Question

	Player 2
		A	B	C
	A	3,5	4,2	1,1
Player 1	B	5,3	3,6	4,5
	C	6,2	8,1	7,0

In the matrix game above, what is the payoff that Player 2 receives in the nash equilibrium outcome?

Answer 1

Answer :

Here Player 1 is a row player and Player 2 is a column player.

From the game matrix we see that Player 1's strategy of playing C dominates over both A and B.

From Player 1's perspective : Payoff in A = 3 , 4 , 1 (Note : 6 > 3 , 8 > 4, 7 >1 when compared to strategy C)

Payoff in B = 5, 3 , 4 (Note : 6 > 5 , 8 >3 , 7 > 4 when compared to strategy C)

Payoff in C = 6, 8, 7

So from that we see that payoffs in C are higher than their corresponding payoffs in A and B both. Thus C is a dominant strategy and Player 1 will play C no matter what so we can delete A and B rows from the game.

The reduced game would look like:

	A	B	C
C	6,2	8,1	7,0

where Player 1 is the row player and Player 2 is the column player.

In this scenario it is best for Player 2 to play strategy A (since Player 1 always plays C).

For Player 2 : A has a payoff of 2 , B has 1 and C has 0. Thus A gives the highest payoff and Player 2 will play A.

Thus the nash equilibrium of this game is (Player 1, Player 2) = (6 , 2) : So in nash equilibrium Player 1 gets a payoff of 6 and Player 2 gets a payoff of 2

Answer : Player 2 receives a payoff of 2 in the nash equilibrium outcome.