“Rational” Duopoly Equilibria

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.