in a Nash equilibrium? Explain why or why not.