Download Deliberation cost as a foundation for behavioral economics

Deliberation Cost as a Foundation for Behavioral Economics
Mark Pingle
“Once one introduces into the subjective expected utility maximization Eden the snake of boundedness, it
becomes difficult to find a univocal meaning of rationality, hence a unique theory of how people
will, or should, decide. Economics, and the social sciences generally, will never have the
certainty of natural science.”----Herbert A. Simon, 2000.
Introduction
What is behavioral economics? Why is the word behavioral necessary? Why is the word economics
not sufficient? So much research could fall under the umbrella of behavioral economics that the
description may not have much meaning. What distinguishes behavioral economic research? The thesis
explored here is that “deliberation cost” a distinguishing feature upon which behavioral economics can be
founded as a useful field of economics.
In his Nobel Lecture, Gary Becker (1993) describes the “rational choice model” as the “economic way
of looking at behavior.” He emphasizes that the rational choice model is an analytical method, as opposed
to being a behavioral postulate. People may be modeled as “selfish, altruistic, loyal, spiteful, or
masochistic.” What is fundamental to the method is the assumption that “individuals maximize welfare
as they receive it.” The maximization assumption greatly simplifies the analysis, for it allows one to
ignore as inconsequential the process the decision-maker uses to find the maximum. In the rational choice
model, behavior is an outcome (the choice), not a process. Explaining behavior involves delineating how
changes in the decision environment affect the optimal choice, and this has proven to be useful.
In the rational choice model, resource scarcity is a central feature. It is resource scarcity that creates
tradeoffs, and therefore costs. Economic analysis often amounts to examining how changes in various
environmental factors influence the allocation of the scarce resource. If we abstract from reality and
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assume resources are not scarce, then most of economics goes away because no choices must be made.
Recognizing that resources are scarce is fundamental to economics, and one way to distinguish economic
analysis from other social science analysis is to say economics examines the implications of resource
scarcity.
One might think moving beyond the rational choice model to examine the decision-making process is
to move beyond economics. However, examining the decision process can be motivated by the desire to
recognize and explore the implications of cognitive scarcity, so doing so is not outside the realm of
economics. Cognitive scarcity forces a decision-maker to how to allocate cognition, and this implies a
deliberation cost is incurred when a set of alternatives is evaluated.1 If we abstract from reality and
assume cognition is not scarce, we are in the world of the rational choice model. There is no reason to
examine the decision process, for unlimited cognition ensures that the optimal outcome is obtained.
However, once we recognize cognitive scarcity and the deliberation cost it elicits, the economist is forced
to examine the process of decision-making, not just the outcome. It is possible, therefore, to distinguish
behavioral economics as the field of economics that explores the implications of cognitive scarcity, with
the goal of better understanding decision-making processes.
Modeling decision-making as an optimization problem has become a tradition so ingrained in
economics that attempts to do otherwise may be labeled “ad hoc.” The belief that people desire to
maximize is reasonable. However, this belief should lead economists to recognize that rational choice
theory also deserves the ad hoc label in the world where deliberation is costly, for some mode of decision
behavior could be more effective than one involving the evaluation of all alternatives.
As indicated by the opening quote from Simon (2000), in the world of behavioral economics, where
cognitive resources are scarce, there is no method for framing a decision problem that is independent of
the context. If you slip and start to fall off a cliff, which branch do you grab to try to save yourself? Do
you consider all alternatives? Do you take the time to decide how to decide? Do you apply a
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preconceived “falling off cliff” rule of thumb? The context not only influences the set of alternatives, as
in rational choice theory, but it also influences the extent to which deliberation is costly, which will tend
to affect how a choice is made.
Concluding his Nobel Lecture, Becker (1993) claims that “the rational choice model provides the most
promising basis presently available for a unified analysis of the social world.” This may be true, but it is
not likely that psychologists and sociologists will ever embrace the rational choice model because they
spend so much of their time examining the decision-making process. By forcing economics into the
realm where the process of making the choice must be considered, recognizing deliberation cost more
closely associates economics with its social science cousins. Consequently, there is reason to think that
what may ultimately do much to unify the social sciences is a behavioral economics research agenda
focused on the implications of deliberation cost.
A Canonical Decision Problem
Suppose a decision-maker’s choice x from the set of alternatives X results in the outcome y from
among the set of possible outcomes Y . Assume that the relationship between x and y is functional
so y = f ( x, a ) , where the function f (•,•) maps the set of alternatives X onto the set of outcomes Y
for the given decision-making environment described by the parameter a . For each given environment a
in the set of possible environments A , assume that the function f (•,•) reaches a unique maximum value
y (a ) at the choice x (a ) . Assume that the decision-maker has perfect knowledge of how choices affect
outcomes, or that the function f (•,•) is known.
Behaviorally, assume the objective of the decision-
maker is to make an optimal choice. That is, the decision-maker’s goal is to find x (a ) from among the
alternatives X so that outcome y (a ) is experienced when environment a is the context.
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Non-Behavioral Choice Theory
If there is no cost to sorting through the set of alternatives X , then the decision-maker can formulate
the decision problem as a mathematical programming problem. By assumption, the problem can be
solved. The solutions are x (a ) and y (a ) .
Different functional forms for the function f (•,•) will
generate different optimal choice and outcome functions x (a ) and y (a ) .
Except for the assumption that people seek an optimal choice, there is little in this choice theory that
can be described as behavioral. The assumption that the decision-maker can search through the set of
alternatives without cost greatly simplifies the analysis by allowing one to entirely abstract from the
process used to evaluate the alternatives. All decision processes are costless and all lead to the same
outcome, so the decision-maker must be indifferent to all decision processes. Ironically, economic
behavior is modeled in a manner that abstracts from the economizing process itself.
However, this non-behavioral choice theory is not trivial because the functions x (a ) and y (a ) relate
the decision environment a to the decision maker’s choice x (a ) and outcome y (a ) . In practice,
economists typically use this choice theory in one of two ways. First, the researcher may specify a
particular functional form f (•,•) believed to be relevant to a decision-making situation of interest. Then,
using the functional form f (•,•) , the predictions x (a ) and y (a ) are derived by the researcher and
offered as predictive descriptions of how the decision-maker’s choice and outcome experienced will be
related to the environment. Second, the researcher may construct the relationships x (a ) and y (a ) from
data observations, and then use these relationships to make inferences about the functional form f (•,•) .
That is, the researcher can make inferences about the decision-maker’s preferences or objectives, given
the choices and environments actually observed. The predictive power of this theory and the ability to
use this theory to infer preferences each depend upon the assumption that people make optimal choices.
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Behavioral Choice Theory
Behavioral choice theory, as defined here, arises from the fact that deliberating is costly because
cognitive resources are scarce.
The production possibilities frontier is a familiar tool used to examine the implications of resource
scarcity. If cognition is a valuable, then it must produce something. While cognition may be an input in
the production of every good, Figure 1 is presented under the assumption that some goods require
cognition and other goods do not. The horizontal axis measures the production of goods that require
cognition. Assume point A represents an outcome in a world where deliberation is free. In this world,
the optimal point A can be found without sacrificing any goods that require the application of cognition.
Now, consider a world where a fixed amount of cognition must be applied to evaluate the set alternatives.
The deliberation cost is the loss of cognitive goods that could be produced with the cognition that must be
applied to evaluating the set of alternatives. This shifts the production possibilities frontier to the left, as
shown in Figure 1. The deliberation cost reduces the size of the production possibilities set and makes
the new best choice point B.
(Insert Figure 1 about here)
Of course, point B does not yield as much satisfaction as point A. Moreover, in the shaded area above
and to the right of point B, there are points in the old production possibilities set in addition to point A
that yield more satisfaction than point B. It is apparent that the size of this shaded area depends upon the
size of the deliberation cost. If the deliberation cost is very small, then point B is very near point A. In
this case, the deliberation cost is rather inconsequential, for the outcome B yield satisfaction close to
outcome A. However, the deliberation cost becomes more consequential as it grows larger. As more
cognitive resources must be expended to evaluate the set of alternatives, the choice (point B) will be
further from the choice (point A) that would be made if deliberation were costless, and the outcome
experienced by the decision-maker becomes less satisfying.
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The general point is that cognitive scarcity binds rationality, and the effectiveness of rationality as a
process of thought is directly related to the size of the deliberation cost that must be expended to
completely evaluate the set of alternatives. Conlisk (1988) succinctly makes this point when he says, “To
say optimization cost is positive is to say rationality is bounded.”
Models of bounded rationality can
therefore be thought of as descriptions of how humans cope with the deliberation cost that arises from
cognitive scarcity.
Non-behavioral rational choice theory could still be applied if one could easily construct a model of
bounded rationality by folding the deliberation cost into the decision-maker’s optimization problem so as
to fully account for it. Baumol and Quandt (1964) speak of an “optimally imperfect” decision, where one
sets the marginal cost of “more refined calculation” equal to its “gross yield.” However, they do not
present an optimization problem that folds in optimization cost, and the logical difficulty with writing one
down is that the higher order problem would also be costly to solve. The inability to formulate an
optimization problem that folds in the cost of its own solution has become known as the “infinite regress
problem,” with Savage (1954) appearing to be the first to use the regress label.2 The presence of a
deliberation cost is responsible for the infinite regress problem, and the infinite regress problem is what
spawns the need for a behavioral choice theory that goes beyond rational choice theory.
Frank Knight (1921, p.67) was one of the first (if not the first in print) to recognize that the presence of
a deliberation cost motivates the use of methods of choice that do not involve evaluating all alternatives.
He said, “It is evident that the rational thing to do is to be irrational, where deliberation and estimation
cost more than they are worth.” That is, the use of non-rational modes of decision-making can be
explained behaviors people choose to economize on the use of scarce cognitive resources. There is a
niche for behavioral economics to explain how people “decide how to decide.”
The As-If Hypothesis
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While Knight (1921) recognized that deliberation tends to be costly, he argued that the rational choice
model would nonetheless be adequate for many purposes because maximization is the decision-maker’s
goal. Friedman’s (1953) “as-if hypothesis” has become the definitive statement of this perspective. The
hypothesis is that, while any of a myriad of decision methods might be used to find the optimal choice,
the rational choice model has its predictive power because the decision process does lead the decision
maker to the optimum. The decision-maker behaves “as-if” he evaluates all alternatives with zero
deliberation cost, even though he may not. Using the terminology of Simon (1978), we would say the
decision-maker is “substantively rational,” so the degree of to which the process is “procedurally rational”
is of no consequence.
In a panel discussion (Archibald, Simon, and Sameulson, 1963), Herbert Simon commented, “The
expressed purpose of Friedman’s principle of unreality (or as-if hypothesis) is to save Classical theory in
the face of the patent invalidity of the assumption that people have the cognitive capacity to find a
maximum.” He went on to say the “unreality of premises is not a virtue in scientific theory but a
necessary evil---a concession to the finite computing capacity of the scientist.” Ironically, we researchers
use simplifying assumptions because of our limited cognitive capacity, but often do not expect that the
decision-makers we create in our models will do the same. Simon proposed that we should replace the
as-if hypothesis with the “principle of continuity of approximation,” which recognizes, “if the conditions
of the real world approximate sufficiently well the assumptions of the ideal type, the derivations from
these assumptions will be approximately correct.”
The as-if hypothesis implies that the decision-maker can so effectively cope with cognitive scarcity that
deliberation cost is near zero. This potentially testable hypothesis may or may not represent reality. The
principle of continuity of approximation indicates, as shown in Figure 1, the rational choice model will be
effective when the decision-maker can effectively make cognitive scarcity a non-binding constraint. In
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this case, behavioral economics can contribute by explaining how this is accomplished. Alternatively, if
the deliberation cost prevents the rational choice model from being a useful approximation, then
behavioral economics can contribute by offering another model that explains how the decision-maker will
procedurally cope with the deliberation cost in the given context.
Transactions costs and Deliberation Costs: A parallel
When transactions can occur without cost, institutional form is insignificant in terms of determining
the allocation of resources and economic efficiency. North (1994) gives Coase (1960) credit for
extending neoclassical theory by recognizing, “When it is costly to transact, then institutions
matter.” North notes that “it is costly to transact,” and presents this fact as the foundation for a
theory of institutions that explains the existence of institutions and their forms as responses to the
fact that it is costly to transact.
Analogously, the notion that “it is costly to deliberate” can be considered a fundamental fact,
and this fact can be used to extend neoclassical theory. When a set of alternatives can be
considered without cost, then there is no need to consider the procedural behavior the decisionmaker. However, once we recognize that it is costly to deliberate, the method used to make a
decision matters. A theory of decision-making can therefore be constructed that explains the
existence and forms of particular modes of decision-making as responses to the fact that it is
costly to deliberate.
Models of Bounded Rationality
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Models of bounded rationality describe individual decision-making in a way that recognizes the fact
that it is costly to deliberate.
Conlisk’s (1988, 1995, 1996) Deliberation Technology
One approach to recognizing deliberation cost is to introduce it at one level, but ignore it at a higher
level. This approach is suggested by Conlisk (1988, 1995, 1996). While ignoring deliberation cost at any
level can be considered ad hoc, the advantage of this approach is that classical optimization methods can
still be used.
As presented by Conlisk (1995), a deliberation technology allows the decision-maker to develop the
approximation X (T ) to the unboundedly rational choice X * if the cognition level T is applied. At one
extreme lies the approximation X (0) that results from some rule of thumb (e.g., randomly choose from
the set of alternatives) that can be applied without expending any cognition. As more cognition is
applied, the approximation improves, with the assumption that X (∞ ) = X * , or that unlimited cognition
yields optimality.
The outcome experienced by the decision-maker is Π ( X (T )) . Assuming that marginal deliberation
cost is the constant C and is measured in the same units as the outcome, the problem for the decisionmaker is to maximize Π ( X (T )) − CT by choosing the level of cognition T to apply to the problem.
The optimal level of cognition to apply is the level T * that equates the marginal benefit of cognition
with the marginal cost. That is, Π ' ( X (T *)) = C .
The model can be used to examine how the optimal allocation of scarce cognition will affect the
location and quality of the choice. The degree of substantive rationality can be measured by the distance
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| X (T *) − X * | , and it is determined endogenously when the optimal level of cognition T * is chosen.
Under standard assumptions, one would expect a decline in the marginal deliberation cost C to increase
the optimal level of cognition T * , which would improve the approximation X (T ) . Besides examining
the impact of the deliberation cost, the influences of other context factors may examined by modeling
their impact as changes in either the objective function Π (•) or in the approximation function X (•) .
Conlisk (1996) applies this deliberation technology to explain market fluctuations.
To not ignore deliberation cost at some level, one must abandon optimization to some degree. Conlisk
(1995) notes that the standard alternative to closing a model by assuming costless optimization is to close
it by assuming some adaptive “rule of thumb” determines the choice. This suggests observed adaptive
behavior can be explained as a response to the fact that people cannot costlessly optimize. Whereas the
deliberation cost binds decision-maker from the optimum in a “one-shot” decision, adaptation gives the
decision-maker the opportunity to approach the optimal choice over time because of its lower cost of
implementation, as the following models illustrate.
Simon’s (1955) Behavioral Model of Rational Choice
Herbert Simon (1955) took on the task to “replace the global rationality of economic man with a kind
of rational behavior that is compatible with the access to information and computational capacities that
are actually possessed.” His approach was to look at how humans actually make decisions. Simon
identifies the traditional “global model of rational choice” as the description of the ideal “economic man,”
and a defining characteristic of this model is the assumption that all alternatives are evaluated before a
choice is made. In contrast to this model, Simon claims actual human decision-making typically involves
the sequential examination of alternatives.
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The contrasting views of decision-making described by Simon (1955) can be associated with optimum
seeking “search plans” mathematicians have defined. Wilde (1964) describes a “simultaneous” search
plan as one that specifies the location of every “experiment” before any results are known, whereas a
“sequential” search plan permits future experiments to be based upon the observed outcomes of past
experiments. The global model of rational choice implies a comprehensive simultaneous search plan,
whereas Simon’s claim is that humans tend to use sequential search plans.
Once one recognizes that cognitive scarcity elicits a deliberation cost, it is not difficult to understand
why humans would choose to utilize sequential search methods. A basic result of mathematical search
theory is that sequential search is more effective than simultaneous search because of the information
obtained from past outcomes allows one to strategically choose the next experiment. Effectiveness is
commonly measured by the size of the “region of uncertainty” that contains the optimum after a given
number of experiments. When there is no cost to applying the search plan, which is true for the ideal
economic man, the efficiency of the search plan is of no concern. However, the prevalence of sequential
search among humans testifies to the existence of a deliberation cost.
If we accept that human decision-making can be modeled using a sequential search algorithm, we must
also accept that people apply some kind of “stopping rule” to determine which alternative is ultimately
accepted as the choice. Simon (1955) introduced the “aspiration level” concept the stopping rule.
Behaviorally, the assumption is that people set a goal for their satisfaction level and stop searching when
goal is achieved. The sequential search algorithm together with a stopping rule can be called a decision
process. Such a decision process is analogous to what engineers and computer programmers call a
“solution,” a design or method that achieves a certain desired end, even though it may not be ideal.
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When it is costly to search, stopping sooner is better, but not if significant benefits from further search
are foregone. Thus, a search algorithm will be more effective if it can somehow effectively estimate the
marginal benefit of an additional experiment so that it can be compared to the marginal cost. Simon
(1955) addressed this problem by suggesting that the decision-maker’s aspiration level might change as
feedback from the search was obtained. In particular, he suggested that the aspiration level would rise
when satisfactory alternatives are easy to find, and would fall when satisfactory alternatives are hard to
find.
Day’s (1963, 1978) Recursive Programming
Recursive programming provides an alternative explanation for how people with cognitive limitations
economize, or evaluate a set of alternatives. The behavioral premise is that people do maximize, but
cognitive scarcity leads the decision-maker to simplify a more complex problem by decomposing it into a
sequence of simpler problems. The form of the problem at each stage in the sequence is conditioned by
past decisions and by observed changes in the decision environment. Solutions at each stage are optimal.
However, because each stage examines only a fraction of the available set of alternatives, the decision
sequence need not converge to a global optimum. In fact, recursive programming models tend to display
rich patterns of behavior, including the oscillation and “phase changes” often observed in reality.
A recursive program consists of three components: a “data operator,” an “optimizing operator,” and a
“feedback operator.” The optimizing operator determines the values of the choice variables based upon
the “objective” of the decision-maker, the set of alternatives defined by the “constraint functions,” and the
“data” or parameter values of the model. The optimizing operator could be a linear programming
algorithm, or some nonlinear programming method. The data operator defines how the data entering the
decision-maker’s objective function and constraint functions depend on the decision-maker’s current
state. The data operator can be used to model cognitive scarcity because it can narrow the size of the set
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of alternatives to any desired degree. The feedback operator specifies how the succeeding state of the
system depends upon the current optimal decision variables, the data, and the previous state.
The degree of rationality present in a recursive program can be varied. At one extreme, the decisionmaker does not evaluate alternatives at all, and decision’s are made using some rule of thumb. In this
case, the model can be considered a system dynamics model of the Forrester (1961) type. Even though
there is no rationality in a system dynamics model in the form of a conscious evaluation of alternatives,
effective adaptation rules can lead the decision maker to a high quality choice over time.
Bounded rationality disappears and unbounded rationality appears as the decision-maker’s cognitive
capacity increases so that the recursive program approaches a dynamic program that is optimally
controlled. Bellman’s principle of optimality tells us that an optimal choice must be made at each stage in
a dynamic program in order for the dynamic sequence of choices to be optimal overall. The unboundedly
rational decision-maker has the cognitive capacity to look forward and solve the dynamic program using
backward induction. That is, the unboundedly rational thinker can effectively anticipate how present
choices will affect the future. The unboundedly rational decision-maker using a recursive program
would optimally choose the optimizing and data operators. Recursive programs typically represent
bounded rationality because the data and optimizing operators are fixed, and can be thought of as the
simplifying and adaptive “rules of thumb” used by the decision-maker.
Lippman and McCall (1976) Search Model and Bayesian Updating
Any economist who examines Figure 1 can readily identify the optimal choice. It is the point where
one finds an indifference curve tangent to the set of alternatives.
However, if one takes away the
indifference mapping, it is no longer obvious where to find the best point in the triangle of alternatives.
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In the real world, it is unlikely that decision-makers formulate indifference mappings, if not for any other
reason than the cost of doing so would likely exceed the benefit. Suppose a decision-maker knows his
preferences in the sense that the ordinal value of any alternative can be ascertained, but suppose an
indifference mapping cannot be readily constructed. How might the decision-maker compare
alternatives?
After sampling one alternative, the decision-maker will not know whether or not the next alternative
sampled will be better. Thus, accepting the first sample as the choice is involves chance. Because it is
unlikely that the decision-maker knows the distribution of outcomes associated with the set of
alternatives, accepting any sample alternative as a choice is not just risky, it is uncertain. If comparing
alternatives were not costly, there would be no uncertainty, for any number samples could be taken to
help identify the best choice. The uncertainty arising in this basic choice problem arises because
deliberation cost precludes unlimited sampling. That is, in the world where deliberation costs are
present, all decision-making is under uncertainty.
Savage’s (1954) subjective expected utility framework is the traditional model for how a decisionmaker with unbounded rationality will behave under uncertainty. In Savage’s model, the decision-maker
subjectively creates an outcome distribution. This distribution provides probability weights to each of the
possible outcomes, which allows the decision-maker to construct an expected utility maximization
problem. The model is attractive because a change in the decision-maker ’s subjective estimate of the
form of the outcome distribution will change the predicted choice in a reasonable way. A problem with
this framework, however, is that presence of a deliberation cost may prevent its application.
An alternative that allows one to recognize a deliberation cost is to assume the decision-maker draws
sequentially from the set of alternatives, using some stopping rule to determine when the choice is made.
If the distribution of outcomes in known, if the draws are independent, and if the cost of making one draw
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is constant, then an optimal search strategy exists. (See Lippman and McCall (1976).) The optimal
strategy for a risk-neutral searcher is to continue searching as long as the expected marginal benefit of
another search exceeds its expected marginal cost. A “reservation” outcome comparable to Simon’s
(1955) aspiration level is implied. The decision-maker should stop once an alternative is found that
exceeds the reservation outcome, meaning there should be no desire to “recall” a draw made previously
and accept it as the choice.
Experimental studies designed to examine human subject behavior in this basic search model find that
the model has predictive power (e.g Schotter and Braunstein, 1981; Harrison and Morgan, 1990;
Offerman and Sonnemans, 1998). However, there is also evidence that subjects search too little and
subjects do want recall and chose previously examined alternatives (Schotter and Braunstein, 1981;
Kogut, 1990). In an environment like this, Sonnemans (1998) examined the strategies of search
individuals used. He found most subjects did not use reservation prices as suggested by the optimal
strategy, but rather used strategies which combined a focus on earnings (like bounded rational satisficers
would do) and a focus on the last or best alternative (like optimizers would). He also observed
“remarkable” individual differences in subject behavior.
One might not expect a model using a stable distribution of outcomes to perform well because the
subjective form of any distribution used by real world decision-makers is likely to change as additional
sample draws provide information. Indeed, the term “learning” in the economics literature is often used
to describe the updating the form of a perceived probability distribution. Bayesian updating is optimal
under a variety of circumstances. Offerman and Sonnemans (1998) present an experiment where learning
from own experience is compared to Bayesian updating. They find that subjects do learn from their own
experience, but fall significantly short of ideal Bayesian updating.
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Another complicating feature of real world decision-making is that it is unlikely that any decisionmaker would sample alternatives at random. If a decision-maker’s knows his preferences are transitive
and exhibit continuity, this information can be used to narrow the search region. Also, mathematical
search theory (Wilde, 1964) indicates that random search can be outperformed by other methods in a wide
variety of circumstances. Thus, while it is clear that the presence of deliberation cost makes any decision
uncertain, it is not clear how to model choice under uncertainty when the decision-maker is not restricted
to random draws.
Roth and Erev (1995) Reinforcement Learning
Recent theoretical and experimental research in game theory has examined the roots of decision
behavior. Game theory predicts the behavior of “players” in “strategic” situations, where the outcome of
an action depends upon the behavior of one or more other players. At one end of the modeling spectrum
are traditional models where the predicted behavior is equilibrium behavior associated with unbounded
rationality and self interest. At the other end of the modeling spectrum are evolutionary game theory
models where behavior evolves (in disequilibrium) as it arises over time from a selection process, and
there need not be any conscious comparison of alternatives involved.
Much recent research has focused on explaining why people do not exhibit the rational behavior
predicted by equilibrium game theory models. For example, because something is better than nothing, the
responder in Guth’s (1982) one shot ultimatum bargaining game should accept any offer received, but
responders regularly reject offers that significantly favor the proposer. One explanation for such nonrational behavior is that the decision-maker is optimizing, but is not purely self-interested (e.g Fehr and
Gachter 2000, Bolton and Ockenflens, 2000). However, much of the “learning literature” is motivated by
the premise that observed behavior is disequilibrium behavior exhibited because the decision-maker does
not have the cognitive capacity to solve the optimization problem. By obtaining feedback from these
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disequilibrium choices, a decision-maker with an effective learning algorithm can move toward the
equilibrium behavior predicted by unbounded rationality.
Roth and Erev (1995) introduced a “reinforcement learning” model and have shown it has predictive
power. They consider learning models as lying between traditional models that assume unbounded
rationality and the evolutionary models that rely upon selection. They develop their model using two
basic principles in the psychological learning literature: (1) The law of effect (Thorndike, 1898) and (2)
the power law of practice (Blackburn, 1936). The law of effect is the notion that more successful
behavior is more likely to be repeated. The power law of practice holds that the learning curve is
steep initially, and then flattens as practice or experience is obtained.
Because it was developed for the game theory context, the decision-maker in the Roth-Erev model
chooses a strategy for play. Each player is parameterized by an initial probability distribution defined
over the available set of strategies. In a case where there is a discrete number of strategies, the strategy k
would be adopted with initial propensity q k . Each player has a probabilistic choice rule p k (t ) that
determines the probability that strategy k will chosen at time t. The reinforcement of receiving a payoff x
is given by an increasing reinforcement function R(x). The heart of the model is the updating of the
probability choice rule, which occurs after a choice is experienced. A player choosing strategy k and
experiencing reinforcement of R(x) will update the probabilistic choice rule p k (t ) for each strategy in a
manner that respects the law of effect. The functional forms used also ensure that the power law of
practice is obeyed. The single parameter in the most basic model is a measure of the speed of learning,
and this parameter can be estimated by fitting simulations of the model to available data.
An important alternative to reinforcement learning is “belief learning.” Belief learning can be
considered a higher form of rationality in that the belief learner tries to learn strategies of others so as to
better anticipate the play of others , whereas the reinforcement learner makes decisions based only upon
own experience. Beliefs are typically based on a weighted average of previous observations of what other
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players have done. The beliefs are then used to compute the expected payoffs associated with different
strategies. Erev and Roth (1998) stress that the pure belief learning model is deterministic, not
probabilistic. Subjective expected utility maximization determines the choice, not a probabilistic draw
from the set of strategies as in reinforcement learning. Roth and Erev favor probabilistic choice because
they claim it is more consistent with the law of effect, and they also note that the maximization and
information gathering requirements of belief learning implies that belief learning forces the use of more
cognitive resources.
Erev and Roth (1998) show that even a one-parameter reinforcement learning model can describe and
predict decision behavior better than static equilibrium models that assume decision-makers have the
cognitive capacity to evaluate all possible strategies prior to play. This is true for both aggregate
behavior and for the individual decisions of each player. For the data they examine, Erev and Roth
conclude a “higher rationality” belief-based model did not appear to have an advantage over “lower
rationality” reinforcement models. Camerer and Ho (1999) find that their “experience weighted
attraction” model, which combines reinforcement learning and belief learning, can explain decision
behavior better than either reinforcement learning or belief learning alone.
Explaining Observed Decision Processes as Responses to Deliberation Cost
Pingle (1992) experimentally demonstrates how the introduction of a deliberation cost can change
choice behavior. A group of human subjects who could costless use trial and error to sort through a set of
alternatives used 20 times more decision time and considered 8 times the number of alternatives as
another group that faced a deliberation cost. A measure of decision-making quality indicated that the
average choice made by subjects not facing a deliberation cost was 2.8 times better than the average
choice made by subjects facing a deliberation cost. The presence of a deliberation cost also substantially
18
increased the variability of decision performance. The standard deviation of the decision quality measure
was 30 times higher when a deliberation cost was present.
How do people respond to the fact that deliberation cost tends to reduce the quality and increase the
variability of decision performance?
An adaptive perspective suggests that decision modes will arise
that consistently produce quality decisions, while economizing on deliberation cost.
The models of
bounded rationality discussed above are decision processes that economize on deliberation cost, while
still giving decision-maker the ability to progress toward a high quality choice. Here, some other
important modes of decision-making are recognized.
Heuristics and Habit
A decision-making heuristic is any device that reduces the search necessary to find a solution to a
choice problem (Schwartz, 1998, 66).
The simplest heuristic is a habit that links a specific context to a
choice: “When in situation A make choice B.” Beyond this, heuristics tend to take three forms: (1) a
device for simplifying preferences, (2) a device for simplifying the information set, or (2) a device
simplifying the process of evaluating alternatives. Cognitive scarcity is the standard explanation for the
use of heuristics. As Simon (1986) explains:
If . . . we accept the proposition that both the knowledge and the computational
power of the decision maker are severely limited, then we must distinguish between
the real world and the actor's perception of it and reasoning about it. That is to say we
must construct a theory (and test it empirically) of the process of decision. Our theory
must include not only the reasoning processes but also the processes that generated
the actor's subjective representation of the decision problem, his or her frame.
19
Payne, Bettman, and Johnson (1988, 1993) emphasize that there tends to be a tradeoff between the
accuracy of a heuristic and the effort required to implement it. They find that people can recognize this
tradeoff as it relates to different tasks and contexts, adapting their decision strategy, though often
imperfectly. As an alternative to conscious decision, Martignon and Hoffrage (2002) suggest that simple
heuristics “owe their fitness to their ecological rationality, that is, to the way in which they exploit the
structure of their task environments.” The notion that heuristics owe their existence to evolution rather
than conscious choice offers an explanation for how decision-makers might effectively skirt deliberation
cost.
Gigerenzer and Todd (1999) show that “simple heuristics make us smart” because they take less time,
require less knowledge, and less computation. They perceive the mind as being “equipped with an
adaptive toolbox of fast, frugal, and fit heuristics.” Simple is defined so as to exclude any calculating any
probabilities or utilities, with the single attribute lexicographic rule being especially attractive. Martignon
and Hoffrage (2002) compare lexicographic, linear, and Bayesian decision heuristics, varying the
computational complexity of each from minimal, to simple, and to sophisticated. They demonstrate that
simple models are fit in a variety of contexts and often generalize to new data.
Kahneman, Slovic, and Tversky (1982) illustrate that heuristics can introduce biases in decisionmaking. As described by Payne, Bettman, and Johnson (1992, 1993), behavioral decision research has
since emerged as a subdiscipline of psychology that tests the descriptive accuracy of heuristics, or
normative theories of judgment and choice. The notion that decision-makers adaptively apply a tool box
of heuristics is an alternative to the rational choice model, an alternative that has deliberation cost at its
foundation and an alternative that simultaneously explains the decision process and ultimate choice.
Imitation
20
Conlisk (1980) theoretically demonstrated that imitation can complement optimizing in an economic
system when there is a deliberation cost. When optimizing is more expensive to apply than imitation,
then imitation and optimizing can coexist. The comparative advantage of optimizing is its ability to find
an improved choice, while the comparative advantage of imitation is its ability to economize on
deliberation cost.
Gale and Rosenthal (1999) examine a social system with less rationality by combining imitation and
experimentation. An experimenter exhibits trial and error behavior, adopting the new behavior if it yields
an improvement and reverting to the old behavior if improvement is not obtained. Imitators adjust their
action in the direction of the average agent. Under reasonable assumptions the system converges to an
equilibrium where all agents behave as predicted by the model that assumes unbounded rationality.
Pingle (1995) experimentally examined an environment where human subjects could make a choice
via imitation or choose to make a choice via experimentation. The tendency to imitate was greatest when
it was first made possible and then decreased as the same decision environment was experienced
repeatedly. Environmental change prompted increased imitation. The introduction of the opportunity to
imitate into an environment where experimentation was the only available choice method increased a
decision-making efficiency measure by more than one-third. Imitation was especially effective when an
inexperience “apprentice” could learn by watching a more experienced decision-maker. As explained by
Day and Pingle (1996), the niche for imitation is in relatively unfamiliar situations, while the niche for
experimentation is finding an improved choice when imitation is not an option or when imitating others is
not effective at obtaining improvement.
Offerman and Sonnemans (1998) also compare learning from own experience to learning through
imitation, but examine how subjects learn the form of a probability distribution that represents beliefs
about an uncertain situation. They find subjects learn both ways, but learning through imitation is more
21
effective in that the results are closer to the ideal Bayesian updating. Less successful subjects choose to
imitate more often and more successful subjects are more often imitated.
Submission to Authority
People often submit to the instructions of authorities. Why do people submit? An obvious
explanation is that the authority wields power. However, Arrow (1974) argues that power “cannot be the
sole or even the major basis for acceptance of authority” because the cost of obtaining the required power
would outweigh the benefits.
Simon (1991) notes that “intense interdependence is precisely what
makes it advantageous to organize people instead of depending wholly on market transactions.” The new
institutional analysis of Williamson (1985) and the principle-agent analysis of Hart and Grossman (1983)
are each based upon the interdependence of subordinates and authorities. While the forms of
organizations have been explained as responses to transactions costs, an information problem, or a public
goods problem, little recognition has been given to the possibility that organizations with authoritysubordinate relationships form in particular ways so that authorities can transmit decision-making rules of
thumb to subordinates to minimize deliberation cost.
Pingle (1997) experimentally examined an environment where human subjects could make a choice via
experimentation, but received a recommended choice from an “authority” (the computer). In one
experiment, subjects in different groups where given prescribed choices of different qualities. Because
the prescribed choice turned out to be an “anchor” for the typical subject’s experimentation, the quality of
the authority’s prescribed choice significantly affected the quality of decision-making. In a second
experiment, where the quality of the authority’s prescribed choice was poor, it was demonstrated that a
severe penalty for disobedience is not necessary to obtain compliance. Poorer decision-makers will tend
to comply because they are unable to make disobedience pay by finding improved choices that can offset
even a small penalty. In a third experiment, the prescribed choice evolved in that it was the best choice of
22
the previous decision-maker. While the choice of the second subject was far from optimal, the prescribed
choice was near optimal by the 10th subject, allowing succeeding subjects to experience near optimal
choices.
Deliberation Cost, Organization, and Social Interaction
North (1994) and Simon (2000) each stress the need to develop better theories of learning in
order to develop better theories of organization. Simon (2000) comments, “As human beings are
adaptive organisms and social organisms that can preserve bodies of learning …., studying their behavior
will not return us to permanently invariant laws, for human learning and social influence will continue to
change people’s ways of making rational decisions.”
Social interaction enhances opportunities to
reduce deliberation cost through imitation and though the submission to authority.
An evolutionary perspective suggests that organizations and social relationships will evolve into forms
that reduce deliberation cost. Simon (2002a) notes that all living systems share the feature of near
decomposability, meaning a more complex system can be decomposed into smaller relatively independent
subsystems. The biological explanation for decomposability is that it contributes to fitness relative to a
single complex system with a large number of highly interrelated components. Simon argues that
“modern business firms and government organizations derive much of their efficiency from conforming
to these biological principles, while inefficiency may be related to a complex (bureaucratic) system that is
not readily decomposable.” Decomposition in organizations allows independent subsystems to specialize
in the solving specific problems, which would reduce deliberation costs.
Simon (2002b) discusses that fact that people identify with groups, for example families, tribes, gangs,
corporations, government organizations, ethnicity, religion, linguistic groups, and nations. Group
23
bonding and social ties in general can be explained as a response to deliberation costs. The experience of
group members may provide rules of thumb that can reduce deliberation costs for those who submit to the
group, making independent living relatively inefficient. Fernandez and Simon (1999) find that
“identification based on professional, ethnic or other characteristics can cause individuals to apply
problem-solving strategies that match the goals or norms of the group identified with.”
Simon (1993) refers to docility as “the tendency to depend upon the suggestions, recommendations,
persuasion, and information obtained through social channels as a major basis for choice.” He goes on
to say “being docile contributes to fitness because we obtain advice (on what to choose) that is for our
own good and obtain information that is better than if we gathered it on our own.” In an unboundedly
rational world, why should a person be sociable? In the world of behavioral economics, to be more
sociable is to be more fit if the people you socialize with anchor your choices in the neighborhood of an
optimum. Alternatively, exceptionally poor life experiences can be explained as being anchored to
choices that are far from optimal by socializing with the wrong people.
Conclusion
Once a deliberation cost is recognized, the rational choice model is no less ad hoc than many others
that might be proposed. The principle of continuity of approximation indicates that the rational choice
model will be more useful when deliberation cost is low. Paradoxically, if people optimize when
deliberation is costly, it is because they do not think or reason. Optimal choice is made possible by very
effective rules of thumb. When deliberation cost is present, all choice is uncertain. If an optimal choice
is made, the decision-maker cannot know it, for knowing it requires that all choices be compared.
24
Decision-making in the face of a deliberation cost may be pursued independently or in a social context.
Models of bounded rationality typically describe how an independent decision maker copes with
deliberation cost. One approach is to limit the comparison of alternatives by satisficing, which involves
defining “good enough” in advance and searching up to that point. A second approach is suboptimization, where a set of alternatives is comprehensively evaluated, but the set is small relative to the
set that could be examined. A final approach is to adapt, which implies no comparison of alternatives is
made prior to choice but method effectively compares successive choices in a similar environment, so that
improvement can be made over time.
Boundedly rational choice theories are economic theories because it is cognitive scarcity that motivates
them. However, because optimization is costly, a decision-maker facing deliberation cost cannot
optimally choose a choice method. Ultimately, optimization must be abandoned to fully explain the
choice methods people use. Adaptive and evolutionary theories are the obvious alternatives. From this
perspective, the heuristics people use are fit responses selected in an evolutionary process that proceeds
because of the presence of deliberation cost.
Adaptation allows improved choices to be found when
optimization is not possible.
The presence of deliberation cost also can also be used to explain socialization and organization. The
perspective suggests that people will organize and socialize in a way that makes decision-making easier.
The observed decomposition of social and organizational units into related but largely independent
subunits can be explained as an evolutionary development that has facilitated the development of
improved decision-making heuristics. Social interaction, group bonding, and loyalty can each facilitate
imitation and the transmission of good heuristics through authorities, meaning deliberation cost may well
motivate their existence and forms.
25
End-Notes
1. See Simon (1990) for a discussion of how human cognition is limited by physiology.
2. For other discussions of the regress issue see Raiffa (1968), Radner (1968), Radner, (1975),
Winter (1975), Johansen (1977), Gottinger (1982), Conlisk (1988), Smith (1991), Lipman (1991),
Day and Pingle (1991), and Conlisk (1995).
References
Archibald, G.C., H.A. Simon, and P. Samuelson. 1963. “Discussion.” American Economic Review 53 (2):
227-36.
Arrow, K.J. 1974. The Limits of Organization. New York, NY: Norton.
Baumol, W.J., and R.E. Quandt. 1964. “Rules of thumb and optimally imperfect decisions.” American
Economic Review 54 (1): 23-46.
Becker, G.S. 1993. “Nobel lecture: The economic way of looking at behavior.” Journal of Political
Economy 100 (3): 385-409.
Blackburn, J.M. 1936. “Acquisition of skill: An analysis of learning curves.” IHRB report no. 73.
Bolten, G.E., and A. Ockenfels. 2000. “ERC: A theory of equity, reciprocity, and competition.” American
Economic Review 90: 160-93.
Braunstein, Y.M., and A. Schotter. 1982. “Labor Market Search: An Experimental Study.” Economic
Inquiry 20: 133-44.
Camerer, C., and T.H. Ho. 1999. “Experience weighted attraction learning in normal form games.”
Econmetrica 67: 827-73.
Coase, R. 1960. “The problem of social cost.” Journal of Law and Economics, 3 (1): 1-44.
Colman, J.S. 1984. “Introducing social structure into economic analysis.” American Economic Review
Papers and Proceedings 74: 84-88.
Conlisk, J. 1980. “Costly optimizers verses cheap imitators.” Journal of Economic Behavior and
Organization 1: 275-93.
______, 1988. “Optimization cost.” Journal of Economic Behavior and Organization 9 (3): 213-28.
______, 1995. “Why bounded rationality.” Journal of Economic Literature 34: 669-700.
______, 1996. “Bounded rationality and market fluctuations.” Journal of Economic Behavior and
Organization 29 (2): 233-50.
Day, R.H. 1963. Recursive Programming and Production Response. Amsterdam: North-Holland.
Day, R.H, and A. Cigno. 1978. Modeling Economic Change: The Recursive Programming Approach.
Amsterdam: North-Holland.
26
Day, R.H., and M. Pingle. 1991. “Economizing economizing.” In Behavioral Decision-Making:
Handbook of Behavioral Economics Vol 2B, ed. R. Frantz, H. Singh, and J. Gerber, 509-22. Greenwich,
CT: JAI Press.
______, 1996. “Modes of economizing behavior: Experimental evidence.” Journal of Economic
Behavior and Organization 29: 191-209.
Erev, I., and A.E. Roth. 1998. “Predicting how people play games: Reinforcement learning in
experimental games with unique, mixed strategy equilibria.” American Economic Review 88 (4): 848-881.
Fehr, E., and K. Schmidt. “A theory of fairness, competition, and cooperation.” Quarterly Journal of
Economics 114: 817-51.
Fernandes, R., and H.A. Simon. 1999. “A study of how individuals solve complex and ill-structured
problems.” Policy Sciences 32: 225-45.
Forrester, J. 1961. Industrial Dynamics. Cambridge, MA: MIT Press.
Friedman, M. 1953. “The methodology of positive economics.” In Essays in Positive Economics, 3-43.
Chicago, IL: University of Chicago Press.
Gale, D., and R.W. Rosenthal. 1999. “Experimentation, imitation, and stochastic stability.” Journal of
Economic Theory 84: 1-40.
Gigerenzer G, P.M. Todd, and the ABC Research Group. 1999. Simple heuristics that make us smart.
Oxford: Oxford University Press.
Gottinger, H.W. 1982. “Computational costs and bounded rationality,” In Philosophy of Economics, ed.
W. Stegmuller, W. Balzer, and W. Spohn, 223-238, Berlin: Springer-Verlag.
Grossman, S., and O. Hart. 1983. “An analysis of the principle-agent problem,” Journal of Political
Economy 51: 7-45.
Guth, W., R. Schmitberger, and B. Schwartz. 1982. “An experimental analysis of ultimatum bargaining.”
Journal of Economic Behavior and Organization 3, 367-88.
Harrison, G.W., and P. Morgan. 1990. “Search intensity in experiments.” Economic Journal 100: 478-86.
Johansen, L. 1977. Lectures on Macroeconomic Planning. Part 1: General Aspects. Amsterdam: NorthHolland.
Kahneman, D., P. Slovic, and A. Tversky. 1982. Judgment under Uncertainty: Heuristics and Biases,
Cambridge, UK: Cambridge University Press.
Knight, Frank H. 1921. Risk, Uncertainty, and Profit. Boston: Houghton-Mifflin; reprinted New York:
Sentry Press, 1964.
Kogut, C.A. 1990. “Consumer search behavior and sunk costs.” Journal of Economic Behavior and
Organization 14: 381-92.
27
Lipman, B., 1991. “How to decide how to decide how to…: Modeling bounded rationality,”
Econometrica 59 (4): 1105-25.
Lippman, S.A. and J.J. McCall. 1976. “The Economics of Job Search: A Survey---Part I.” Economic
Inquiry 14: 155-90.
Martignon, L. and U. Hoffrage. 2002. “Fast, frugal and fit: Heuristics for pair comparison,”
Theory and Decision 52, 29–71.
North, D. 1994. “Economic performance through time.” American Economic Review 84 (3), 359-68.
Offerman, T. and J. Sonnemans. 1998. “Learning by experience and learning by imitating successful
others.” Journal of Economic Behavior and Organization 34 (4): 559-575.
Payne, J. W., J.R. Bettman, and E.J. Johnson, 1988. “Adaptive strategy selection in decision making.”
Journal of Experimental Psychology 14 (3): 534-52.
__________. 1992. “Behavioral decision research: A constructive processing perspective.” Annual
Review of Psychology 43: 87-131.
__________. 1993. The Adaptive Decision Maker. Cambridge, U.K.: Cambridge University Press.
Pingle, M. 1992. “Costly optimization: An experiment.” Journal of Economic Behavior and
Organization 17: 3-30.
__________. 1995. “Imitation verses rationality: An experimental perspective on decision-making.”
Journal of Socio-Eonomics 24 (2), 281-315.
__________. 1997. “Submitting to authority: Its effect on decision-making.” Journal of Psychology 18,
45-68.
Radner, R. 1968. “Competitive equilibrium under uncertainty.” Econometrica 36 (1): 31-58.
Radner, R. 1975. “Satisficing.” Journal of Mathematical Economics 2 (2), 253-62.
Raiffa, H. 1968. Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Reading, MA:
Addison-Wesley.
Roth, A. E. and I. Erev. 1995. “Learning in extensive-form games: Experimental data and simple dynamic
models in the intermediate term.” Games and Economic Behavior 8(1): 164-212.
Savage, L.J. 1954. The Foundations of Statistics. New York, NY: Wiley.
Schotter, A., and Y.M. Braunstein. 1981. “Economic search: An experimental study.” Economic Inquiry
19: 1-25.
Schwartz, H. 1998. Rationality Gone Awry? Decision Making Inconsistent with Economic and Financial
Theory. Westport, CT: Praeger.
28
Simon, H.A. 1955. “A behavioral model of rational choice.” Quarterly Journal of Economics 69 (1): 99118.
__________. 1978. “Rationality as a product and process of thought.” American Economic Review
Papers and Proceedings 68, 1-16.
__________. 1986. “Rationality in Psychology and Economics,” In Rational choice: The Contrast
Between Economics and Psychology. ed. R.M. Hogarth and M.W. Reder, 25-40. Chicago, IL: University
of Chicago Press.
__________. 1990. “Invariants of human behavior.” Annual Behavioral Psychology 41: 1-19.
__________. 1991. “Organization and markets.” Journal of Economic Perspectives 5 (2): 25-44.
__________. 1993. “Altruism and economics.” American Economic Review 83 (2): 156-61.
__________. 2000. “Review: Barrier and Bounds of Rationality.” Structural Change and Economic
Dynamics 11: 243–53.
__________. 2002a. “Near decomposability and the speed of evolution.” Industrial and Corporate
Change 11 (3): 587-99.
__________. 2002b. “We and they: The human urge to identify with groups.” Industrial and Corporate
Change 11 (3): 607-10.
Smith, H. 1991. “Deciding how to decide: Is there a regress problem?” In Foundations of Decision
Theory, ed. M. Bacharach and S. Hurley, 194-217. London: Basil Blackwell.
Sonnemans, J. 1998. “Strategies of search.” Journal of Economic Behavior and Organization 35 (3): 30932.
Thorndike, E.L. 1898. “Animal intelligence: An experimental study of the associate process in animals.”
Psychological Monographs 2 (8).
van Dijk, F., Sonnemans, J., and F. van Winden. 2002. “Social ties in a public good experiment.” Journal
of Public Economics 85 (2): 275-99.
Wilde, Douglass J.. 1964. Optimum Seeking Methods. Englewood Cliffs, NJ: Prentice-Hall.
Williamson, O. 1985. The Economic Institutions of Capitalism. New York, NY: Free Press.
Winter, S. 1975. “Optimization and evolution in the theory of the firm.” In Adaptive Economizing
Models. ed. R.H. Day and T. Groves, 73-118. New York: Academic Press.
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Figure 1: Recognizing Cognitive Scarcity and Deliberation Cost
Non-Cognitive Goods
A
B
Deliberation
Cost
Cognitive Goods, Excluding Deliberation
30