2. A startup, VR1 has some interesting intellectual property , but has hit a manufacturing constraint that means it sonly option is to sell the IP. After much search, VR1 has found that the only player in the market with any interest in the IP is Facebook . If VR1 can sell the IP to Facebook, it will be worth $20 million to Facebook; if Facebook does not buy it, the IP gets shelved permanently. Negotiation over the price of the IP proceeds as follows:Facebook gets to make an initial offer to VR1. If VR1 does not accept the offer price, it gets to make a counteroffer. Finally, Facebook can respond by either accepting VR1's offer or making a final offer. If VR1does not accept Facebook' final offer both of them get nothing. VR1and Facebookdiscount the future at 10% (i.e. a payment in the second round is worth 10% less than the same dollar offer made and accepted in the first round, and the same for the third and second rounds).Calculate the Nash equilibrium of this bargaining problem.

3. Consider a duopoly where total industry demand is given by q = 100 - 5p and both firms have unit production costs of $10.

(a) Derive the Cournot (quantity) reaction functions for both firms. Plot them. What is the Nash equilibrium? How much profit does each firm make?

(b) How much is produced when the two firms collude to maximize profits? Assume they split the quantity produced and the profits so derived evenly. What is each firm's profit? How much are consumers hurt by collusion?

(c) Now assume that firm A has unit production costs of $10, while firm B has unit production costs of $5. Compare the reaction functions and the Nash equilibrium in this case with the one you derived in part (a).