  Film release dates play an important part in box office revenues because of
the facts of obvious seasonality demand in the film industry and severe
competition among films shown at the same time. In this paper, we study how
film studios choose release time for movies they produce to maximize their box
offices. We first formalize this problem as an attraction competition game
where players (film studios) consider both potential profits and competitors'
choices when deciding the release time. Then we prove that there always exists
a pure Nash equilibrium and give the sufficient condition of the uniqueness of
the Nash equilibrium. Our model can be generalized to an extensive game and we
compute the subgame-perfect equilibrium for homogeneous players. For the case
that one film studio could have multiple movies to release, we prove that
finding a player's best response is NP-hard and it does not guarantee the
existence of a pure Nash equilibrium. Experiments are provided to support the
soundness of our model. In the final state, most of film studios, accounting
for 84 percent of the market, would not change their release time. The
behaviors of film studios imply they are following some strategies to reach a
Nash equilibrium.
