On expectations and stability

In many decision making situations it is necessary for the decision maker to anticipate the actions of his opponents or rivals. In the area of economics this is typically the case in a market in which a number of different brands of a particular product are sold by competing producers. This problem was first formulated and analyzed in 1838 by Augustin Cournot who made the assumption that each producer believes that his rivals will take the same actions in the current period as in the preceding period. One of the implications of the Cournot model which invites serious criticismis the fact that the decision maker never changes his strategy in spite of the fact that his forecasts about his rivals' actions are always wrong. This article considers a number of alternative models into which learning processes are incorporated. One of the main results is that the introduction of a learning rule may be detrimental to the stability of the model. More generally, in choosing among alternative formulations, it may be the case that the model which is most attractive from the point of view of decision making, may turn out to be less stable than other models. Since the reasonableness of the behavioral assumptions as well as the stability of the underlying dynamical process are desirable features of such models, the findings of this research imply the existence of methodological conflicts.