Bose-Einstein Dynamics and Adaptive Contracting in the Motion Picture Industry, Arthur De Vany, W. David Walls
Following from an earlier post about information cascades and the movie industry that referenced Arthur De Vany’s example, I dug up a paper by Arthur De Vany and W. David Walls called “Bose-Einstein Dynamics and Adaptive Contracting in the Motion Picture Industry.” De Vany and Walls explain a very interesting phenomena of the motion picture industry by modeling the information cascade in an audience that can make a film either a hit or a flop as a Bose-Einstein process, which affects the dynamics of cinema screen revenue.
As a matter of background, the Bose-Einstein theory comes from statistical mechanics and is used to describe the statistical distribution of bosons. Einstein predicted that if a Bose gas were cooled to almost absolute zero, the bosons would suddenly crowd together into the lowest energy state. This singular quantum state achieved is called the Bose-Einstein condensate. It is the probability of particles “crowding together” in the same state in the Bose-Einstein distribution that is relevant to modeling audience behavior in the movie industry.
De Vany and Walls analyze the movie industry’s distribution of revenue between different movies being shown by looking at audience behavior over a movie’s run at the cinema. We start with a Bayesian probability of the likelihood that some movie-goer will choose a certain movie out of a set of movies being shown. Since the successive outcomes of this random variable are not independent, each trial will be a Bayesian model of a movie-goer who keeps track of information about the quality of the movie by observing previous trials. So then the probability that a new movie-goer will see a movie depends on who has already seen it (and has reported positively on it) and the distribution of the other viewers who see other movies. Then the unconditional distribution of cinema revenue based on the succession of movie-goers’ choices is shown mathematically to follow a Bose-Einstein distribution, where the probability that a customer selects a particular movie is proportional to the fraction of all other movie-goers who select that movie, so that previous selections will attract new selections of the same movie. This produces potential leverage for movies that undergo an information cascade of this sort, where differences between movie revenues can grow exponentially. This fact reinforces the property of the Bose-Einstein distribution that all possible outcomes are uniform and equally likely (so the probability that 20 people see one movie and only 1 sees another is equally as likely as the scenario where no one goes to either).
The moral of the story is that production companies in Hollywood cannot make accurate expectations on a movie’s revenue. Because of information cascades, modeled in this paper as a Bose-Einstein process, movies that are expected to do well could rapidly decline in viewers and low-budget movies could become hits when it receives a mass of positive reinforcement from early viewers and then attracts new viewers exponentially. This is precisely what happened to the $175M production “Waterworld” that flopped with $88M in revenue, while the low-budget no-big-star film “Home Alone” grossed almost $300M. The stochasticity of how well Hollywood movies do, such that production companies can never accurately determine success rates, certainly reminds me a great deal of the book A Random Walk Down Wall Street, which first popularized the idea that a monkey throwing darts at a board of stock names can typically out-do the average professional institutional investor ~ this is the best analogy to production companies and the scripts they choose to produce.
* You can follow any responses to this entry through the RSS 2.0 feed.