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Learning and stability of the Bayesian-Walrasian equilibrium

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  • Pesce, Marialaura
  • Yannelis, Nicholas C.

Abstract

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.

Suggested Citation

  • Pesce, Marialaura & Yannelis, Nicholas C., 2010. "Learning and stability of the Bayesian-Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 762-774, September.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:762-774
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    1. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-377, October.
    2. Dionysius Glycopantis & Allan Muir & Nicholas Yannelis, 2009. "On non-revealing rational expectations equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 351-369, February.
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    7. Allen, Beth E, 1981. "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, Econometric Society, vol. 49(5), pages 1173-1199, September.
    8. Roy Radner, 1997. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Levine's Working Paper Archive 1594, David K. Levine.
    9. Krasa, Stefan & Yannelis, Nicholas C, 1994. "The Value Allocation of an Economy with Differential Information," Econometrica, Econometric Society, vol. 62(4), pages 881-900, July.
    10. Koutsougeras, Leonidas & Yannelis, Nicholas C., 1999. "Bounded rational learning in differential information economies: core and value," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 373-391, April.
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