Let’s return to the chapter’s discussion of Jack and Jill’s water duopoly. Suppose that Jack and Jill are at the duopoly’s Nash equilibrium (80 gallons) when a third person, John, discovers a water source and joins the market as a third producer.
a. Jack and Jill propose that the three of them continue to produce a total of 80 gallons, splitting the market three ways. If John agrees to this, how much profit will he make?
b. After agreeing to the proposed deal, John is considering increasing his production by 10 gallons. If he does, and Jack and Jill stick to the agreement, how much profit will John make? What does this tell you about the proposed agreement?
c. What is the Nash equilibrium for this market with three producers? How does it compare to the Nash equilibrium with two producers?