Question

nt Paragraph Styles 7. Boeing an Airbus are considering whether to build a new factory. What is the Nash equilibrium of this game? Air Bus Build (-10, -10)A (-5, 5)c Don't Build Boeing Build Don't build (10, 0)D a. A ь, с c. D d. B

Answer 1

Solution:

		Airbus
		Build	Don't build
Boeing	Build	(-10, -10)	(-5, -15)
	Don't build	(-5, 5)	(10, 0)

Finding the Nash equilibrium of the given game: (Note that with way of representation of Boeing and Airbus in the matrix form above, for any payoff combination (x, y), x refers to the payoff received by Boeing and y refers to the payoff received by Airbus)

If Boeing chooses to build a new factory, best response of Airbus would be to build a new factory as well, as that way Airbus receives a higher payoff (-10 > -15). If Airbus decides to build a new factory, however, Boeing's best response would be to not build a new factory (-5 > -10). So, this is not a Nash equilibrium.

If Boeing chooses not to build a new factory, best response of Airbus would be again to build a new factory, as now, that way Airbus receives a higher payoff (5 > 0). If Airbus decides to build a new factory, we have already seen above that Boeing's best response would be to not build a new factory (as -5 > -10, already mentioned). So, this is a Nash equilibrium.

Notice that both the companies have a dominant strategy. In such as case of two player game, when both (or even if at least one of them) have a dominant strategy, there exists a unique Nash equilibrium. In this case, Airbus has a dominant strategy of building a new factory while Boeing has a dominant strategy of not building a new factory (as no matter what the other company does, their respective best strategy remains unchanged due to a higher payoff).

Thus, Nash equilibrium strategy profile is for Airbus to build a new factory, and Boeing to not build a new factory, generating a payoff combination of (-5, 5). So, the correct option is (b) C. (-5, 5).