A Game-theoretical Approach to Analyze Film Release Time

TL;DR

This paper models film release timing as a game among studios, analyzing equilibrium strategies and demonstrating the complexity of optimal release decisions, with implications for understanding industry behavior and competition.

Contribution

It introduces a formal game-theoretic model for film release timing, proving existence and uniqueness of equilibria, and analyzing multi-movie release complexities.

Findings

Most studios (84%) do not change their release times, indicating strategic equilibrium.

Existence of pure Nash equilibrium is proven, with conditions for its uniqueness.

Finding best responses with multiple movies is NP-hard, showing computational complexity.

Abstract

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.