Consider a small, growing community, Blueville, large enough to support a single cement maker but will never be large enough to support two firms. A cement plant requires sunk costs of $$10$ million; net lifetime profits equal net discounted future profits minus the $$10$ million entry cost. Big $D$ Cement and Giant E Cement are the only two potential entrants in Blueville. If either firm enters today and faces no competition in the future, the discounted present value of future monopoly profits would be $$16$ million, giving it net lifetime profits of $$6$ million. But if both firms enter today, the duopolists will generate postentry future profits of $$6$ million, incurring net lifetime losses of $$4$ million apiece. What is the Nash equilibrium$($a$)$ of this game?

Giant E stays out, Big D stays out

Giant E stays out, Big D enters

Giant $E$ enters, Big D enters

None

Giant E enters, Big D stays out