Question

Consider the following simultaneous-move, one-shot game facing two firms (Firm A and Firm B), with the payoffs given in Table I. Assume the firms are not able to coordinate or communicate. Firm A and B each has three strategic options.

Table I

		Firm B
Firm A	Strategy	Low	average	high
	Small	100, 125	300, 200	200, 190
	Medium	250, 0	470, 340	480, 300
	Large	300, -100	450, 450	475, 360

(a). For each of the firms, identify the dominant strategy, if it exists. What outcome will be achieved if each firm plays their best strategy?

(b). If the two firms could coordinate, would this be mutually beneficial? If so what would be the outcome? Explain

(c). Would you advise Firm A to play its secure option strategy? Explain? [2 marks]

Answer 1

	L	A	H
S	100, 125	300, 200	200, 190
M	250, 0	470, 340	480, 300
L	300, -100	450, 450	475, 360

a. Each firms' best response has been underlined in the matrix above. Assume Firm A = Player 1 and Firm B = Player 2

When player 2 plays L, player 1's best response is to play L and receive the highest payoff 300 out of 100, 250 and 300.

But when player 2 plays A, player 1's best response is to play M and receive the highest payoff 470 out of 300, 470 and 450. Similarly, when player 2 plays H, player 1's best response is to play M.

Hence player 1 has no dominant strategy which it can play regardless of what the other player does.

But for player 2, A is the dominant strategy. When player 1 plays S, player 2's best response is to play A and receive the highest possible payoff 200 out of 200, 190 and 125. Similarly, when player 1 plays M, player 2's best response is to play A and player 1 plays L, player 2's best response is to play A. Hence, regardless of what the other player does, player 2 plays A.

Outcome achieved if each play their best responses is (M,A), from the matrix. Player 1 gets 470 and player 2 gets 340.

(b) If they could coordinate, they can move to an outcome that gives them both better payoffs i.e. (L,H). Player 1 gets 475>470 and player 2 gets 360>340.

c. If you decide to coordinate to (L,C) and instead of doing that, if player 1 chooses to play M: If player 2 cooperates and plays H, you reach the outcome (M,H) which fetches you an even higher payoff and if he also cheats, then you get the Nash equilibrium payoff. But if you cooperate and player 2 deviates, you get 450 which is less than your NE payoff. Therefore, you should play your secure Nash Equilibrium option as you will get 470 or more.