Cinemath: The Game Theory Behind the Snow White War [Updated]

     May 23, 2011


It’s probably clear to you from my nightly journalistic incompetence, but my day job (at which I’m equally incompetent) is student research based in math and statistics.  I’ve been looking for an opportunity to introduce a semiregular feature that combines the two worlds (Cinemath!), and Hollywood obliged this past week.

Universal Pictures and Relativity Media each spent the last year developing movies based on the Snow White fairy tale, both targeting a 2012 release.  Relativity scheduled The Brothers Grimm: Snow White to be the first audiences see on June 29, 2012.  Last Tuesday, Universal made the bold — and quite possibly idiotic — move of rescheduling Snow White and the Huntsman from December to June 1, 2012.  This brand of cutthroat competition is hardly novel among movie studios, but the Snow White war serves as an illustrative case study for the strategic reasoning described in game theory.

After the jump, I explain how the battle between Universal and Relativity is mathematically identical to the Cuban Missile Crisis.

[Update: Relativity moved The Brothers Grimm to March 16, 2012.  We must discuss this after the jump.]


a-beautiful-mind-posterGame theory describes the dynamics at play when the best strategy depends on the actions of your competitor, another player in the game.  As moviegoers, your first introduction to game theory was likely A Beautiful Mind.  Russell Crowe played John Nash, one of the most prominent contributors to the field.  The movie focuses on the period when he went crazy, but prior to the schizophrenia, Nash’s work helped lay the foundation for game theory.

The most immediate application of game theory to the movie business is seen in the jostling over release dates.  The essential goal of the modern movie studio is to lure as many of you as possible into the theater.  This becomes more difficult when a rival studio has a convinced a sizable group to see the movie in the theater next door.

There are a limited number of weekends available each year, and even fewer “prime real estate” weekends.  The best weekends ensure the maximum possible audience, when kids are out of school (the summer months) and/or adults are off work (Thanksgiving, Christmas).  The scarcity of weekends and abundance of wide releases turn studios into vultures circling over these weekends.  That’s why DreamWorks announced How to Train Your Dragon 2 for June 20, 2014 more than three years in advance.  That’s why Marvel waited just one day to swoop in when the would-be Spider-Man 4 was delayed.  And that’s part of why Universal and Relativity are racing to get their multimillion-dollar fairy tales in theaters first.

In game theoretical terms, this race is represented in the game of “chicken.”  The primitive form of chicken is itself very cinematic, seen in such movies as Rebel Without a Cause, Footloose, and Faster, Pussycat! Kill! Kill!.  In the most basic variation, two cars drive directly at one another; each driver has the option to continue driving straight or to swerve.  The best outcome for the driver is to bravely continue straight while his opponent swerves like a yellow-bellied chicken.  In accordance with the male machismo, the driver is shamed if he swerves, but this shame is mitigated if the opponent also swerves.  The worst outcome for both drivers is, of course, a fiery car crash.  Each possible scenario is captured in the payoff table below, which lists the value both drivers place on each outcome.  For instance, the first box shows what happens if both drivers swerve: {Driver 1: Tie, Driver 2: Tie}.


The game is not limited to gearheads.  Perhaps the most famous (and certainly the most terrifying) real-life game of chicken is the Cuban Missile Crisis.  Game theory is especially relevant to sports fans right now as the owners and players are threatening a lockout next season in both the NFL and the NBA.  And, as I’m about to argue, Universal and Relativity are embroiled in a game of chicken over Snow White

The Snow White War

snow_white_illustrationAt this stage, both Universal and Relativity are in pre-production with a cast and crew, but neither studio has shot a frame of film.  Either studio can still cease production (“Swerve”), absorbing the moderate losses of pre-production cost.  Alternatively, either studio can plow forward (“Drive Straight”) toward that June release date.  To formulate this as a game of chicken, we’ll briefly simplify with a few assumptions:

  • The two films are interchangeable in terms of market potential
  • The audience is indifferent between which Snow White movie they attend
  • There is not enough demand to accommodate two Snow White movies at the same time — both Relativity and Universal would prefer to release the movie into a market with only one Snow White movie.
  • Disney has its own Snow White film in development, but it will not hit theaters before 2013, probably later.  Snow and the Seven does not factor into this game.

Below is a hypothetical payoff table measured in profit/loss.  (Please note these numbers are entirely made up for the purpose of ranking each outcome.)  If a studio backs out now, it loses $10 million in pre-production cost.  If a studio goes forward with the production, it incurs a much higher cost.  If there is no competition, the active studio earns $100 million in profit.  If both studios must split the market, both studios lose $50 million on their investment.


One of the core concepts in game theory is the Nash equilibrium, which borrows its name from the aforementioned Russell Crowe John Nash.  A Nash equilibrium predicts the outcome of the game — it is not necessarily the best outcome for either player, but at the Nash equilibrium each player has chosen the best strategy after taking into account the other player’s decision.  In a game of chicken, there are two Nash equilibria, where one player swerves and the other drives straight.  This backs up intuition (or mine, anyway) that there is no way there will actually be two Snow White films in theaters next June.

(As I mentioned, I simplified the scenario to fit comfortably in a payoff table.  I discuss other possibilities in the appendix.)

So who swerves?  Universal’s move to June, in game theoretical terms, is “signaling” — a public display of pre-commitment to a strategy.  In the vehicular chicken, one party may signal their intention to drive straight by disabling the steering wheel, removing the option to swerve.  This signal is a declaration that Universal will have their Snow White movie in theaters first.  Universal’s message: “Your move, Relativity.”

Relativity’s Move

I like to think of game theory as a kind of mathematical soap opera, so let’s back up and flesh this story out a bit.  In February 2008, Relativity signed a deal with Universal to co-finance 75% of the studio’s slate through 2011.  Seven months later, the studios reupped their partnership through 2015.  At the time, Relativity CEO Ryan Kavanaugh remarked, “Our deal has been very profitable to date, and the Universal creative, marketing and distribution team is unparalleled. They are true partners.”  Universal executive Michael Joe added, “We have had a genuine collaborative partnership to date, and we look forward to expanding on our ambitions together in the future.”

snow-white-illustration-2Relativity had ambitions beyond the co-financing business, though — the studio started distributing its own films last year.  In June 2009, Relativity picked up Melissa Wallack’s script The Brothers Grimm: Snow White to produce and distribute.

Three months later, a spec script by Evan Daugherty titled Snow White and the Huntsman sparked a bidding war among the studios, including Sony, Paramount, Fox, New Regency Summit, and, of course, Universal.  In the end, Universal paid a large sum to compete with Relativity, testing the bounds of their “genuine collaborative partnership.”

Since then, Universal has generally pretended that Relativity’s Snow White movie does not exist.  Even in this week’s scheduling announcement, Universal chairman Adam Fogelson and co-chairman Donna Langley attributed to the move to efficiency:

“As [the filmmakers] were finalizing casting and preproduction of Snow White and the Huntsman, we realized that the ambitious and fully-formed world they had promised was blowing away all expectations.  We’re thrilled that Universal will be bringing this singular version of a timeless story almost seven months earlier than anticipated.”

The move is transparently motivated by the competition, but nope, Snow White and the Huntsman is a “singular version.”  There is bad blood between the two studios, and that must be taken into account when evaluating their strategies as an additional incentive to act irrationally.  (Interestingly, irrationality is a good strategy in a game of chicken.  If you are convinced the other driver is crazy enough to drive straight no matter what, your best option is to swerve.)

And so, with that oral history laid out, what are Relativity’s options?

1. Release the film earlier

If the craziest studio wins the game, Relativity could try to out-crazy Universal by announcing a release date before June 1, 2012.  I am rooting for this to happen, to extend the soap opera.  But it’s inadvisable.  Currently, Relativity has just over a year to shoot and add copious special effects to The Brothers Grimm: Snow White.  That’s already a very tight turnaround.  How much further can they push it?  Universal is in the same position, and there’s a reason Fogelson and Langley didn’t promise eight months earlier than expected.

Rushing to finish a film that will eventually be sold as a big-budget fantasy will negatively affect the quality and commercial prospects of said film.  There is a date that is too early, such that it is no longer viable to produce enough for the necessarily awesome two-minute trailer.  I obviously don’t know the exact date, but anything earlier than June approaches that limit.

[Update: Since posting, Relativity rescheduled The Brothers Grimm: Snow White for March 16, 2012.  On one hand, this makes sense.  Relativity decided to go all in on Snow White — depending on how Immortals performs in November, this could be their first major property as an independent distributor.  And if you’re going all in, you might as well leapfrog a busy May already populated by The Avengers, Battleship, Men in Black III, and head straight for March where the likeminded Alice in Wonderland earned $1 billion.

On the other hand, this is crazy!  Production will begin in June, allowing just nine months to create a viable blockbuster fantasy.  The studio was reportedly considering 3D, but that cannot still be a possibility, right?  The director, Tarsem, has made three films in 12 years.  Maybe the technology really has gotten to the point where Hollywood can churn out a tentpole in nine months, and Tarsem, post-Immortals, has evolved into the man who can achieve such a feat.  That’s a cool idea, and I really would like to see this be a good movie.  However, no precedent comes to mind.

I love the audacity, though.  (“Au contraire, Universal: your move.”)  Can Universal go any earlier than March with a movie that was originally scheduled for December?  I’d love to see them try.  I actually think the best move is to move Snow White and the Huntsman back to December.  The studio loses a little face, but the marketing department can react to the success or failure of Relativity’s movie.  Clearly, though,  studios have no interest in what I think is best.  So look on the front page of Collider next week for the headline “Universal Moves SNOW WHITE AND THE HUNTSMAN to Yesterday.”

To be clear, both studios are still signalling.  There’s still time to bail.  Outside of these brackets, I’ll leave the post as is for now.]


2. Keep the film where it is

Relativity could keep the June 29, 2012 release date.  I’d like to see the studio try, just to see how audiences would respond.  But I cannot imagine a scenario where this will happen.  Relativity will either announce an earlier release date or…

3. Put a hold on development

I believe either Universal or Relativity will eventually be forced to push the release date back or, more likely, cease production altogether.  Universal has the upper hand, so my best guess suggests Relativity will put The Brothers Grimm: Snow White on hold.  Let Universal be the guinea pig that tests just how much audiences are yearning for a modern Snow White.  Depending on how Snow White and the Huntsman does, revisit Wallack’s script in a year or two.  In the meantime, maybe see if you can get in on the co-financing, or seek compensation for backing out of the game.  I am admittedly a risk-averse individual, but this is what I’d do if I were Relativity.


Studios are not necessarily mathematically rational entities, and that makes this whole process really exciting.  I am not even remotely certain about my best guess.  At this point, I’m more interested in the behind-the-scenes game than either of the movies.

Further Reading

Mathematicians are great at maintaining Wikipedia, so check out the pages on game theory in general and the game of chicken.

Mind Your Decisions and The Quantitative Peace offer a really cool rundown of the game theory in The Dark Knight.

The Baltimore Sun uses Dr. Strangelove to a touch point to discuss the game theory involved in nuclear war.  Included is an interview with Thomas Schelling, a famous game theoretician who consulted Stanley Kubrick prior to shooting the film.

Rebel Without a Cause depicts a game of chicken where the goal is to not drive off a cliff.

The Joker facilitates a game between prisoners and theoretically upstanding citizens at the end of The Dark Knight

Kevin Bacon learns how to ride a tractor to prove his manhood in Footloose


Chris Hemsworth Thor_PremiereIn formulating the game, I treat the movies as essentially interchangeable and the month between release dates as negligible.  In reality, things will not be quite so simple.  Before I continue, allow me a simple test.  These people are all cast in one of the two Snow White movies: Lily Collins, Chris Hemsworth, Kristen Stewart, Julia Roberts, Armie Hammer, and Charlize Theron.  Now, without looking at IMDB, can you link each to actor his or her movie?  I do this for a living, and I can’t.  I have to look it up with every new casting report.  This is anecdotal evidence for movies that still have a year to advertise, and thus entirely meaningless.  I don’t intend this to be condescending (it is), but I wonder how much audiences can distinguish between two movies trading on the familiarity of the Snow White brand.  Individually, Snow White and the Huntsman will draw more Chris Hemsworth fans, and The Brothers Grimm: Snow White will appeal to the Julia Roberts fanbase.  But overall, these movies will be defined by their Snow Whiteness in the public eye.

(In this sense, the Snow White war is fundamentally different than Deep Impact vs. Armageddon or Volcano vs. Dante’s Peak.)

I believe this much is true: both movies would be better off if the other movie did not exist.  But if the audience is split, the movies are unlikely to perform identically.  There is arguably major benefit to being first, evidenced by the race between Universal and Relativity.  I assume the studios would bombard the public with two massive Snow White-centric marketing campaigns from January to May.  In this case, the dual marketing creates one large mass of general Snow White brand awareness.  The first Snow White movie reaps the benefits; by the time the second rolls around, demand for Snow White has largely been satisfied, limiting the potential audience.

Alternatively, a discerning audience may shun the first and opt for the second movie.  Though again, I am skeptical this audience is large enough to make a difference, especially since a movie is an experience good.  There is also an argument that the first movie, if successful, actually rachets up demand for more Snow White.  That seems counterintuitive to me, but what do I know?

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