Question

Player 2

Left Right

Up (4,3)    (-1, -1)

Player 1 (bold)

Down (0,0) (3,4)

Refer to the payoff matrix above. How many Nash Equilibriums this game has?

A.1

B.2

C.0

D.3

Answer 1

Nash Equilibrium is a collection of strategies in which there is one strategy for each player in such a manner that for each player in a game there is no benefit to switch strategies.          

We have the following information

		Player 2
		Left	Right
Player 1	Up	(4, 3)	(-1, -1)
Down	(0, 0)	(3, 4)

From the above one can see that, there are no Nash Equilibriums in this game. For instance, Player 1 will choose Up only if Player 2 choses Left. In case, Player 2 choses Right, then it is profitable for Player 1 to choose Down. So, in this game there is no strategy that dominates every other strategy for the players.