4) Two rms are engaged in Cournot competition: each simultaneously produces a quan- tity Qt and then the price is determined based on the total quantity Q from demand by P(Q) = 18 Q. Each rm is identical, with marginal cost 0 = 6. Suppose that a third rm exists that does not compete in this market, but has developed technology that could make the production process for this market more efcient. If either competing rm were to adopt this technology, its marginal cost would be reduced to zero. For simplicity, assume that the third rm can provide the technology at no cost to itself. a) Suppose that the third rm can only sell its technology to rm 1. What price will the third rm charge for the technology? What will the resulting payoffs for the rms be? b) Suppose that the third rm can sell its technology to both rms. It does so by giving sequential offers to each rm. First, it offers a price p1 to rm 1 for its technology, which then decides whether to purchase the technology. After the outcome of this transaction is revealed (either rm 1 purchases or does not), the third rm offers a price 292 to rm 2 for its technology, which then decides whether to purchase. After this outcome is revealed, the rms compete in the market. Find all subgame perfect Nash equilibria of this game. c) Given the structure of part (c), is the third rm better or worse off selling to both rms instead of just rm 1'? d) Consider the same structure as part (b), but suppose that regulations prohibit the third rm charging different prices to each rm. Thus, the third rm sets the price p, then offers this price to rm 1. The outcom eof the transaction is revealed, then this price is offered to rm 2. Find all subgame perfect Nash equilibria of this game