Learning and stability of the Bayesian-Walrasian equilibrium

Under the Bayesian-Walrasian Equilibrium (BWE) (see Balder and Yannelis, 2009), agents form price estimates based on their own private information, and in terms of those prices they can formulate estimated budget sets. Then, based on his/her own private information, each agent maximizes interim expected utility subject to his/her own estimated budget set. From the imprecision due to the price estimation it follows that the resulting equilibrium allocation may not clear the markets for every state of nature, i.e., exact feasibility of allocations may not occur. This paper shows that if the economy is repeated from period to period and agents refine their private information by observing the past BWE, then in the limit all agents will obtain the same information and market clearing will be reached. The converse is also true. The analysis provides a new way of looking at the asymmetric equilibrium which has a statistical foundation.