1. Two theaters are located on the same street. They advertise and, by so doing, attract customers to the area so that each of the two theaters’ advertising is beneficial to both. Let x1 be the advertising intensity of theater 1 and x2 be the advertising intensity of theater 2. The profit functions for theaters 1 and 2 are respectively:
!
𝜋!=(30+𝑥")𝑥! −2𝑥"
"
𝜋"=(30+𝑥!)𝑥"−2𝑥"
i) What are the Nash equilibrium advertising levels of the two theaters?
ii) What are their equilibrium profits?
iii) Could the theaters increase total profits if they could commit to given advertising levels? What advertising levels would they choose? (Hint: what would a firm that owns both theaters choose? Note that the profit functions for the two theaters are the same, so 𝒙𝟏 = 𝒙𝟐)