3) A SIMPLE MODEL OF MOVIE-LAUNCH TIMING Consider the following model of how movie studios might think about the optimal timing of launching a movie (and thereby entering a market). Suppose there are two studios (or movies), X and Y, and there are two holiday weekends, 1 and 2. In weekend 1, there is a total of 8 movie fans, evenly divided into regular moviegoers {A,B,C,D} and occasional moviegoers {E,F,G,H}. In weekend 2, there is a total of 8 movie fans, evenly divided into the same regular moviegoers from before {A,B,C,D} and new occasional moviegoers {I,J,K,L}. All fans want to watch movies (produced at zero cost) and the price per ticket is $1. How should we envision demand? Suppose that all moviegoers will watch a movie that they have not seen before, but will never watch a movie for a second time. Also suppose that if two previously-unseen movies are available, the customers will "flip a coin" and be split evenly, with alphabetically-earlier moviegoers choosing X and others choosing Y. E.g., if both movies are available in weekend 1, then A and B will watch X while C and D watch Y, and if both movies are still available in weekend 2, then A and B will watch Y while C and D watch X. A movie launched in weekend 1 is still available in weekend 2. a) Determine the total box office revenue (or profit) for each firm under each combination of launch weekends: (X enters in 1, b) c) Y enters in 1), (1,2), (2,1), and (2,2). TIP: Don't worry about discounting future payoffs; just add the two weekend revenues to find the total revenue for each firm. HINT: Complete the tables below! Find the pure strategy Nash Equilibrium for this 2x2 game of launch timing between X and Y. Intuitively explain the result. Critique this model. What positive things can you say about this model? What negative things can you say about this model? TIP: What seems unrealistic, overly optimistic, oversimplified, or missing from this model? Both X and Y Both X and Y Only X Both X and Y Wknd 1 Wand 2 Wknd 1 Wand 2 XXXX QUALI 120AHH AQUALSI Only Y Both X and Y Wknd 1 Whand 2 Neither Wknd 1 Both X and Y Wand 2 за глинопод XXXX AQUALSI 11 11 Firm Y 2 хилу DI 1111