Question

			B
		red		white
	red	X,Y		4,13
A
	white	12,8		6,Z

4. Consider Figure 1. Say that X = 14, Y = 14 and Z = 8. The game has ____ Nash equilibrium.

(a.) zero

(b.) one

(c.) two

(d.) three

Answer 1

4. Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.

If B chooses Red then best response of A is to choose Red because it gives higher payoff to A.

If A chooses Red then best response of B is to choose Red because it gives higher payoff to B.

Therefore, (Red; Red) is the Nash Equilibrium.

If B chooses White then best response of A is to choose White because it gives higher payoff to A.

If A chooses White then best response of B is to choose Red or White because both gives equal payoff to B.

So, this can't be nash equilibrium.

Answer is b) One.