"Inside  every small problem is a large problem struggling to get out."

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Respond to the question: applicability of game theory?

 05/02/2001 08:34 PM by Rodrigo; applicability of game theory
Well, I wouldn't be so hard on game theory. Many people criticize it for its informational requirements. Playing the devil's advocate, I'd tell a story. When you cross a street, you mentally solve a highly nonlinear stochastic partial differential equation whose solution is not yet known. Nevertheless, you're able to solve it without knowing it, even if you don't know any math. The informational requirements are huge. You'd have to know the distribution of cars passing by your path across the street, their velocity, you'd have to guess whether the drivers see you or not; even you don't know the true distribution, you'd have to simulate a large sample and apply the central limit theorem,...lots of things. The point is, you act as if you knew all of these informational requirements.

Clearly the equation above is not the natural law that rules the phenomenon of crossing the street, but it describes it within a logical language.

The mathematical model of a game is a description (in terms of symbols within a consistent logical system) of what is the likely thought process in our minds and our relation with others. It doesn't have to describe the true process, but have to be able to explain the result.

Even in physics, for instance, cinematics, nobody expects the models to uncover the true laws of movement in the nature.

Even if we don't agree on the validity of this argument, we still may relax many informational requirements, like, for instance, rationality. many models deal with bounded rationality. At one extrem, we could assume that knightian uncertainty is a better model, since it allows us to have beliefs about things and we in addition don't have to feel 100% confident on that belief, and we could even preclude beliefs about beliefs.

I think you're right when you say that some models don't have any intuitive appeal. However, I thing that many of them have a reasonable degree of intuitive appeal, provided we understand that mathematics, the language of game theory, is indeed a language, like Portuguese or Esperanto (though more perfect, but not totally perfect). Even in our own language, we're not able to express perfectly what goes through our mind. But this doesn't make us think that our language has no intuitive appeal as a description of what really goes inside us.

We usually tend to take the math description of the game for the economic content of the game theoretic model. If we think this way, we'll always conclude that informational requirements are excessive (each parameter of the model, and each statement about paraemters, is a piece of informational requirement). But when we understand that the model is just a "mathematical representation" of a phenomenon, not the phenomenon itself, then we're able to realize the potential for applicability and its usefulness.
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