Entry Deterrence 2:Consider the Cournot duopoly game with demandp=100(q1+q2)and variable costsci(qi)=0 fori {1,2}. The twist is that there is now a fixed cost of productionk >0 that is the same for both firms.

1. Assume first that both firms choose their quantities simultaneously. Model this as a normal-form game.
2. Write down the firm's best-response function fork=1000 and solve for a pure-strategy Nash equilibrium. Is it unique?
3. Now assume that firm 1 is a "Stackelberg leader" in the sense that it moves first and choosesq1. Then after observingq1firm 2 choosesq2. Also assume that if firm 2 cannot make strictly positive profits then it will not produce at all. Model this as an extensive-form game tree as best you can and find a subgame-perfect equilibrium of this game fork=25. Is it unique?
4. How does your answer in (c) change fork=225?