"One of the most difficult challenges of all is rooted in the very origins of game theory: it was developed by men of nearly superhuman intellect like Nash and von Neumann. That is both its great strength and its great weakness, because for game theory to be successful, it must provide insight into what mere mortals will do. Game theory expresses the way people would act as the solution to a mathematical equation. It presumes hyperrational players who are instantly able to solve very tough problems, and this description starts to look unrealistic if game theory is to be a practical tool for explaining how real people actually behave. Nash and von Neumann really could solve such problems instantly. The rest of us cannot."
-Tim Hartford, The Undercover Economist, 2006
You'll remember John Nash from the movie "A Beautiful Mind."
Hartford points out that a great many people thought John von Neumann the most brilliant person alive, and since he worked at Princeton with Albert Einstein, that's saying something.
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for game theory to be successful, it must provide insight into what mere mortals will do.
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Why? I mean, obviously knowing what people will do is of great interest, but why is that the only question? For example, isn't the non-existence of a better strategy than a particular strategy a worthy result?
Furthermore, doesn't asking "what is the best possible strategy" represent a good first step in approaching, "what do non-hyperrational people actually do"? Seems like the latter question is much harder.
Then again, I've only had the briefest introductions to game theory.
You are right, it is much harder to actually predict behavior. Sometimes game theory is used as a kind of "normative" model (this is the Right answer) rather than a "positive" model (this is what happens).
One problem with game theory as a model of 'best possible strategy' is that in Real Life, (that is in experiments), ordinary people actually outperform the theoretically 'best' outcome. The common example is the finitely repeated prisoner's dilemma . In that game, a rational person always defects (and thus takes a small return), while normal people can often cooperate, at least for a while, and thus get a higher payoff.
Rationality can also lead to some odd outcomes. Using prisoner's dilemma, a finitely repeated series of, say, 10 games has defect as the single rational strategy for each iteration and player, while a game of uncertain length - say an 80% chance of continuing after each game - can easily have a completely rational strategy of always cooperating, unless the other guy defects, and then you defect as punishment. This even though the expected length of this game would only be 5 games.
It also isn't difficult to create games where there is not a single rational strategy, or it is uncomputable. (Example - Chess.)
Ah, Ed, spoken like a future math PhD! Who cares about the real world anyway? ;) But you do have a point that finding a best strategy may itself be of interest; I guess it depends on the purpose of your endeavor whether that constitutes "success" or not.
It does seem like trying to model what non-perfectly rational people do would quickly become a mathematically intractable problem.
Robert, I think it's pretty interesting that these experiments suggest that people are not rational...to their mutual benefit. Does this mean that if a person had the option to chose her own Prisoner's Dilemma opponent, she would be better off picking someone unfamiliar with game theory (perhaps proxied by choosing someone who hasn't taken much math or econ)? Funny to imagine a couple of French lit students outperforming econ majors at such a game.
Note: my own exposure to game theory is minimal and can be best described as me understanding and then forgetting then understanding again (sometimes within the space of minutes, sometimes days or weeks) what the hell a Nash equilibrium is again. So I am definitely not speaking from a position of strength here.
I keep imagining a pro-rationality movement that encourages people to wear plastic bracelets inscribed "WWvND?" (What would von Neumann do?)
Weird, OK.
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I keep imagining a pro-rationality movement that encourages people to wear plastic bracelets inscribed "WWvND?" (What would von Neumann do?)
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Ok, I must have that T-shirt now.
If I had time, I'd search cafepress. I wouldn't be surprised at all.
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