What Standards Should Be Applied to Game Theory?
Michael Mandel was not happy with the recent Nobel Prize in Economics that went to Thomas Shelling and Robert Aumann. He writes,
In my opinion, however, game theory represents an evolutionary dead-end in the development of economics. Game theory tries to use the principle of rationality to explain conflict and cooperation in a wide range of economic and social situations. For example, game theory has been used to analyze why the apparently insane buildup of nuclear weapons in the postwar period was actually a rational method of deterring war, and why aggressive price-cutting by airlines was an effective means of deterring competition.
Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes — from full cooperation to near-disastrous conflict — are consistent with the game-theory version of rationality.
To put it a different way: If the world had been blown up during the Cuban Missile Crisis of 1962, game theorists could have explained that as an unfortunate outcome — but one that was just as rational as what actually happened. Similarly, an industry that collapses into run-amok competition, like the airlines, can be explained rationally by game theorists as easily as one where cooperation is the norm.
Tyler Cowan responded with,
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.
This prompted a response from Mendal. What caught my interest was this part,
I’m sorry…I just don’t understand what Tyler means by #1-4.
Tyler’s responses 1-4 basically deal with how to refine our notion of equilibrium so that we don’t have the multiplicity of equilibria that currently plagues game theory results. The problem is most accute in games where the (stage) game is repeated many times and the ending stage is not known with certainty (these are infinite horizon games). In these types of games just about any outcome can be supported as a Nash equilibrium. Since it is accepted that whatever “solution” a game has (i.e., what outcome players are going to end up at) has to be a Nash equilibrium game theory predicts just about any outcome. A theory that predicts every outcome really isn’t a very good theory.
The thing is that Tyler’s number 4 suggests that not every possible outcome is all that common. That is people usually end up playing in certain ways again and again. In ultimatum games people tend to pick a “fair” amount and any offer below that they reject the offer of the other player even when it makes sense to accept the offer. How have economists tried to explain this? With Tyler’s number 3. Evolutionary stable strategies is one response to the multiplicity of equilibria in standard game theory.
The point is that the standard theory does have the problem noted by Mendal, but researchers are aware of it and are working on it. I personally have high hopes for evolutionary game theory. Evolutionary game theory results have suggested that economics needs to move beyond the basic assumption of Homo economicus. When this is done, some of the problems with multiple equilibria are reduced.
At the end of his article Mendal writes,
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.
Gadzooks, you mean we have to choose? We want both, and can we have a theory that is not falsified and yet consistently makes inaccurate predictions? Seems to me, such a theory would be falsified.
In his earlier model Mendal also offers this observation,
In other words, Kahneman and Smith won their 2002 prize precisely for showing that people mostly don’t behave the way that game theory assumes they do. Game theory is based on a finely honed sort of reasoning: “If I do this, then he’ll do that, then I’ll do this” ad infinitum, assessing the probability of different final outcomes. In reality, though, that’s not how most people think or make decisions.
In part Mendal is right. The problem though isn’t that game theory is “wrong”, but that the wrong assumptions are used. Instead of assuming people follow the laws of probability, game theorists should change their games to factor in how people actually do deal with uncertain events. This is where the behavioral part of Tyler’s answer comes in.
The bottom line is that yes, game theory offers a wide array of predictions. However, this is not the end of game theory. Researchers are taking game theory and bringing in new concepts that have some hope of reducing this problem and perhaps even eliminating it. With regards to Tyler’s response I’d also add that the answer doesn’t have to come from just one of the possibilities that he suggested, but each could contribute something to find the solution. Basically Mandel reminds me a little bit of Intelligent Design theorists/Creationists. They point to evolutionary theory’s inability to explain some observation and they are all too willing to throw out not only the bath water, but the baby, the bottles, diapers, kitchen sink and toilet as well.