Heterogeneous Agents in Finance : different
heuristics and different representations of
problems
Massimo Egidi
Luiss University
[email protected]
Prepared for The Conference on Quantitative Behavioral Finance,
Nice Dec. 8-11, 2010
Heterogeneous Agents in Finance : different heuristics and
different representations of problems
“Economics and finance are witnessing an important
paradigm shift, from a representative, rational agent
approach towards a behavioral, agent-based approach in
which markets are populated with boundedly rational,
heterogeneous agents using rule of thumb strategies. “
(Cars Hommes)
Heterogeneous Agents in Finance : different heuristics and different
representations of problems
  Simon built the idea of bounded rationality on close
observation of the behavior of employees and managers
in large organizations. During the 1950s and early
1960s, he took part in numerous collaborations and
research projects at the Graduate School of Industrial
Administration of Carnegie Mellon, among them a study
of decision making under uncertainty conducted jointly
with Charles Holt, Franco Modigliani and John F. Muth.
  The aim of the study was to develop mathematical tools
to improve inventory control systems for production
planning at a plant of the Pittsburgh Plate Glass
Company. It was in this context of the concrete study of
empirical data that Simon developed his early notions of
“satisficing” behavior, and that the two opposite ideas of
Rational Expectations (Muth) and Bounded Rationality
emerged.
Heterogeneous Agents in Finance : different heuristics and
different representations of problems
In a perfectly rational EMH world all traders are rational and
it is common knowledge that all traders are rational. In real
financial markets however, traders are different, especially
with respect to their expectations about future prices and
dividends.
A quick glance at the financial pages of newspapers is
sufficient to observe that difference of opinions among
financial analysts is the rule rather than the exception. In
the last decade, a rapidly increasing number of structural
heterogeneous agent models have been introduced in the
finance literature
Heterogeneous Agents in Finance : different heuristics and
different representations of problems
In the traditional approach, simple analytically tractable
models with a representative, perfectly rational agent have
been the main corner stones and mathematics has been the
main tool of analysis.
The new behavioral, heterogeneous agents approach
challenges the traditional representative, rational agent
framework.
It is remarkable however, that many ideas in the
behavioral, agent-based approach in fact have quite a long
history in economics already dating back to earlier ideas
well before the rational expectations and efficient market
hypotheses.
Heterogeneous Agents in Finance : different heuristics and different
representations of problems
  Rational behavior has two related but different
aspects (e.g. Sargent (1993)).
  First, a rational decision rule has some microeconomic foundation and is derived from optimization
principles, such as expected utility or expected profit
maximization.
  Second, agents have rational expectations (RE) about
future events, that is, beliefs are perfectly consistent
with realizations and a rational agent does not make
systematic forecasting errors.
Heterogeneous Agents in Finance : different heuristics and different
representations of problems
  In a rational expectations equilibrium, forecasts of
future variables coincide with the mathematical
conditional expectations, given all relevant
information.
  Rational expectations provided an elegant and
parsimonious way to exclude ‘ad hoc’ forecasting rules
and market psychology from economic modelling.
Since its introduction in the sixties by Muth (1961)
and its popularization in economics by Lucas (1971),
the rational expectations hypothesis (REH) has
become the dominating expectation formation
paradigm in economics.
Heterogeneous Agents in Finance : different heuristics and different
representations of problems
  Milton Friedman has been one of the strongest
advocates of a rational agent approach, claiming that
the behavior of consumers, firms and investors can be
described as if they behave rationally. The Friedman
hypothesis stating that non-rational agents will not
survive evolutionary competition and will therefore be
driven out of the market has played an important role
in this discussion.
Heterogeneous Agents in Finance : different heuristics and
different representations of problems
  In a similar spirit, Alchian (1950) argued that biological
evolution and natural selection driven by realized profits
may eliminate non-rational, non-optimizing firms and
lead to a market where rational, profit maximizing firms
dominate. The question whether the Friedman
hypothesis holds in a heterogeneous world has played an
important role in the development and discussion about
Heterogeneous Agents .
Market Efficiency
 
Another important issue in the discussion of rational versus
boundedly rational behavior is concerned with market efficiency, as
emphasized by Fama (1965).
 
If markets were not efficient, then there would be unexploited
profit opportunities, that would be exploited by rational arbitrage
traders. Rational traders would buy (sell) an underpriced
(overpriced) asset, thus driving its price back to the correct,
fundamental value. In an efficient market, there can be no
forecastable structure in asset returns, since any such structure
would be exploited by rational arbitrageurs and therefore
disappear
 
Fama’s Efficient Markets Hypothesis (EMH), i.e. the assumption
that market behaviour can be described by a random walk process,
because rational traders do not miss unexploited profit
opportunities, has been drastically challenged by the recent
developments of “Behavioral Finance”.
Comment (Thaler)
  In the traditional framework where agents are rational
and there are no frictions, a security’s price equals its
“fundamental value”.
  The hypothesis that actual prices reflect fundamental
values is the Efficient Markets Hypothesis (EMH). Put
simply, under this hypothesis, “prices are right”, in that
they are set by agents who understand Bayes’ law and
have sensible preferences.
  Behavioral finance argues that some features of asset
prices are most plausibly interpreted as deviations from
fundamental value, and that these deviations are
brought about by the presence of traders who are not
fully rational.
Comment (Thaler)
  Friedman’s line of argument is initially compelling, but it
has not survived careful theoretical scrutiny. In essence,
it is based on two assertions. First, as soon as there is a
deviation from fundamental value – in short, a
mispricing – an attractive investment opportunity is
created. Second, rational traders will immediately snap
up the opportunity, thereby correcting the mispricing.
  Behavioral finance disputes the first step. The argument,
is that even when an asset is wildly mispriced, strategies
designed to correct the mispricing can be both risky and
costly, rendering them unattractive. As a result, the
mispricing can remain unchallenged.
Thaler :Behavioral Finance an example
  In 1907, Royal Dutch and Shell Transport, at the time
completely independent companies, agreed to merge
their interests on a 60:40 basis while remaining separate
entities.
  Shares of Royal Dutch, which are primarily traded in the
USA and in the Netherlands, are a claim to 60% of the
total cash flow of the two companies, while Shell, which
trades primarily in the UK, is a claim to the remaining
40%. If prices equal fundamental value, the market
value of Royal Dutch equity should always be 1.5 times
the market value of Shell equity. Remarkably, it isn’t.
  Figure 1, taken from Froot and Dabora’s (1999) analysis of
this case, shows the ratio of Royal Dutch equity value to
Shell equity value relative to the efficient markets
benchmark of 1.5. The picture provides strong evidence of
a persistent inefficiency. Moreover, the deviations are not
small. Royal Dutch is sometimes 35% underpriced relative
to parity, and sometimes 15% overpriced.
  While irrational traders are often known as “noise
traders”, rational traders are typically referred to as
“arbitrageurs”. Strictly speaking, an arbitrage is an
investment strategy that offers riskless profits at no
cost. Presumably, the rational traders in Friedman’s
fable became known as arbitrageurs because of the
belief that a mispriced asset immediately creates an
opportunity for riskless profits. Behavioral finance
argues that this is not true: the strategies that
Friedman would have his rational traders adopt are
not necessarily arbitrages; quite often, they are very
risky.
  Where the variety of behavior comes from? Euristics
and Biases
  Overconfidence. Extensive evidence shows that
people are overconfident in their judgments. This
appears in two guises. First, the confidence intervals
people assign to their estimates of quantities – the
level of the Dow in a year, say – are far too narrow.
Their 98% confidence intervals, for example, include
the true quantity only about 60% of the time [Alpert
and Raiffa (1982)]. Second, people are poorly
calibrated when estimating probabilities: events they
think are certain to occur actually occur only around
80% of the time, and events they deem impossible
occur approximately 20% of the time [Fischhoff,
Slovic and Lichtenstein (1977)].
  Where the variety of behavior comes from? Euristics
  Representativeness. Kahneman and Tversky (1974)
show that when people try to determine the
probability that a data set A was generated by a
model B, or that an object A belongs to a class B,
they often use the representativeness heuristic. This
means that they evaluate the probability by the
degree to which A reflects the essential characteristics
of B.
  Anchoring. Kahneman and Tversky (1974) argue
that when forming estimates, people often start with
some initial, possibly arbitrary value, and then adjust
away from it. Experimental evidence shows that the
adjustment is often insufficient. Put differently, people
“anchor” too much on the initial value.
The micro foundations
  From Bernoullian Expected Utility Theory to Kahneman
and Tversky’ Prospect Theory
  In 1952, at a symposium held in Paris, Allais presented
two studies in which he criticized the descriptive and
predictive power of the choice theory of the “American
School” and especially Friedman’s stance, (Allais, 1953),
demonstrating some experiments in which subjects
underwent alternative choices in conditions of risk
systematically violating the assumptions of the expected
utility theory.
  Kahnemann and Tversky
Kahneman and Tversky’s Prospect Theory and framing effect
  Individuals behave as risk takers when facing a problem
presented in terms of loss while they behave as risk
averse when the same problem is presented in terms of
gain)
  This behavioral inconsistency is called “framing effect”,
and shows clearly that the mental representation
(framing) of a problem may be crucial to elicit individual
behavior.
2 – Changing Representation: Kahneman’s Prospect Theory
From Bernoullian Expected Utility Theory to Kahneman’
Prospect Theory
  Framing effect , preference reversal,…lead to an
advanced vision of bounded rationality and suggest to
adopt new, non EUT theories based on the properties of
human reasoning
  They suggest that in order to understand a decision one
must thoroughly analyze the cognitive processes that are
at the base of the decision. It is thus necessary to
understand how people represent problems, how the
complex process of editing is carried out and how
construction of mental models is built in order to make a
particular decision.
A second class of deviations from rationality
  One of the most investigated reasoning problems in the
literature, in which the dual model’s prediction have
been tested, is the Wason selection task. This task it is
known to be very difficult in its conceptual version, if
represented in different, “deontic”, version is it is quite
easy and – interestingly - may lead either to the right or
to the wrong response depending on the form in which is
presented.
1 - Wason “four-card selection task” (1966)
A
B
2
3
Subjects are given the following conditional rule:
“If a card has an A on one side, then it has a 2 on the other side”
1 - Wason “four-card selection task” (1966)
Drinking
Beer
Drinking
Coke
16 Years
Old
22 Years
Old
  Here is a rule:
if a person is drinking been, then the person must be over 19
years of age.
  Select the card, or cards that you definitely need to turn over
to determine whether or not people are violating the rule.
The “perspective effect” by Gigerenzer and Hug
  “The cards below have information about four employees.
Each card represents one person.
  One side of the card tells whether the person worked on the
weekend, and the other side tells whether the person got a
day off during the week.
  Is given the following rule: “If an employee works on the
week-end, than that person gets a day off during the week”
  Indicate only the card(s) you definitely need to turn over to
see if the rule has been violated.”
Worked on the
weekend
Did get a day off
Did not work on
the weekend
Did not get a day
off
The “perspective effect” by Gigerenzer and Hug
  Gigerenzer’ thesis is that a "cheating detection
mechanism" guides reasoning in the following type of
selection task:
If the conditional statement is coded as a social contract,
and the subject is cued into the perspective of one party in
the contract, then attention is directed to information that
can reveal being cheated. (Gigerenzer and Hug 1992)
This thesis can be proved or falsified by comparing two
different version of the selection task by changing the
subject that can be cheated in the contractual relation.
A different view based on behavioral evidence
  1 – Framing effect , preference reversal,…lead
to an advanced vision of bounded rationality
and suggest to adopt new, non EUT theories
based on the properties of human reasoning
  2 – Wason effect leads to the idea that new
microfoundations can be institutionally framed
(social norms).
  4 - Heterogeneity of agents can be based both
on a new description of rational behavior and a
norms ?
Invariance
  The most important feature of framing effect and
inter temporal preference reversal is the violation of
invariance: the same object if considered from two
different viewpoints is not recognized as it is; the
same happens for a problem described in two
different ways.
  The alternatives of a choice are not elaborated,
mentally manipulated to check their eventual
similarities and therefore to set the choice in the
simplest form.
  Invariance means that the same problem or the same
choice , is solved in the same way however is
described.
Kahneman
  “Invariance. An essential condition for a theory of
choice that claims normative status is the principle of
invariance: different representations of the same
choice problem should yield the same preference.
That is, the preference between options should be
independent of their description.
  … This principle of invariance (or extensionality [Arrow
1982]), is so basic that it is tacitly assumed in the
characterization of options rather than explicitly
stated as a testable axiom.
The dual model account of reasoning
  The idea of a dualism in the process of reasoning was
raised by Posner and Synder (1975) by wondering
what level of conscious control individuals have over
their judgements and decisions.
  decision is supposed to be based on two different
cognitive processes: on the one hand a controlled,
deliberate, sequential and effortful process of
calculation (“reasoning”); on the other a non
deliberate process, which is automatic, effortless,
parallel and fast ( “intuition”). The two processes
have been described in many different ways, by
different authors, but there is nowadays considerable
agreement among psychologists on the characteristics
that distinguish them.
The dual process account of reasoning
  The interactions between System 1 and System 2 are
related one the one hand to “accessibility”,i.e “the ease
with which particular mental contents come to mind” on
the other hand to attention/memorization processes.
  According to Schneider and Shiffrin in a repeated problem
solving activity specialized mental skills are created and
settled in long-term memory through the process of
learning / solving of the problems.
  in their view automatic processing is the activation of
learned sequence of elements in long-term memory that is
triggered by appropriate inputs.
The dual process account of reasoning
from Kahneman Nobel Lecture
The dual process account of reasoning
  If dual model approach predictions are correct, acquired
capabilities may interfere with each other and more
crucially, may interfere with Sistem 2 general
capabilities.
  Accessibility. The core concept of Kahnemann analysis of
intuitive judgments and preferences is accessibility – the
ease with which particular mental contents come to mind
(Higgins, 1996). A defining property of intuitive thoughts
is that they come to mind spontaneously, like percepts.
To understand intuition, then, we must understand why
some thoughts are accessible and others are not.
The dual process account of reasoning
  Framing effects in decision making arise when different
descriptions of the same problem highlight different
aspects of the outcomes.
  The core idea of prospect theory is that changes and
differences are much more accessible than absolute
levels of stimulation.
  Judgment heuristics, which explain many systematic
errors in beliefs and preferences are explained by a
process of attribute substitution: people sometimes
evaluate a difficult attribute by substituting a more
accessible one.
The meaning of representation
  Kahneman emphasizes the essential role of the
“framing” effect for understanding the origin of
biases in decision making and reasoning; he suggest
that framing must be considered a special case of the
more general phenomenon of dependency from the
representation: the question is how to explain the fact
that different representations of the same problem
yield different human decisions.
  This suggests again that the crucial aspect of the
decision-making process is the ability to construct
new representations of problems.
Invariance
  The impossibility of invariance raises significant doubts
about the descriptive realism of rational-choice models
(Tversky & Kahneman, 1986).
  Absent a system that reliably generates appropriate
canonical representations, intuitive decisions will be
shaped by the factors that determine the accessibility of
different features of the situation.
  Highly accessible features will influence decisions, while
features of low accessibility will be largely ignored.
Unfortunately, there is no reason to believe that the
most accessible features are also the most relevant to a
good decision.
Invariance
  Violations of invariance are originated by different
accessibility and give rise to dependency from
representation
Changing Representation
  “The representation problem was addressed by Newell
[2] in 1965. Newell used the mutilated checkerboard
problem to illustrate his point that the greatest
"limitation of the current stock of ideas about problem
solving" is that "we do not yet have any useful
representations of possible representations". Most of the
work on this problem was centered around a 1966
seminar at Carnegie—Mellon University which included
Saul Amarel, Steven Coles, Richard Fikes, Allen Newell,
Laurent Siklossy and Herbert Simon.
Changing representation
  In The Sciences of the Artificial, Simon [9] discusses
representation in the context of design.
  He suggests that all of problem solving may be viewed
as changes of representation; that solving a problem can
be seen as representing it so that the solution becomes
transparent.
Changing representation
Korf defined a representation change as a transformation of
the state space and considered two main types of
transformations:
isomorphism and homomorphism.
An isomorphic representation change is renaming of the
states without changing the structure of the space.
An homomorphic transformation is a reduction of the space
by abstracting some states and transitions.
Changing representation
  Two representations are isomorphic iff there exists a
bijective mapping between them (recodifying the
language you describe the same problem)
Representation change
isomorphism and homomorphism.
Examples of Isomorphic representation : Wason effect,
Framing Effect, Simon and Hayes experiment.
Examples of Homomorphic transformation : Problem Solving
in state space.
Isomorphism : an example
  Simon and Hayes (1976) … constructed a collection of
transformation puzzles, all formally identical to the
tower of Hanoi problem, and found that these
‘problem isomorphs’ varied greatly in difficulty. For
example, the initial state and the target state were
described in two of the versions as three monsters
holding balls of different colors. The state transitions
were described in one version as changes in the color
of the balls, and in the other as balls being passed
from one monster to another. The puzzle was solved
much more easily when framed in terms of motion.
Representations: Hanoi Tower
Abstracting the Tower of Hanoi
Craig A. Knoblock
isomorphic changes of representation
Representations: Redefining through abstraction
the elements of the problem
  More generally, we can compute a
finite number of categories, extracted
from a given representation, with
which build a new, omomorphic
rapresentation of a given problem.
Aggregating graphs
  One can build-up a simplified aggregate representation by
grouping toghether the nodes in clusters, in such a way
that
  1 all nodes of a cluster are connected with the nodes of a
parent cluster through the same move.
  2 clusters span perfectly the original graph, i.e. every
node belongs to one only cluster and the set of clusters
covers all nodes.
  Thanks to property 1, we can transform the original graph
into a new one, where each node is an “aggregate node”
connected with other nodes through one move. Of course
the new aggregate graph is smaller than the original one,
depending on the size of clusters.
Aggregating graphs
  It may happen that clusters have some common
properties that allow to represent them in a more
compact description: categorization is the usual way with
which humans reduce a description to a more compacted
one.
  To discover a game strategy, individuals decompose the
problem according to their “intuitions”, i.e. their ways to
categorize and conceptualize the game’s properties.
According to Bellman’s principle, by decomposing a
problem into sub-problems and optimizing each of them,
the outcome is an optimal solution of the original problem
only under very restrictive conditions.
Different abstract representations of a game may lead to
hidden systematic deviations from rationality
  The global solution to a problem may therefore be suboptimal, in relation to the pattern of decomposition that
has been adopted. Therefore biases are interpreted as
sub-optimal behaviors originated by the decomposition
pattern that individuals adopt, and ultimately by their
categorization of the problem.
Categorization leads to Conceptual Distortion
  The role of categorization is fundamental during the
creation of mental competences because it direct the
creation of new specialized skills ( that will be stored into
the System1 (intuition) and later automatically
triggered). Categorization allow individuals to simplify
the representation of a problem to be solved and to
achieve more easily a solution;
  but categorization is not a “rational” process and
therefore an “imperfect” categorization may lead to
solve a problem in a very sub-optimal way, i.e. leads
individual to systematic deviations from rational/optimal
behavior.
Concluding Remarks
  Due to different accessibility of thoughts, individuals
have difficulties to recognize the same problem if
presented with different representations. Isomorphisms
are related with dual model , intuition, accessibility and
social norms
  homomorphisms are related with abstraction and
categorization ( a new language)
  The variety of different representations of a given
problem can be computed and used to predict different
agents’ behaviors.
Back to the quotation at the beginning of this talk
 
Economics and finance are witnessing an important paradigm shift,
from a representative, rational agent approach towards a
behavioral, agent-based approach in which markets are populated
with boundedly rational, heterogeneous agents using well defined
strategies based on different representations of their environment.
“
ThankYou
Summary
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Dual Model
Accessibility
Euristics
Framing and Representations
Categorization
Social Norms
Deontic Character
Context Stories (Gigerenzer, Shiller)
  Being cheated in a social contract means that someone
takes the benefit, but does not pay the cost.' In other
words, a subject should select those cards that
correspond to "benefit taken" and "cost not paid,"
whatever the cards' logical status is.
  The employer takes the benefit of the employee working
on the weekend, without paying the cost of giving the
employee the promised day off.
  Therefore for the employee, being cheated meant that
some colleague "did work on the weekend and did not
get a day off;"
  For the employer, being cheated meant that the
employee "did not work on the weekend and did get a
day off;" that is, in this perspective, subjects should
select the cards which correspond to the not-p- and qcards.
  Thus, perspective change can play cheating detection
against propositional logic. The two competing
predictions are: If the cognitive system attempts to
detect instances of "benefit taken and cost not paid" in
the other party's behavior, then a perspective switch
implies switching card selections; if the cognitive system
reasons according to propositional logic, however,
pragmatic perspectives are irrelevant, people should
reason "logically," and there should be no switch in card
selections.
  The results showed that when the perspective was
changed, the cards selected also changed in the
predicted direction. The effects were strong and robust
across problems. For instance, GIGERENZER and HUG
[1992] report that in the employee perspective of the
day-off problem, 75% of the subjects had selected
"worked on the weekend" and "did not get a day off,"
but only 2 % had selected the other pair of cards. In the
employer perspective, this 2% (who had selected "did
not work on the weekend" and "did get a day off") rose
to 61 %.