Bar Flight, Part 2

When I first discussed the Clear and Sapphire situation, I characterized it as a coordination game, i.e., a game in which the players wish to coordinate their choices. The sides-of-the-road game is the classic example of a coordination game: it doesn’t really matter which side of the road people drive on, so long as all drivers do the same thing. The model applies to bars because people generally want to go where other people go.

However, Ellen made an interesting comment in the comments box: “Reminds me of the star-bellied sneeches [sic] and the plain-bellied sneeches [sic].” Although there are some similarities, this is actually a quite different game. For those who don’t know Dr. Seuss’s parable of racism, the story goes like this: Some Sneetches had stars on their bellies, while other Sneetches did not. The plain-bellied Sneetches wanted to hang out with the star-bellied Sneetches, but the star-bellies excluded them. So the plain-bellies went through Sylvester McMonkey McBean’s Star-On Machine, which gave them stars. Upon discovering this, the star-bellied Sneetches had their stars removed using McBean’s Star-Off Machine. And then the once-plain-but-now-star-bellied Sneetches went through the Star-Off Machine, and then the once-star-but-now-plain-bellied Sneetches went through the Star-On Machine, ad infinitum.

This game is identical to other famous games of game theory, including Matching Pennies and One-Two-Three-Shoot. In all these games, there is one player who wants an outcome in which both players take the same action (the initially plain-bellied Sneetches wanted to blend in), while the other player wants an outcome in which the players take different actions (the initially star-bellied Sneetches didn’t care whether they had stars or not, as long as their bellies differed from those of the initially plain-bellied Sneetches). Unlike the sides-of-the-road game, in which there are two equilibria, in the Sneetches game there is no equilibrium unless the players randomize. Instead, you get a round-and-round chase effect like the one described by Seuss.

So how does all this apply to the bar situation? Suppose there are two kinds of bar customers, the “hip” and the “unhip.” The unhip want to hang with the hip, but the hip do not want to hang with the unhip. The analogy to the Sneetches is straightforward. The hip will colonize bars, thereby attracting the unhip, whose presence eventually drives away the hip, who then colonize another bar, where they are eventually followed by the unhip, ad infinitum.

So now we have two game theoretic representations of the bar situation. Which is correct? Both have plausible characteristics. One the one hand, it is certainly true that people tend to want to coordinate their bar choices, at least with the kind of people they like. On the other hand, it also clearly true that some people seek to avoid other kinds of people (without the other people necessarily feeling the same).

I suspect that a complex combination of both games is going on. Early in the game, a new bar is discovered (or rediscovered) by some fraction of the hip. A coordination game ensues, because hip people want to hang with other hip people. The bar acquires a reputation as a hipster hangout, which is good because it attracts even more hip people, but bad because word eventually gets out to the unhip, transforming the coordination game into a Sneetches game. Once enough unhip people start showing up, the desirability of the bar begins to wane, and some hip people eventually try a new place with fewer hip people but a better hip-to-unhip ratio. A new round of the coordination game follows.

This combined model provides a better explanation than the coordination game alone. The basic story is one of coordination – people want to congregate in the same place. But the Sneetches aspect of the game helps to explain the switching phenomenon I described in the earlier post. The arrival of an undesirable crowd creates instability in an equilibrium that would otherwise be hard to escape.