Learning and Convergence to a Full-Information Equilibrium are not Equivalent

Efficiency of Rational Learning with Private Information

“…As in Jun and Vives (1996), the analysis is based upon a simple linear model of a competitive market with a set of risk‐neutral firms I =[0,1]. In every period t =1,2,…, a firm i ∈ I must decide on its output before the realization of a stochastic demand is known, where inverse demand is given by p t = θ − φx t + u t .…”

“…Proposition 1 (Jun and Vives (1996). In every period t =1,2,… there exists a unique market equilibrium, at which every firm i ∈ I chooses its supply x ( i ) t according to the linear rule that is, the price expectation of firm i is given by , where The market solution described in Proposition 1 implies that the precision τ W , t of the public statistic evolves according to For an understanding of the properties of the model and the results that will be derived below, is of central importance.…”

“…Proposition 1 (Jun and Vives (1996). In every period t ¼ 1,2,y there exists a unique market equilibrium, at which every firm iAI chooses its supply x(i) t according to the linear rule…”

“…This paper analyses the welfare implications of a rational learning process in a private information environment. As in Jun and Vives (1996), the framework of the analysis is a simple infinite‐horizon model of a competitive market with linear demand and risk‐neutral firms. Firms have to form expectations regarding the next period's market price in order to reach their profit‐maximizing supply decision.…”

“…As shown by Jun and Vives (1996), the model considered here is one in which private information has no asymptotic effect on the learning process: learning will result in convergence towards the full-information rational expectations equilibrium. This result, however, does not allow for conclusions regarding the welfare properties of the learning process, even though welfare issues might be important: the fact that the full-information rational expectations equilibrium is reached only asymptotically means that throughout the learning process there are welfare losses relative to this welfare benchmark.…”