Does bounded rationality lead to individual heterogeneity? The impact of the experimentation process and of memory constraints

In this paper we explore the effect of bounded rationality on the convergence of individual behavior toward equilibrium. In the context of a Cournot game with a unique and symmetric Nash equilibrium, firms are modeled as adaptive economic agents through a genetic algorithm. Computational experiments show that (1) there is remarkable heterogeneity across identical but boundedly rational agents; (2) such individual heterogeneity is not simply a consequence of the random elements contained in the genetic algorithm; (3) the more rational agents are in terms of memory abilities and pre-play evaluation of strategies, the less heterogeneous they are in their actions. At the limit case of full rationality, the outcome converges to the standard result of uniform individual behavior.

Money and prices in models of bounded rationality in high inflation economies

This paper studies the short run correlation of inflation and money growth. We study whether a model of learning can do better than a model of rational expectations, we focus our study on countries of high inflation. We take the money process as an exogenous variable, estimated from the data through a switching regime process. We findthat the rational expectations model and the model of learning both offer very good explanations for the joint behavior of money and prices.

Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

Approximate knowledge of rationality and correlated equilibria

We extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. Wereplace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probability p or more. We show that behavior in this case constitutes a kind of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one,with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interimtypes, to games of incomplete information, as well as to the case of non-common priors.

Stock market volatility and learning

Introducing bounded rationality in a standard consumption-based asset pricing model with time separable preferences strongly improves empirical performance. Learning causes momentum and mean reversion of returns and thereby excess volatility, persistence of price-dividend ratios, long-horizon return predictability and a risk premium, as in the habit model of Campbell and Cochrane (1999), but for lower risk aversion. This is obtained, even though our learning scheme introduces just one free parameter and we only consider learning schemes that imply small deviations from full rationality. The findings are robust to the learning rule used and other model features. What is key is that agents forecast future stock prices using past information on prices.

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs up to level li about the state of nature coincide, weobtain quotient type spaces that are typically smaller than the original ones, preserve basic topologicalproperties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash(li; l-i)-equilibria capture players inability to distinguish types belonging to the same equivalence class.The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustratethe constructions.

Choice by sequential procedures

We propose a rule of decision-making, the sequential procedure guided byroutes, and show that three influential boundedly rational choice models can be equivalentlyunderstood as special cases of this rule. In addition, the sequential procedure guidedby routes is instrumental in showing that the three models are intimately related. We showthat choice with a status-quo bias is a refinement of rationalizability by game trees, which, inturn, is also a refinement of sequential rationalizability. Thus, we provide a sharp taxonomyof these choice models, and show that they all can be understood as choice by sequentialprocedures.

Simple models for multi-attribute choice with many alternatives: When it does and does not pay to face tradeoffs with binary attributes

Working Paper no longer available. Please contact the author.

One, two, (three), infinity: Newspaper and lab beauty-contest experiments

"Beauty-contest" is a game in which participants have to choose, typically, a number in [0,100], the winner being the person whose number is closest to a proportion of the average of all chosen numbers. We describe and analyze Beauty-contest experiments run in newspapers in UK, Spain, and Germany and find stable patterns of behavior across them, despite the uncontrollability of these experiments. These results are then compared with lab experiments involving undergraduates and game theorists as subjects, in what must be one of the largest empirical corroborations of interactive behavior ever tried. We claim that all observed behavior, across a wide variety of treatments and subject pools, can be interpretedas iterative reasoning. Level-1 reasoning, Level-2 reasoning and Level-3 reasoning are commonly observed in all the samples, while the equilibrium choice (Level-Maximum reasoning) is only prominently chosen by newspaper readers and theorists. The results show the empirical power of experiments run with large subject-pools, and open the door for more experimental work performed on the rich platform offered by newspapers and magazines.

Take-the-best and other simple strategies: Why and when they work 'well' in binary choice

The effectiveness of decision rules depends on characteristics of bothrules and environments. A theoretical analysis of environments specifiesthe relative predictive accuracies of the lexicographic rule 'take-the-best'(TTB) and other simple strategies for binary choice. We identify threefactors: how the environment weights variables; characteristics of choicesets; and error. For cases involving from three to five binary cues, TTBis effective across many environments. However, hybrids of equal weights(EW) and TTB models are more effective as environments become morecompensatory. In the presence of error, TTB and similar models do not predictmuch better than a naïve model that exploits dominance. We emphasizepsychological implications and the need for more complete theories of theenvironment that include the role of error.

Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Rational reasoning or adaptive behavior? Evidence from two-person beauty contest games

Many experiments have shown that human subjects do not necessarily behave in line with game theoretic assumptions and solution concepts. The reasons for this non-conformity are multiple. In this paper we study the argument whether a deviation from game theory is because subjects are rational, but doubt that others are rational as well, compared to the argument that subjects, in general, are boundedly rational themselves. To distinguish these two hypotheses, we study behavior in repeated 2-person and many-person Beauty-Contest-Games which are strategically different from one another. We analyze four different treatments and observe that convergence toward equilibrium is driven by learning through the information about the other player s choice and adaptation rather than self-initiated rational reasoning.

A characterization of sequential rationalizability

A choice function is sequentially rationalizable if there is an ordered collection of asymmetric binary relations that identifies the selected alternative in every choice problem. We propose a property, F-consistency, and show that it characterizes the notion of sequential rationalizability. F-consistency is a testable property that highlights the behavioral aspects implicit in sequentially rationalizable choice. Further, our characterization result provides a novel tool with which to study how other behavioral concepts are related to sequential rationalizability, and establish a priori unexpected implications. In particular, we show that the concept of rationalizability by game trees, which, in principle, had little to do with sequential rationalizability, is a refinement of the latter. Every choice function that is rationalizable by a game tree is also sequentially rationalizable. Finally, we show that some prominent voting mechanisms are also sequentially rationalizable.

Imitation of succesful behavior in Cournot markets

In an experimental standard Cournot Oligopoly we test the importance ofmodels of behavior characterized by imitation of succesful behavior. Wefind that the players appear to the rather reluctant to imitate.