Question

Solve the game below, assuming that both players A & B play simultaneously. What is the dominant strategy for A and for B. (payoffs shown are A, B).

   B

B1 B2

A A1 3, 3 7, 2

   A2 1, 7    6, 6

If the players could collude, would this alter the outcome? How so?

Answer 1

Payoff matrix:

		B
		B1	B2
A	A1	(3, 3)	(7, 2)
	A2	(1, 7)	(6, 6)

(a) Dominant strategy is the strategy chosen by one player irrespective of strategy chosen by the other player.

Player A will choose A1 for whichever strategy Player B chooses, since payoff are higher (3 > 1, 7 > 6). So Player 1's dominant strategy is A1.

Player B will choose B1 for whichever strategy Player A chooses, since payoff are higher (3 > 2, 7 > 6). So Player 2's dominant strategy is B1.

(b) Nash equilibrium is obtained as follows.

When Player A chooses A1, Player B's best strategy is B1 since payoff is higher (3 > 2).

When Player A chooses A2, Player B's best strategy is B1 since payoff is higher (7 > 6).

When Player B chooses B1, Player A's best strategy is A1 since payoff is higher (3 > 1).

When Player B chooses B2, Player A's best strategy is A1 since payoff is higher (7 > 6).

Therefore, Nash equilibrium is: (A1, B1) [see below].

(c) If players collude, they will seek to maximize individual payoff and joint payoff, so Player A will choose A2 and Player B will choose B2 [(6 + 6) = 12 > (3 + 3) = 6, and 6 > 3, 6 > 3].