How useful is game theory?

http://scienceblogs.com/cortex/2010/02/too_many_fastballs.php

by cwan • 16 years ago

27 16 16 years ago

lmkg• 16 years ago

Game theory is a prescriptive theory, not a descriptive one. It's designed to find the decision that maximizes or optimizes the return, based on the availble information about the circumstances. In doing so, it sometimes arrives at counter-intuitive results. The fact that the results are counter-intuitive should immediately imply that it will not predict behavior. The fact that game theory is a poor predictor of behavior is an object of study for psychology, not for game theory[1].

So yes, game theory is useful for making decisions. It's just not useful as a predictor of human behavior.

[1] Except insofar as if you want to apply it, you have to make different assumptions about the behavior of your opponents. But game theory is still perfectly amenable to adding those constraints.

_delirium• 16 years ago

There's some parts of economics that have used game theory as an analysis tool based on the set of assumptions: 1) humans, at least when they engage with markets, are rational actors; and therefore 2) markets will converge to the equilibria specified by game theory. Some of the empirical tests of game theory have had a not-so-hidden subtext of casting doubt on that kind of economics.

thaumaturgy• 16 years ago

It's funny, I was thinking about game theory applied to economics earlier, as a result of Dani's essay. So, anyway: I have a certain fondness for game theory as an overarching description of some aspects of economics.

But it doesn't describe the whole picture.

Game theory is great for example if you're trying to understand (or even predict) what'll happen when all parties involved are acting merely in the interests of their profits, and none of them are being especially innovative -- "cheating" in terms of game theory. What will industry Z do when faced with regulatory oversight? Let's ask game theory.

At smaller and smaller scales, game theory breaks down due to the greater and greater influences of other aspects of psychology, sociology, and sciences. For example, a business may not act totally rationally in terms of its profits because one or more individuals is more concerned with the business's image.

Flankk• 16 years ago

If "lab tests" show game theory to not work as a predictor, then the scientists performing the test made incorrect assumptions. This does not however mean that game theory does not work or is not useful.

As far as I know, estimating player's ability to reason is part of game theory. The less rational the player, the more variance in outcomes. Game theory is still useful with less rational players because you can still exclude dominated strategies.

scott_s2• 16 years ago

That's rather the point: are humans rational agents in circumstances where there are objectively better strategies? If you're interested in more on that question, check out "Predictably Irrational" by Dan Ariely.

scott_s2• 16 years ago

Alamar admits that a successful running game contributes to the success of the passing game, since you want the defensive backs to have to worry about the possibility of a run. But he isn't convinced that coaches need to run the ball quite so often.

And I'm not convinced that he fully understands the implications of how the game would change if running plays were much less frequent. I know I don't.

For example, if running plays were extremely rare, then defenses would change accordingly. But then there's an obvious exploit. It's possible that a much lower number of running plays is not an evolutionary stable strategy (http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy).

It's an interesting column with interesting research. I just think the problem is more complicated than even what was presented.

jriddycuz• 16 years ago

I'd argue that game theory could be tremendously more useful if its practitioners made a better habit of questioning their own assumptions about the situations they model.

In the study cited in the article, the authors (seemingly) assume that pitch and play selection have constant or near constant marginal returns. That is, they assume that if pitchers just threw fewer fastballs, they'd be more successful. There is really no reason from the data presented to assume that. Perhaps pitchers need the fastballs to set up better pitches (they do), and perhaps other pitches wear their arms out faster (curve balls tend to). The author of the main article hints at this possibility in the context of NFL plays, but doesn't address it very seriously.

In general it's dangerous to look at data without a solid understanding of the theory behind that data and then claim to have a better understanding of that field than those who operate in it vocationally.

roundsquare2• 16 years ago

On top of that, they coach has to deal with players morale. If a passing play failed last time, the players may be wary of of another passing play. This gets worse if a pass play has failed a bunch that day.

On top of that, you have to deal with player fatigue, risk of injury, etc...

There are a lot of finite resources (or resources that don't replenish quickly) in real life games.

In football as well (I don't know much about baseball), you may not go for maximum yards in each play. If its fourth down with 1 yard to go, you don't care about getting 12 yards, you one your 1 yard (usually). Assuming each play is like the previous is 100% false.

Improperly applied theories are worse than human instinct. Properly applied theories can be better than human instinct.

emilind• 16 years ago

Game theory is great for predicting the behavior of game theorists (see telecom auctions).

presidentender• 16 years ago

Classical game theory is useful in some circumstances if correctly applied. Correct application, however, requires understanding that your opponent is not perfectly rational. This does not enter into most of the game theory exercises I've read.

On a related note, Combinatorial game theory (John Conway's study of a very restricted set of games) was described as being the most totally useless branch of mathematics. Conway was very proud of this.

toby• 16 years ago

The whole argument here is based on the questionable assumption that coaches and players are actually trying to make decisions that maximize the team's score. An individual might do something that's "perceived to be less risky" because if it doesn't work, he can't be blamed for taking too big a risk.

I don't know a lot about sports, but this is clearly the case in corporate environments where the incentives of the individuals deviate from the good of the corporation.

Groxx• 16 years ago

Game theory is as useful as you question the problem to be. The problem is never as simple as it seems on the surface when you couch it in game theory terms.

It is not the end-all solution to anything. It is often illuminating, and shows how at least some of the problem set acts, but it's a very hard-edged theory that, to work perfectly, requires a hard-edged theoretical problem (like the pirates). Knowledge of it, though, is fantastic at helping predict things. Helping, not doing all the prediction for you. Nothing is ever as clear as theories need.

endtime• 16 years ago

I've found it to be useful every few weeks in day-to-day situations. It's also useful if you ever design and/or run competitive games/events.

I'm not sure everyone needs to be able to prove the optimality of truthful bidding in Vickery auctions, but a basic understanding of Nash equilibria and imperfect information games is useful for anyone who's not a hermit.

roundsquare2• 16 years ago

Wouldn't natural selection want to endow us with a mind capable of maximizing competitive outcomes?

As far as I know, this doesn't make any sense. If there are two traits in a population, A and B, and A is better for survival than B, natural selection will generally filter B out of the population.

However, its not likely that a trait for "maximizing competitive advantage" has ever emerged (at least, I wouldn't think so).

khingebjerg• 16 years ago

Looks like the Colts are all over this, with 601 pass attempts vs. only 366 rush attempts, during the 2009 regular season. Has the head coach Jim Caldwell, or more likely Peyton Manning, been reading up on Game Theory?

proemeth• 16 years ago

Risk aversion does not have to interfer with rationality like the author seems to suggest. We can fit the utility function to take risk aversion into account.

How useful is game theory?

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