Rational Expectations and Rational Learning (original) (raw)

Bounded Rationality and Learning in Complex Markets

Handbook of Research on Complexity

This chapter reviews some work on bounded rationality, expectation formation and learning in complex markets, using the familiar demand-supply cobweb model. We emphasize two stories of bounded rationality, one story of adaptive learning and another story of evolutionary selection. According to the adaptive learning story agents are identical, and can be represented by an "average agent", who adapts his behavior trying to learn an optimal rule within a class of simple (e.g. linear) rules. The second story is concerned with heterogeneous, interacting agents and evolutionary selection of different forecasting rules. Agents can choose between costly sophisticated forecasting strategies, such as rational expectations, and freely available simple strategies, such as naive expectations, based upon their past performance. We also confront both stories to laboratory experiments on expectation formation. At the end of the chapter, we integrate both stories and consider an economy with evolutionary selection between a costly sophisticated adaptive learning rule and a cheap simple forecasting rule such as naive expectations.

DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES LIMITS TO RATIONAL LEARNING

A long-standing open question raised in the seminal paper of is whether or not the play of a repeated game, in the rational learning model introduced there, must eventually resemble play of exact equilibria, and not just play of approximate equilibria as demonstrated there. This paper shows that play may remain distant -in fact, mutually singular -from the play of any equilibrium of the repeated game. We further show that the same inaccessibility holds in Bayesian games, where the play of a Bayesian equilibrium may continue to remain distant from the play of any equilibrium of the true game.

Bounded rationality and learning

Economic Theory, 1994

Many have objected to the use of the Nash equilibrium (or more generally, Bayesian Nash equilibrium) concept in game theory, and similarly to the use of the rational expectations concept in the theory of competitive markets, on the grounds that the theory assumes too much sophistication and coordination of beliefs on the part of decision-markers. The papers in this volume are among those which study the implications of relaxing those assumptions. * The first author thanks the C. V. Starr Center at New York University for their generosity. 2 Indeed, associate with each play of an agent, i, a type, %. Let #~ denote the ex ante belief of player i so that #i (-[%) denotes the beliefs of player-type z~. The Kalai-Lehrer assumption requires that the true play, induced by collection {#~ (. I%)}~, be absolutely continuous with respect to the beliefs of each agent, #~ (. 1%) for each i. It is straightforward to see that this in turn implies that the set of possible types is either finite or countable, which is violated in the coin-tossing example. See Nyarko (1992) for details.

Learning non-rational expectations equilibria

Rivista di Matematica per le Scienze Economiche e Sociali, 1995

Versione definitiva pervenuta il 09/06/95 A hyperinflation model is analyzed under bounded rationality learning. Agents believe in a misspecified model which is correctly specified at the Rational Expectations Equilibrium of the model and they adjust their beliefs by means of the Least Mean Squares algorithm. Convergence of the bounded rationality learning activity to a non-Rational Expectations Equilibrium point is obtained for any set of parameters of the model.

Rational expectations equilibrium: An alternative approach

Journal of Economic Theory, 1984

We study a dynamic market process in which traders condition their beliefs about payoff-relevant parameters on past endogenously generated market data and current exogenous data. We say that a market process is informative if the beliefs of traders who receive only endogenously generated market data converge almost surely to the true parameter value. Our main result is that under standard regularity hypotheses, the generic market process is informative. We define an equilibrium as the limit points of the market process.

A General Approach to Rational Learning in Games

This paper provides a general framework for analysing rational learning in strategic situations in which the players have private priors and private information. The author analyses the behaviour of Bayesian rational players both in a repeated game and in a recurrent game when they are uncertain about opponents' behaviour and the game they are playing. The aim of the paper is to explain how Bayesian rational agents learn by playing and to characterize the outcome of this learning process. By studying the concept of`conjectural equilibrium' and analysing the process of convergence of players' behaviour, the roles played by the notions of merging and of consistency are demonstrated.

Behaviorally Rational Expectations and Almost Self-Fulfilling Equilibria

SSRN Electronic Journal, 2000

Rational expectations assumes perfect, model consistency between beliefs and market realizations. Here we discuss behaviorally rational expectations, characterized by an observable, parsimonious and intuitive form of consistency between beliefs and realizations. We discuss three case-studies. Firstly, a New Keynesian macro model with a representative agent learning an optimal, but misspecified, AR(1) rule to forecast inflation consistent with observed sample mean and first-order autocorrelations. Secondly, an asset pricing model with heterogeneous expectations and agents switching between a mean-reverting fundamental rule and a trend-following rule, based upon their past performance. The third example concerns learning-to-forecast laboratory experiments, where under positive feedback individuals coordinate expectations on non-rational, almost self-fulfilling equilibria with persistent price fluctuations very different from rational equilibria.