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The Wall Street Journal (John Lippman, “The Producers: ‘The Terminator’ Is Back,” March 8, 2002, A1) reported that Warner Bros. agreed to pay $50 million for its U.S. distribution rights, plus an additional $50 million in marketing costs, so that it could release Terminator 3 (T-3) in the summer of 2003. It paid this large sum because it did not want anyone else to release T-3 on the same weekend in 2003 that Warner Bros. released its movie Matrix 2.
Suppose that Warner Bros. had not purchased the distribution rights to T-3 and that the film’s producer retained the rights. Warner Bros. decides whether to release Matrix 2 on the July 4 weekend or on the July 18 weekend. Simultaneously, T-3’s producer decides which of those two weekends to release its film. The payoff matrix (in millions of dollars) of the simultaneous-moves game is:
a. What is the Nash equilibrium to this simultaneous-moves game?
b. Which release dates maximize the sum of the profits? Explain.
c. What is the greatest price Warner Bros. is willing to pay to purchase the distribution rights to T-3? What is the lowest price that T-3’s producer is willing to accept to sell the rights? Are there mutually beneficial prices at which the trade takes place?
d. If Warner Bros. purchases the distribution rights of T-3, when does it release the film and when does it release Matrix 2? Explain. V