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October 12, 2005

What Standards Should be Applied to Game Theory?

Michael Mandel

Tyler Cowen of Marginal Revolution responds to my criticism of game theory here:

I can think of possible responses:

1. Behavioral approaches will flesh out how humans actually behave. Game theory will end up with clear predictions, just give it time.

2. Computational approaches will flesh out how humans actually behave. Game theory will end up with clear predictions, just give it time.

3. Evolutionary approaches will flesh out how humans actually behave. Game theory will end up with clear predictions, just give it time.

4. Experimental approaches will flesh out how humans actually behave. Game theory will end up with clear predictions, just give it time.

5. The real world is in fact indeterminate or close to indeterminate. The indeterminacy and multiple equilibria of game theory are not a problem, but rather reflect how closely the theory mirrors reality. Yes you might prefer sharp, clear predictions, but tough tiddlywinks, you're not going to get them. Faithfulness to reality is more important than fulfilling abstract methodological strictures.

Any one of these answers would suffice and allow us to push full steam ahead, or in the case of #5 declare victory and go home. The problem is that we don't know which one is true.

The bottom line: Like so much of economics, the strongest argument for game theory is simply to chat with someone who doesn't know any.

I'm sorry...I just don't understand what Tyler means by #1-4.

I completely agree with Tyler's #5, about the essential indeterminacy of the real world, but I don't agree that game theory helps us think about it in the right way. The set of possible equilibria of a repeated game is far too broad to be useful. We can get good equilibria, bad equilibria, and everything in between.

Behavioral economics embodies uncertainty as well, since the reference level or status quo can be hard to determine. But in the end I feel more comfortable that I've learned something general about the way that people behave from behavioral economics (i.e. the principle of loss aversion) than from game theory.

There's also a broader question: What do we expect from economics-accurate predictions, falsifiability, or what? I sometimes get the feeling that economists are applying too low a standard.

09:01 AM

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Mr. Mandel,

What Professor Cowen means by #1-4 is that you are mistakenly conflating game theory with the concept of rationality. "Rationality" is commonly defined in terms of actors with complete and transitive preferences over outcomes. Subjective expected utility theory is a more elaborate construct for modeling rational individual decision-making under uncertainty. Game theory deals with "interdependent" (rather than individual) decision-making, by which I mean situations in which the outcome each player receives depends not only upon his or her behavior but also upon the behavior of the other players (for example, in hide-and-seek, one player decides where to hide and the other decides where to look, but neither player can simply choose "win the game").

Although many game-theoretic models make use of expected utility theory, not all do. Professor Cowen is saying that game theory is not necessarily wedded to expected utility theory or any other specification of "rationality." If expected utility theory is eventually replaced by some other model of decision-making, we will likely move many of our existing game-theoretic models over to the new set of foundations.

For example, you cite Daniel Kahneman, who won the 2002 Nobel Prize for his work on prospect theory. Prospect theory is a model of individual choice under uncertainty, which means that it is an alternative to expected utility theory, not to game theory. Even if we were to reject "rationality" in favor of prospect theory, we would still need some set of tools for discussing how decision-making changes when individuals' fortunes are interdependent. We will still need game theory, in some form or another.

Similarly, items #2 and #3 refer to game theoretic models that abandon the traditional concept of decision-making altogether (to say nothing of rationality). Over-simplifying a bit, evolutionary game theory envisions rather stupid adaptive agents who adopt a behavior, bump into each other for a while, and eventually either switch to some other behavior that seems more successful or die off. Computational models are quite varied, but many share the approach of treating players as adaptive rather than forward-looking.

The basic point is that your misgivings about the traditional approach to characterizing decision-making in terms of "rationality" have little to do with game theory per se. Neither game theory nor the contributions of Schelling and Aumann rely entirely upon the formulation of "rationality" that you mistrust. (In fairness, Aumann's influential work on the meaning of "common knowledge" in bayesian games is much more closely tied to the notion of rationality than the work on repeated games cited by the award committee).

As for Professor Cowen's point #5, I think he's letting you off the hook too easily. Your concern that game theory does not yield precise, testable predictions strikes me as both incorrect and misguided, and your examples make no sense to me at all. But I'll have to let that issue rest, since this post is already much too long and pedantic.

Posted by: Yet another professor at October 12, 2005 11:33 PM