A Note on the Consistency of Game Theory
Abstract
It has been claimed in the literature that classical game theory is inconsistent, since it (implicitly) assumes that all players are rational and that this is common knowledge among them, while these two assumptions seem to be contradictory. The purpose of this note is to suggest a framework which allows the formalization of these implicit axioms in a consistent way. The main idea is to distinguish between conceivable and possible states of the world, while both exist as formal objects in the theory. Thus we may require that the players would make rational choices only at possible states of the world, and that this fact be common knowledge at all (conceivable) states, where the impossible ones are present in the model for the sole purpose of formally presenting the players' reasoning. It seems that the new concept of possible states of the world is an analytical tool which may have further (theoretical) applications.