Two identical ?rms, Firm 1 and Firm 2, are competing in the pork market and have to decide how much marketing to do for their products. The revenues of each ?rm depend on the number of ads the ?rm makes as well as on the number of ads that the other ?rm makes. In particular, if Firm 1 makes k1 ads and Firm 2 makes k2 ads, the ?rms' revenues are R1 = 240k1-10k1(k1 +k2) R2 = 240k2-10k2(k1 +k2) Firms can either outsource marketing to an marketing agency or create an marketing department inside the ?rm and produce ads in-house. If a ?rm outsources marketing, it pays a price of 120 (thousands of dollars) per ad. (That is, if Firm i chooses to outsource marketing, its costs are 120ki if it makes ki ads.) If a ?rm produces ads in-house, it must pay a ?xed cost of 300 to create the marketing department, but then the cost per ad is 60. (That is, if Firm i chooses to produce ads in-house, its costs are 300+60ki if it makes ki ads.)
The game: First, the ?rms play the outsourcing game,where they secretly and simultaneously choose whether to outsource marketing or produce marketing in-house. Second, the ?rms observe their outsourcing decisions and then they play the ads game, where they secretly and simultaneously decide how many ads to make (k1 for Firm 1, k2 for Firm 2). The number of ads that a ?rm chooses to make can be any number greater than or equal to zero. The payoff to each ?rm is equal to the revenues from marketing minus the total costs of marketing.
a) Suppose that in the outsourcing game, both ?rms chose to outsource marketing to the marketing agency. Solve for the Nash equilibrium of the ads game in this case. How many ads will each ?rm make? Compute the ?rms' payoffs.
b) Now solve for the credible Nash equilibrium of the whole game, where the ?rms ?rst play the outsourcing game and then, having observed their outsourcing decisions, they play the adsg ame. Draw the game matrix for the outsourcing game. Will the ?rms choose to outsource marketing? Is the resulting outcome socially ef?cient, or is there another outcome where both ?rms could obtain higher payoffs?
c) Concerned that the ?rms may choose to create marketing departments and not require its services, the marketing agency makes the following offer to Firm 2 (assume this offer can be legally enforced, so there is no credibility problem): "If you (Firm 2) choose to outsource marketing while Firm 1 creates an marketing department to produce ads in-house, I lower my price to 60 per ad. If Firm 1 chooses to outsource, then regardless of what you choose, I charge 120 per ad as before." Both ?rms are aware of this offer. Solve for the credible Nash equilibrium of the whole game where the ?rms ?rst play the outsourcing game and then, having observed their outsourcing decisions, they play the ads game. Draw the game matrix for the outsourcing game. Will the ?rms choose to outsource marketing?