Convergence of Bayesian learning to general equilibrium in mis-specified models

A central unanswered question in economic theory is that of price formation in disequilibrium. This paper lays the groundwork for a model that has been suggested as an answer to this question in, particularly, arrow [toward a theory of price adjustment, in: m. Abramovitz, et al. (ed.), the allocation of economic resources, stanford university press, stanford, 1959], fisher [disequilibrium foundations of equilibrium economics, cambridge university press, cambridge, 1983] and hahn [information dynamics and equilibrium, in: f. Hahn (ed.), the economics of missing markets, information, and games, clarendon press, oxford, 1989]. We consider sellers that monopolistically compete in prices but have incomplete information about the structure of the market they face. They each entertain a simple demand conjecture in which sales are perceived to depend on the own price only, and set prices to maximize expected profits. Prior beliefs on the parameters of conjectured demand are updated into posterior beliefs upon each observation of sales at proposed prices, using bayes’ rule. The rational learning process, thus, constructed drives the price dynamics of the model. Its properties are analysed. Moreover, a sufficient condition is provided, relating objectively possible events and subjective beliefs, under which the price process is globally stable on a conjectural equilibrium for almost all objectively possible developments of history.