3. When movie studios decide to release a blockbuster, they must select a release date in advance.

3. When movie studios decide to release a blockbuster, they must select a release date in advance. Certain weekends (Memorial Day, 4th of July, Christmas, etc.) are particularly desirable because many people who normally do not go to the movies will show up on those dates. However, since many big movies come out on or around those weekends, the competition is also fiercer. There are three blockbuster movies that are finished production and will be released early in Summer 2021: Black Widow, Wonder Woman 1984, and No Time to Die. Each belongs to a different studio: Marvel, Warner Brothers, and MGM, respectively. Suppose there are two possible opening weekends during summer 2021: the weekend of Memorial Day, which starts 5/28, and the weekend of Independence Day, which starts 7/2. Movies released on Memorial Day weekend will split (evenly) $900 million in ticket revenue. Movies released on July 4th weekend will split $400 million in ticket revenue.

a. Write down the studios’ payoffs from different combinations of actions. Provide the payoffs in two separate payoff matrices, where each matrix reflects a different action played by MGM.

b. Suppose studios make release date choices simultaneously. Determine the Nash equilibrium(a).

c. Now suppose that the game is played sequentially, with Marvel announcing first, followed by Warner Brothers, and finally by MGM. Draw the game tree. What is the unique subgame perfect Nash equilibrium?

d. Suppose that you are an executive at Warner Brothers in charge of marketing strategy. You learn that Marvel is going to announce the release date of Black Widow in a week. You also realize that by investing an extra $40 million in an ad campaign you would be able to move up your own announcement date for Wonder Woman 1984. (MGM still moves last in this game.) Should you do it? Explain your reasoning.