Economic and Game Theory
|"Inside every small problem is a large problem struggling to get out."|
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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.