Problem Set #5, Answers
(1) Two competing firms are each planning to introduce a new product. Each will decide
whether to produce Product A, Product B or Product C. They will make their choices at
the same time. The resulting payoffs are shown below.
Firm 1: A
(a) Are there any Nash equilibria in pure strategies? If so, what are they?
There are two Nash equilibria: option A&C(10,20) and C&A(20,10)
(b) If both firms are pessimistic, what outcome will result?
Firm 1 will chose A, Firm 2 will also chose A. Thus they will end up at (-10, -10)
(c) If Firm 1 is pessimistic and Firm 2 knows that, what will Firm 2 do?
Firm 1 will chose A, Firm 2 will chose C. They will end up at (10,20)
(d) If both firms are optimistic, what outcome will result?
The Maximax outcome is: Firm 1
action C, Firm 2
action C. They will end up at the
worst point (-30,-30)
(2) Cournot Competition
Lambert-Rogers Co. is a manufacturer of petrochemical products. The firm’s research
efforts have resulted in the development of a new auto fuel injection cleaner that is
considerably more effective than other products on the market. Another firm, GH Squires
Co., independently developed a very similar product that is as effective as the Lambert-
Rogers formula. To avoid a lengthy court battle over conflicting patent claims, the two
firms have decided to cross-license each other’s patents and proceed with production. It is
unlikely that other petrochemical companies will be able to duplicate the product, making
the market a duopoly for the foreseeable future. Lambert-Rogers estimates the demand