Abstract
In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist.
Similar content being viewed by others
References
Aliprantis C.D., Tourky R. and Yannelis N.C. (2001). A theory of value with non linear prices. J Econ Theory 100: 22–72
Debreu G. (1959). Theory of Value. Wiley, New York
Glycopantis D., Muir A. and Yannelis N.C. (2005). Non-implementation of rational expectations as a perfect Bayesian equilibrium. Econ Theory 26: 765–791
Glycopantis, D., Yannelis, N.C.: On non-revealing rational expectations equilibrium. University of Illinois (2007)
Glycopantis, D., Yannelis, N.C.: Equilibrium concepts in differential information economies. In: Glycopantis, D., Yannelis, N.C. (eds.) Differential Information Economies. Studies in Economic Theory vol. 19. Springer, Berlin (2005)
Hahn G. and Yannelis N.C. (1997). Efficiency and incentive compatibility in differential information economies. Econ Theory 10: 383–411
Herves-Beloso C., Moreno E. and Yannelis N.C. (2005). An equivalence theorem for a differential information economy. J Math Econ 41: 844–856
Kreps M.D. (1977). A note on ‘fulfilled expectations’. J Econ Theory 14: 32–43
Neveu, J.: Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco (1965) (original French edition: Masson, Paris, 1964)
Podczeck, K., Yannelis, N.C.: Equilibrium theory in asymmetric information economies with infinitely many commodities. Mimeo (2005)
Radner R. (1968). Competitive equilibrium under uncertainty. Econometrica 36: 31–58
Radner R. (1979). Rational expectations equilibrium: generic existence and information revealed by prices. Econometrica 47: 655–678
Yannelis N.C. (1991). The core of an economy with differential information. Econ Theory 1: 183–198
Author information
Authors and Affiliations
Corresponding author
Additional information
We wish to thank an associate editor and two knowledgeable referees for useful comments and suggestions.
This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.
Rights and permissions
About this article
Cite this article
Balder, E.J., Yannelis, N.C. Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium. Econ Theory 38, 385–397 (2009). https://doi.org/10.1007/s00199-007-0288-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-007-0288-6