Not All Rivals Look Alike: An Empirical Model for Discrete Games with Asymmetric Rivals
Strong seasonality in demand, a short product life cycle, and the absence of any price competition make the release date of first-run movies one of the main strategic decisions taken by movies' distributors. Movies are typically released on a Friday within a short release season, thus making the release decision a discrete one. In estimating the discrete timing game, just as in many other competitive environments, the identity of the competing players matters: high quality movie is a tougher competitor than a low quality one. Such heterogeneity in the toughness of competition among potential rivals cannot be accommodated by the existing empirical models of discrete games. Therefore, this paper constructs a new empirical model for such games, which imposes no restrictions on the payoff structure. The model is of a sequential-move game with asymmetric information. The Perfect Bayesian Equilibrium of the game can be found using a pseudo backward introduction algorithm. The conceptual multiplicity of equilibria problem is solved for by the sequential structure, while the asymmetric information structure avoids the typical complex regions of integration, thus leading to a relative computational simplicity. By using some of the demand estimates computed in Einav (2003), the estimation results of the movie-release timing game suggest that release dates of movies are too clustered, and that too many good movies are released on holiday weekends. This suggests that more revenues could have been made by shifting some of the holiday releases by one or two weeks. Alternative explanations for these results are discussed
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