"Rational" Duopoly Equilibria

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Abstract
This paper examines duopoly models in which each firm tries to guess the reaction of its rival to a change in its output. We seek equilibria in which the guesses are accurate, or “rational.” For static models we discover that many output combinations (X, Y) can fit into such equilibria and that our concept of “rationality” must necessarily be one-sided: if a firm has accurate expectations at (X, Y) about its rival's reactions, the competitor's reactions cannot themselves be based on “rational” calculations. Turning to a dynamic model, we find that an oversupply of solution pairs continues to be a problem.

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