Bounded Rationality and Directed Cognition

Bounded Rationality and Directed Cognition Xavier Gabaix David Laibson MIT Harvard University and NBER∗ October 15, 2000 Preliminary and incomplete. Abstract This paper proposes a psychologically sensible bounded rationality model which can be operationalized. The model formalizes the well- known idea that cognitive resources are scarce and should be econo- mized. The model makes quantitative predictions and can be realistically applied to decision problems that require an arbitrarily large number of cognitive state variables. We test the model using experimental data, and find that it significantly outperforms the rational actor model with zero cognition costs. JEL classification: C70, C91, D80 Keywords: directed cognition, optimization, bounded rationality, heuristics, biases, experimental economics. ∗Gabaix: Department of Economics, MIT, Cambridge, MA 02142, [email protected]. Laibson: Department of Economics, Harvard University, and NBER, Cambridge MA 02138, [email protected]. We are grateful for the advice of Philippe Aghion, Abhijit Banerjee, Gary Becker, Glenn Ellison, Drew Fu- denberg, Lars Hansen, Oliver Hart, Robert Lucas, Paul Milgrom, Andrei Shleifer, Al Roth, Richard Thaler, Martin Weitzman, and Richard Zeckhauser. Our paper benefitted from the comments of seminar participants at the University of Chicago and Harvard University, and the University of Michigan. Numerous research assistants helped implement and analyze the experiment; we are particularly indebted to Guillermo Moloche and Stephen Weinberg. Laibson acknowledges financial support from the National Science Foundation (SBR-9510985), the National Institutes of Health (XXX), and the MacArthur Foundation. 1 1 Introduction Cognitive resources should be allocated just like other scarce resources. Consider the problem of a chess player who must decide what move to make. This chess player faces a tradeoff between his desire to choose well, and his desire to economize on decision time. The player should cut corners when analyzing his options, ignoring certain lines of play, even if there is a chance that he will consequently overlook some critical element of the game. Similar issues arise in almost every decision task. Where should I go to college? Which job offer should I take? Which house should I buy? In all of these problems, the decision-maker should not insist on identifying the best possible selection. Rather, he should make an educated decision and hope for the best. Often the decision-maker must make educated guesses, say when time constraints preclude a complete analysis of the available options. All economists are familiar with the arguments of the previous para- graph. Since the work of Herbert Simon (1955), economists have recognized that cognition/attention is costly and the efficient allocation of cognition is a critical element of human decision-making. This paper moves beyond such observations by providing an operational theory of cognition, which makes sharp quantitative predictions that can be empirically tested. We provide such a test in this paper. Our model has three elements: a set of cognitive operations, a set of state variables that encode the current state of beliefs, and a value function. Cognitive operations include the different categories of analysis that we use to deepen our understanding of a given problem. For example, consider the selection of an undergraduate college. Thinking more deeply about a particular college is a cognitive operation that will refine one’s estimate of the value of attending that college. For the college choice problem, we could define a long list of cognitive operations (e.g., thinking about Boston Uni- versity, thinking about Brown University, thinking about Cornell University, etc...). Cognitive state variables encode the current state of the decision-maker’s beliefs. For example, cognitive state variables will capture one’s expectations about the value of each of the colleges in one’s choice set. Naturally, one’s expectations about any given college will be revised if one devotes incremental thought to that college. Cognitive state variables will also capture one’s sense of how thoroughly each college has been considered. After dedicating hours of thought to Brown and no thought to other schools, the decision-makerwillknowthatshehaslesstolearnaboutBrownthanCor- nell. 2 The value function is used to evaluate the expected benefitofeachcog- nitive operation. For example, should the decision-maker invest additional time thinking about Boston University or Cornell? Thinking incrementally about Cornell may substantially deepen one’s knowledge about Cornell, but this information will not be useful if the decision-maker has a strong pref- erence for an urban lifestyle. There is little use thinking about an option that is unlikely to be chosen at the end of the day. The value function en- ables the decision maker to reason in such an option-theoretic way, directing thought in the most productive directions. Our value function approach uses the standard dynamic programming toolbox, but our approach does not assume that the decision-maker knows the optimal value function. Instead, we propose a modelling strategy which uses ‘proxy value functions’ which provide good approximations of the optimal value function. Just like optimal value functions, these proxy value functions encode knowledge states and evaluate the usefulness of potential cognitive operations. We argue that proxy value functions are method- ologically superior to optimal value functions because proxy value functions generate similar qualitative and quantitative predictions but are easy to work with. By contrast, optimal value functions can not be calculated for realistically complex bounded rationality problems. To model complex decisions, we propose a three-step search-theoretic decision algorithm. First, the algorithm evaluates the expected benefitof various cognitive operations. The expected benefitisrelatedtothepre- dicted likelihood that a cognitive operation will reveal information that will change the decision-maker’s planned action. Second, the algorithm exe- cutes the cognitive operation with the greatest expected benefit. Third, the algorithm repeatedly cycles through these first two steps, stopping when the cognitive costs of analysis outweigh the expected benefits. We call this the directed cognition model. This paper shows how to practically operational- ize this framework for complex decision problems with any number of state variables. To demonstrate the operation of our approach, we analyze a one-player decision problem. We then compare the results of this analysis to the decisions of experimental subjects. In this application, we effectivly use hun- dreds of continuous state variables. Nevertheless, such an application is easy to execute with our proxy value functions, though it is impossible to execute with optimal value functions. We believe that our model realizes several goals. First, our model is psychologically plausible because it is based on the actual decision algorithms that subjects claim to use. Second, the model is broadly applicable, because 3 it can be used to analyze a wide range of decision problems including se- quential games. Third the model generates precise quantitative predictions and can be empirically tested; such tests are provided in this paper using data from an experiment on Harvard undergraduates. The data rejects the rational model (i.e., zero cognition cost) in favor of our bounded rationality alternative. Our approach combines numerous strands in the existing literature on bounded rationality. First, our conceptual approach extends the satisficing literature which was pioneered by Herbert Simon (1955) and subsequently formalized with models of deliberation costs by Conlisk (1996), Payne et al (1993) and others. Second, our approach extends the heuristics literature started by Daniel Kahneman and Amos Tversky (1974) and Richard Thaler (1991). Third, our approach is motivated by experimental work by Colin Camerer et al (1994) and theoretical work by Philippe Jehiel (1995) that argues that decision-makers may solve problems by looking forward, rather than using backward induction. Fourth, our emphasis on experimental evaluation is motivated by the work of Ido Erev and Alvin Roth (1998) and Colin Camerer and Teck-Hua Ho (1999) who develop and then econometrically test learning models. In section 2 we describe our theoretical approach and motivate our use of proxy value functions. In section 3 we introduce a class of one-player decision trees and informally describe the way in which our model applies to this class of problems. In section 4 we provide a detailed description of this application. In section 5 we describe other algorithms that could be used to approximate human analysis of these decision trees. In section 6 we describe an experiment in which we asked undergraduates to solve these decision trees. In section 7 we compare the predictions of the models to the experimental results. In section 8 we discuss other implications and extensions of our framework. In section 9 we conclude. 2 The directed cognition approach to bounded rationality 2.1 A simple model of choice Consumers routinely choose between multiple goods. We begin with the simplest version of such a decision problem. The consumer must choose either good B or good C. Thevalueofthetwogoodsisnotimmediately known, though careful thought will better reveal their respective values. 4 For example, two detailed job offers may be

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