Friday, February 18, 2011


My previous post wasn't fair.  I left a lot of my thinking about it out, and put in only tidbits, leading one reader to respond with some good questions about consistency and terminology, below:

I'm confused as to what meanings you attach to a lot of the terms you're using, such as "fairness", "equilibrium", or "coordination game". You start off saying that things aren't fair, without explaining which idea of fairness you mean (there's like five trillion of them, counting just the ones that are precisely defined). Then you talk about an inefficient equilibrium of an n-person prisoner's dilemma (your driving example). Then you say "In sum, we play very large coordination games," even though what you've talked about one sentence before is not a coordination game, and you also say "When disequilibrium occurs..." even though the example you've just set up is an equilibrium, not a disequilibrium.

To sum up, I have four questions (which of course you are welcome to ignore!):

1. What do you mean by "fair"?
2. What do you mean by "equilibrium"?
3. What is the driving example an example of? (An unfair outcome? A fair outcome? A disequilibrium? An equilibrium? Something else altogether?)
4. What is the main thought you're trying to communicate in this post?

So, to respond.  My notion of fairness here is admittedly weak.  It is closely associated with a recent post about the importance of de-emphasizing ego and entitlement.  The point was to say that we don't always get out of a situation what we put into it, and that our reward for buying into something is affected by collective decision making that may make sense when viewed in the aggregate, but not make us happy individually. It is a very basic idea to diffuse some of the self-centered notion that persists in my own thinking about my own priority in the world.

Equilibrium was a term used to describe the flow of traffic. It relates to the amount of cars, the capacity of the roadway, and the speed of cars.  An equilibrium is met when the flow of cars getting on and off the highway balance to keep the average speed of cars at 55mph.  Disequilibrium occurs when one of the elements changes--traffic ensues.  There's snow, so the cars must go slower, but the same amount of drivers come on the highway.  Or an exit is blocked because of an accident. 

The main point of the post was to say this: at times it might seem to make sense to act in a certain way individually--to speed onto the highway and beat out other cars, for instance--but that individual act actually constrains the aggregate a little bit more (because, for instance, one car leaving the highway stays at the average speed instead of speeding off to balance the oncoming car).  We think we make gains individually, but it is much harder to tell whether there was net gain or not.  Ultimately, and here's the take-home, understanding net gain will help us attain higher levels of individual gain.

I think.


Anonymous said...

Thanks for your reply. My comments:

With respect to your definition of fairness, I'm not able to understand it, and I'll just leave it at that for now.

Now with respect to your use of the term "equilibrium," I understand what you mean, and I think it's extremely misleading. It basically stretches the meaning of the word beyond any recognition. The word itself has multiple meanings, as most words do; there's the informal meaning, and there's more than one technical meaning (for example a strategic one, as in game theory (that's what I initially thought you meant by the word, since you were talking about coordination games), or a parametric one, as in dynamic systems). But in all uses that I am familiar with the term retains a certain essence which your use of it completely ignores: an equilibrium is a situation that is stable on its own, self-sustaining. It does not change without some (usually large) changes in outside conditions. There's nothing inherently "stable" about a situation where everyone drives 55mph; in fact, depending on the details of your traffic model, it can be extremely unstable (in other words, it can be a "disequilibrium" in the sense in which the rest of the world understands the word). Conversely, there's nothing inherently unstable about a traffic jam. In all dynamic models of traffic flow that I am familiar with, traffic jams are equilibria. So it looks like your criteria for deciding whether a situation fulfills your definition of "equilibrium" do not have anything to do with stability. In which case why on Earth would you use this particular word?

Sorry for being long winded here.

hmm said...

I don't have any real experience with game theory, but stability at the root of an equilibrium makes sense to me. Would you provide an example of disequilibrium? Thanks.

Anonymous said...

This isn't really about game theory; the colloquial meaning of equilibrium is the same (a situation that's self-sustaining).

Anyway here are some examples of disequilibria in dynamic systems. Imagine a world with no law enforcement. In such a world, a population consisting only of non-thieves is in disequilibrium: since stealing doesn't carry any bad consequences, those steal will do better than honest folk and will start "outbreeding" them. A dynamic system can have more than one equilibrium or it can have none (in which case it will keep changing forever). An example of a system in constant disequilibrium is the fashion industry. Since payoffs in fashion come mostly from being original (i.e. different than other people), there can be no equilibrium fashion standard on which the whole population will converge.

An interactive example of a dynamic system (which is an implementation of Thomas Schelling's segregation model) can be found under this link. Try it. Press "setup" then press "go." You'll see the system settle on an equilibrium in which everyone's happy where they are and no one wants to move. Now move the bottom slider (the one that says "%-similar-wanted") right to 70%, then press "setup," then press "go." You'll see a different equilibrium emerge (and it will take the system a bit longer to settle on it). Now move the slider to the right even further, anywhere past 80%, press "setup" and then "go." Now the little digital society is in a state of constant disequilibrium: given the large percentage of folks similar to themselves that everyone wants to live around plus spatial constraint, it's impossible for everyone all at once to be happy where they are, so people will just keep moving around forever.