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Friday, October 14, 2005

Mark Kleiman comments on Game Theory and Michael Mandel

Update: Shorter John Quiggin works fine as shorter and smarter Robert Waldmann

Shorter JQ: the word ‘rational’ has no meaning that cannot better be conveyed by some alternative term. Avoid it.

I think very highly of Mark Kleiman, but I can't understand what he thinks he is saying here. Roughly his conclusion amounts to saying that economists aren't totally confused and can be considered scientists (broadly speaking). I am an economics professor and have been exposed to this view freequently over the past 20 years. I still can't convince myself that anyone can possibly seriously believe such a thing.

Kleiman notes that game theory is a branch of mathematics. Game theorists do not necessarily claim that their models have anything in particular to do with the world we happen to inhabit. It is math as p-adic analysis is math. No one thinks that anything much in the real world can be be analysed using p-adic numbers (the real world can pull some funny tricks, Gauss and Lobachefsky thought that non Euclidean geometry was the purest of pure math). So far so good. I have no problem with given John Nash a Fields medal.

Separately one can consider considering the "hypothesis" that the world is in Nash equilibrium (Von Neuman for one was quite sure this was not true even of zero sum games). I use the scare quotes because, as noted by Kleiman, this alleged hypothesis has no implications without assumptions about peoples aims. In some experimental settings it seems reasonable to assume that people are largley motivated by the desire for prizes and also eager to not seem totally stupid. This rather weak claim about motives is enough to test the hypothesis that they have such a combination of motives and are rational in the sense that they play Nash equilibrium strategies (from now on I will just write rational)

As noted by Kleiman experimental results strongly reject the Nash equilibrium hypothesis. Thus Nash equilibrium is a mathematical concept. With assumptions about aims, which basically everyone considers reasonable, one can derive testable implications of the hypothesis that the world is in Nash equilibrium. These implications are inconsistent with the data. This makes game theory a branch of mathematics which gave rise to a false hypothesis in the social sciences.

Kleiman, however, seems to feel that the developement and rejection of a theory has not effect on its scientifid standing or usefulness. Roughly Kleiman agrees that people are not rational. For game theory to be useful to social scientists it is necessary that people be fully rational (apparently tiny deviations from 100% rational 100% of the time often completely eliminate implications of the theoretical analysis). This seems to me to imply that one can't use game theory as a guide when studying society. The implications might or might not correspond to reality. Somethimes you get the right answer with game theory. Sometimes you get the right answer flipping a coin. Neither is a reasonable approach to trying to understand the world.

Kleiman's positive claim is qualified to the extent that it is almost meaningless, but does manage to be meaningful enough to be false "In terms of real-world applications, if I want to act rationally (in the economist's sense of that term) myself, and have reason to think that someone I'm interacting with will also act more or less rationally, then game theory can help me figure out my optimal strategy."

This is actually a statement about game theory. Roughly if standard game theory implies I should do something if everyone is 100% rational then I should do something like that if people are more or less rational. I suppose I have to admit that game theorists (Roy Radner in particular) have proven the useful theorem that this is totally absolutely not true at all. It is well known from theory that tiny deviations from rationality can cause huge differences in outcomes and in optimal strategies. Unfortunately it is not possible to define all possible small deviations from rationality so positive implications of "more or less rational" have not been developed. It is however known that analysis of Nash equilibria can be totally misleading if people are a tiny bit irrational in some arbitrary ways of being irrational which were chosen for tractability.

My main concern was to understand when I should " someone I'm interacting with will also act more or less rationally,". It seems to me that the thing do do would be to solve for a Nash equilibrium,
then use data to find out what happens in such situations,
then my empirical analysis shows that the outcome in situations like this corresponds to the Nash equilibrium use the game theoretic analysis to predict the outcome in situations like this.

This is what economists do. However there is a more efficient strategy which is effective in solving exactly the same problems.
When you want to figure out what happens in some situation use data to find out what happens in such situtations. Since we know that "All Nash equilibria have this property" doesn't imply "the real world has this property" the game theory adds nothing to raw data analysis.

This, by the way, is my personal experience when I have mixed game theory and empirical work.

back to Kleiman "The Nash Equilibrium, the Prisoner's Dilemma, the difference between one-play and repeated games, the difference between constant-sum and variable-sum games, first-mover advantage (or disadvantage), focal points: these are all vital tools in any analyst's toolkit. Mandel can take them away from me and my colleagues only by prying them from our cold, dead fingers."

I disagree on Nash Equilibrium (when it comes to game theory Nash equilibrium is most of it). The Prisoner's Dilemma is a game in which clear implications of game theory are correct predictions only of the behavior of economics PhD candidates. In theory there is a huge huge difference between fixed sum and variable sum games. This mathematical result has no noticible verified implications. Focal points are work of Schelling (brilliant and empirically confirmed). However, they are not respectable game theory (maybe the problem is that the idea is contaminated by correspondence to mere reality). The other two points are negative claims. It is not always an advantage (or a disadvantage) to move first and different situations (one shot or repeated) make a difference. Some theoretical results are of the form that finitely repeated games are like one shot games (true for the prisoner's dilemma). The second law of thermodynamics guarantees that the game we are all playing won't last forever. Infinitely repeated games can't fit in this particular universe (oddly I hadn't thought of this when Brad DeLong told me). The fact that analysis of such games is very common in applied game theory shows, to me, that people delibarately avoid the implications of game theory knowing them to be false and prefer to make impossible assumptions in order to reconcile game theory with reality.

Now I stress that I have no particular complaint about Kleiman. His position is the standard view in the field of economics. I am regularly amazed that people can say such things. Look at the definition of a degenerative research program, look at economic theory, try to find any difference.

1 comment:

Anonymous said...

maybe I understood the interpretation of an infinatly repeated game wrong but I thoguht the infinatly repeated game analysis of game theory (changing some parameters, that is making cooperation harder mainly) hold for games which can be played some probabilitic number of times.

so for example lets say that at any given round there is a 0.1% chance that the game will end, the I thought we could look at the situation as an infinatly repeated game and that there was even a way of putting the .1% in there (through i forget which)

this is just a note on why the thermodynamics comment is irrelevant. but mostly it is to check that i have not forgotten all my game theory.