Prospect Theory and Its Impact on Economic Decisions

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Prospect Theory and Economic Decisions
By John McGinn

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Contents
1. Introduction
1.1 Background on Kahneman and ProspectTheory……………………1-2
1.2 Defining the Thesis on Economic Decisions………………………...2-3
2. Literary Review
2.1 Origins of ProspectTheory and Expected Utility…………………....3-5
2.2 Neoclassical Assumptions and Contradictions………………………5-12
2.3 Introduction of ProspectTheory and Value Function………………12-13
2.4 Game Theory in Economic Decisions………………………………13-14
3. Application to Financial Markets
3.1 The Performance of Financial Advisors……………………………14-16
3.2 Heuristics and Anchoring in Sales, Trading, and Real Estate……...16-17
3.3 Kahneman’s Perspective of the Financial Markets………………....17-19
4. Application to Poker and Gambling
4.1 Behavioral Economics in Gambling……………………………….......19
4.2 Description of Texas Hold’em Poker………………………………20-22
4.3 Poker’s Relationship to ProspectTheory and Value Function……..22-24
5. Conclusion…………………………………………………………………….24
6. References…………………………………………………………………24-25

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1. Introduction
1.1 Background on Kahneman and Prospect Theory
Daniel Kahneman was born in Tel Aviv, Israel in the 1934 and raised in Paris. He comes
from a Lithuanian Jewish family who moved to France in the 1920s where Khaneman’s father
was the chief of research at a large chemical factory. When Kahneman was younger in the 1940s,
he graphed his family’s wealth as a function of time, which his first economic representation was
explaining how his family lost fortunes when Germany swept France in the 1940s. Kahneman
explains how his interest in Psychology came from his natural tendencies to analyze the
complexity of humans in his parent’s social class. Environmental nature and animals were not as
stimulating enough for his Kahneman’s precocious young brain. Kahneman and his family were
victims of the anti-Semitic movement as his father interned in an intermediation station for
extermination camp in Drancy. Kahneman’s family ultimately escaped to safety towards the
center of France before his father died of untreated diabetes six weeks before D-day and their
eventual liberation. As a child, Kahneman was clearly intellectually gifted while his first
proclivity towards psychology came through his insights and essays written about religious faith
and how it is a perception of the human mind.
Kahneman’s family moved to Palestine shortly after their liberation where Kahneman
attended high school and started becoming intellectually curious about the human perspective of
religion and ethics while strictly adhering to his initial interest in the motives of human beings.
Kahneman was guided as a student primarily into Psychology and Economics, which eventually
led to his first degree in Psychology with a minor in Mathematics. In pursuit of his first degree,
Kahneman became interested in Neuropsychology, specifically Kurt Lewin’s maps of life space,
which essentially explains the topological representation of forces that help or counteract a
human being towards their motivations and values. As a curious student in college, Kahneman
became enamored by the possibility of switching his studies to medicine as his interest in basing
conceptual and philosophical human were catalyzed by Kurt Goldstein’s theory, which explains
how brain injuries automatically eliminates a human’s capacity for abstract thinking.
In 1954, Kahneman was drafted into the military as second lieutenant and a platoon
leader before being transferred to the Psychology branch. One of the major cognitive illusions
was pulled from his experience analyzing potential recruits for the British Army in WWII.
During his time recruiting candidates, he discovered and coined the term “the illusion of
validity”. His studies were founded on his observations of a recruitment exercise that rated
potential candidates and making predictions based on leadership quality to determine whether or
not these candidates were a suitable fit for the officer training program. The statistical results
showed that successful leaders in the recruitment exercise did not show a causal relationship to
successful leadership in the officer training program. This cognitive illusion was commonly
found in technical literature during the 1970s. Kahneman’s eventual assignment was to figure out
what personality dimensions were synonymous with particular combat units of the army. He
ultimately devised a statistical technique for heteroscedastic data that provided an intricate
explanation of psychological requirements essential to various units of the army. His analysis on

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this topic became his first published article and sparked his perpetual interest in predictive
analytics.
Kahneman exited the army in 1956 and pursued his graduate degree at Berkeley. He
directly mentions that much of his experience in graduate school was covering all of psychology
from a broader perspective rather than specific apprenticeships and publishing works. During his
time in graduate school, he studied at the Austen Riggs Clinic for a few months in Massachusetts
under a prestigious psychoanalytic theorist named David Rappaport. Kahneman’s dissertation
was eventually written in 1961 on statistical and experimental analysis. In the summer of 1961,
Kahneman conducted research in the ophthalmology department of Austen Riggs before
ultimately returning to Jerusalem to teach psychology at the Hebrew University.
During Kahneman professional studies, Kahneman taught undergraduates in first-year
statistics classes and a second-year course in research methods. At the same time, he conducted
research specifically in the psychology of single questions in order to gain insightful information
on child backgrounds. After realizing his work needed more statistical significance, Kahneman
conducted research on and developed psychological training programs flight school of the Air
Force and immigrants from undeveloped countries for farming practices. Within the lab of the
University of Michigan under Jerry Blum, Kahneman developed works on vision, specifically in
the dilation of pupil size as it relates to humans being exposed to digits and their ability to recite
them. His findings showed pupil dilation during the initial exposure of digits and contracting
when it came time for the human to recite the digits. The following year, Kahneman focused on
the research of mental effort and his curiosity for attention was strongly influenced by Anne
Treisman, who later became his wife. The results of his research studies qualified him as a
professional research psychologist in 1967 and he returned home to Jerusalem.
1.2 Defining the Thesis on Economic Decisions
In order to understand the decisions that humans make involving financial risk, it is
important for us to understand the intrinsic motives guiding economic decisions and the
impending rationality that is assumed as a result. Many studies within the field of behavioral
have shown that the human instinct has often led to economic decisions that are irrational and
unprofitable. At the same time, the analytical part of our brain has allowed humans to extract the
information necessary to make proper or rational economic decisions. My goal is to analyze the
merits of both our intuition and the analytical side of our behavior as well as their influences on
economic decisions in order to determine which approach is the most profitable. My analysis
will review the vantage point of both professional investors and poker players versus individuals
that are just beginning to take financial risks in order to determine how much these particular
groups rely on intuitive thinking. Once a conclusion is made regarding the type of decisions that
are made from each group, my studies will demonstrate whether or not our intuitive judgment is
more or less profitable than our analytical judgment when making economic decisions. Lastly,
this analysis will review the issues that arise when relying on our intuition and behavior.
My assumption is that when individuals are just beginning to take an economic risk, the
more profitable decisions would have to rely on analytical thinking. At the same time, my

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hypothesis is that our intuition can become more profitable than analytical thinking if we have
more experience managing risk and are continuously addressed with scenarios that involve
economic decisions. My believe is also that the confidence following profitable decision will
lead to irrationality and risk seeking behavior. At the same time, my belief is that humans have
an inclination towards exhibiting risk aversion when that have lost large amounts of their income.
Finally, my contention is that our ability to profit when taking an economic risk is uniquely
influenced by factors outside of analytical and intuitive thinking such as the time horizon and
risk appetite affiliated with our decisions.
2. Literary Review
2.1 Origins of Prospect Theory and Expected Utility
The analysis of prospect theory scrutinizes the inner-workings of expected utility theory
and an understanding of making decisions with uncertain outcomes. After understanding these
common themes, Kahneman and Tversky develop an alternative model that essentially negate
the basic assumptions of utility theory through the thorough analysis of the certainty effect, the
isolation effect, the alternative theory of choice and decision weights. Initially, the expected
utility theory was pioneered by Bernoulli in an attempt to explain that decisions under risk
should not solely be based on expected value calculations, but it should also take into account the
current circumstances of the person who is making the prediction or decision. In this particular
theory, Bernoulli discovered a key determination about the way individuals make decisions,
which is that individuals do not necessarily care about the expected value of outcomes and there
is a subjectivity or utility attached to a decision. As a result, Bernoulli graphed a utility function,
which measured the relationship between income and utility. His discovery was that this
relationship was concave as higher levels of income decreased the marginal utility associated
with an additional dollar of wealth. As a result, individual’s economic decisions become less
influenced by wealth and makes them more prone to participate in risk taking behavior at higher
income levels. The opposite is true for the utility function as $1 is significantly different from $0
while $101 is does not influence utility significantly for individuals when making their decision.
As the studies of utility developed into the 1940s, Von Neumann and Morgenstern discovered
that individuals have a proclivity towards certainty when making economic decisions. An
example of this is shown below:
This particular equation measures the probability of a coin landing heads or tails with
heads paying the participant $100 while tails pays the
participant $0. The probability of obtaining $100 for
the participant is 50% while the probability of
obtaining $0 is also 50%. The sure thing shows that ,no matter how the coin flips, the individuals
will receive $50. Due to the uncertainty of the first scenario, the participant will always choose
the “sure thing”
As an extension to Von Neuman’s theory of expected utility, he introduced game theory
to utility preference. This introduction of game theory made decision making include another

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variable, which is the participant’s intepretation of what their counterparty may decide. The
assumption under this theory is that one cannot necessarily control what their counterparty is
going to do when there is uncertainty regarding future outcomes. Due to the fact that multiple
parties act in self-interest, the particpant will have a strong understanding of the preferences of
the multiple agents involved in the game. Therefore, one must weigh the assumptions made
about the thoughts of their oppenent or counterparty into the expected value calculation that is
described in the previous paragraph. Expected utility is a variable that is transitive, which is
denoted as the following mathematical statement: If A?B and B?C, then A?C. For example, if
U(A)>U(B) and the U(B)>U(C), the U(A)>U(C).
There are three notabloe assumptions to the theory of utility that uncover useful
informatuion about the way that individuals make decisions involving risk. The first assumption
is that utility is an entity that is not directly observable and quantifiable but must be estimated.
Utility is also something that is not necessaruily similar when comparing individuals as every
individual rates life experiences and rewards on a different level, which makes it hard to
determine what particular scenario created the most amount of pleasure for the relevant
counterparties. The most important assumption to be made under expected utility theory is that
the preferences that motivate individuals are revealed through the gambles they make and the
decisions they take. While decisions are being made, there is a clear discrepency between the
monetary utility that is affiliated with the actual reward received upon the result of a decision
and the actual preference that someone has. This particular phenonom was noted by Lichtenstein
and Slovic in the 1970s. There studies revlieved that when decision makers are confronted with a
gamble in which the expected values are very similar, they will choose to hold more utility in the
higher monetary reward regardless of the probability affiliated with it. The example used during
this study includes the following:
Bet 1: Probability=29/36, Monetary Reward= $2, Expected Value=+$1.61
Bet 2: Probability=7/36, Monetary Reward=$9, Expected Value=+$1.75
The results of Slovic and Lichtenstein’s studies are that the majority of people would
prefer the comfort of bet 1 based on the notion that they consume more utility with the monetary
reward that does not assume the risk inherent in bet 2. Although any rational individual would
mathematically value bet 2 higher, there are some individuals that put more weighting on their
personal preference towards risk during their calculations affiliated with an economic decision.
Another factor to consider in the theory of expected utility is analyzing when preferences
reverse while analyzing decision options that require 3 or more variables. This is also known as
preference reversal in 3 option intransitives. In particular, Teversky conducted Tests of
Transivity among college applicants across three dimensions, which include Intelligence,
Stability, and Social abilities. When looking at the chart below, college administrators accepted
Applicant A over B, B over A, C over D, and D over E, but accepted E over A. In this particular
case shown below, the transitive property holds true regardles of the change in all 3 variables up
until applicant E where the level of intelligence reached a certain thershold that resulted in a
change in preference among college administrators. Although the intelligence increase from

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applicant D to applicant E was the same, college administrators decided to put more weight in
the intelligence variable beyond 78, which further reinforces the hypothesis of Tversky about
preference reversal.
In conclusion, choices that involve risk under uncertain situations is denoted by the equation
presented, which shows that expected utility is the combination of utilities and possible outcomes
weighted to the proper probability.
2.2 Neoclassical Assumptions and Contradictions
Descriptive invariance is one of the key assumptions to note when analyzing some of
Tversky and Kahneman’s work. This concerns the fact that variances which do not affect the
actual outcomes should not go on to affect the choice. These assumptions are also in line with
neoclassical assumptions, which are concerned with the consistency regarding a decision whose
variables or explanations have changed. One of the major contradicitions to the neoclassical
assumptions are confirmed by a phenononom known as pseudo-certainty, which is the effect that
when a certain step to a problem involves a monetary gain, then it still carries extra weight even
if getting to that particular step leading to the decision is uncertain. The particular test of
descriptive invariance is utilized by Kahneman and Tversky in the explaination of the following
scenario:
If there is a two-stage game in which the first stage provides a 75% chance to end the
game immediately and a 25% chance to move onto the next stage of the game. In the next stage
of the game, the participant has the option of a sure win for $30 or an 80% chance to win $45.
The results show that the majority of people or approximately 74% of people will choose the
sure win. This particular example essentially explains the idea thati, if the instance of a decision
takes an additional stage of uncertainty, then the option with less risk is the one that is chosen.
The next contradiction to the neoclassical assumptions regarding economic decision
making is the what Kahneman and Tversky call reflection effect, which essentially has to do with
the way a decision is framed. One domain is known as risk aversion and the other is known as
risk seeking. This phenonomon can be explained in a survey I conducted introducing a particular
stock market scenario. Consider the following example:

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Pretend that an investor is looking to invest in the company Tesla with the ticker symbol
TSLA. The current stock price is $201 and the volatility of the stock demonstrates that it can
move within a range of $18 going into the company’s earnings report, which means the stock can
cause the investor to gain $9 or lose $9. Consider the following options for 2 separate problems.
Problem 1:
 You receive a $3 gain and TSLA will move to 204 with complete certainty
 You have a 1/3 probability of gaining $9 and TSLA will move to 210 while this potential
gain’s compliment is a 2/3 probability of gaining $0.
Problem 2:
 You incur a $3 loss and TSLA will move to $198 with complete certainty
 You have a 2/3 probability of losing $0 with its compliment of a 1/3 probability of losing
$9 and TSLA moving to $192.
This particular survey was conducted as 2 separate problems to the candidates. For Problem
1, the data shows that the majority of people or 65% of people would choose the first option or a
$3 gain with complete certainty while 35% of people would take the risk of gaining $9. For
Problem 2, the data shows that the majority of people of 85% of people would choose the second
option, which gives the candidate a 2/3 probability of losing $0. The results of this survey
essentially demonstrate that ,even though the options presented in both particular problems have
the same exact expected utility, candidates were more risk averse in Problem 1 and more risk
seeking in Problem 2. This is due to the fact that humans have a naturally tendency to want to
avoid losses and are willing to take a gamble in order to potentially avoid the negative feeling
associated with a loss. On the other hand, individuals are more likely to take a monetary gain that
is certain as there is not as much value or pleasure present in the potential large gain. In
conclusion, the positive domain reference frame is affiliated with risk aversion while the
negative domain reference frame is more linked to risk seeking behavior.(talk about potentially
indifference curves)
One of the other primary assumptions of the neoclassical assumptions as it relates to decision
making in uncertain circumstances is that the option that will be chosen should depend solely on
the outcome of a decision and not necassrily on the differences in the outcomes or the current
status quo, expectations, or the magnitude of a the particular decision. In particular, Kahneman
and Tversky developing a way to test status quo by making a market for a particular product
while having both buyers and sellers value the products with regards to how much it would be
sold for or bid for. In particular, one group of individuals were given a product and asked to
value the sale of their product while the group of buying individuals were asked to determine
how much they would be willing to pay for it. The studies also implemented a choosing group,
who were asked to determine the value of the T-Shirt relative to the value of their cash in order
to make a decision. The status quo aspect of decision making can be better explained in the
following example:

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The numbers in this problem are striclty hypothetical and meant to provide accuracy of the
psychological reactions assumed by the individuals tested under Kahneman and Tversky Status
Quo studies in 1990. Imagine there is a T-shirt that is given to a group of sellers. The goup of
sellers are asked to say the price at which they would be willing to sell the T-Shirts. The buyers
are the group that is asked to determine the price at which they would be willing to purchase the
T-shirt. The values that would make sense under Kahneman’s studies are that the sellers would
value the T-Shirt at an average of $15 while the buyers would value the T-shirt at an average of
$6. Although this is true, the choosing group mentioned ealier would prefer the T-shirt over their
cash if the value of the T-Shirt was $6.67 or less. This just demonstrates the fact that the
choosers, who have neither a biased towards the T-Shirt nor cash, value the T-Shirt closer to the
purchasing price that buyers are willing to pay. This just exemplifies that sellers tend to grossly
overvalue their products due to the mere fact that they are in possession of it. This psychological
effect in market making is what is known as the endowment effect, which shows that humans
exhibit loss aversion even in relation to the objects they are given.
Another contradiction to the diffefrences in outcomes is relatable to a human’s mental
accounts and expectations, which was proven in studies that were conducted by Kahneman and
Tversky in 1981. In order to better understand the merits of this study, I introduced a question in
a survey to 50 different participants, which was very similar to the one question studies that
Kahnemand was well known for during his graduate, doctoral studies,and time in military
service as a pschological evaluator. In my particular survey, I asked more specific questions that
may have influences on the natural preference towards a decision and the overall magnitude of a
decision. The first question I asked is very similar to the questions Kahneman and Tversky asked
candidates when determining the importance of expectations and mental accounts. The questions
that I asked to participants were the following:
***Note that all of the following questions were contructed by me based on my interpretation of
the studies Kahneman and Tversky published on mental accounts and expectations in economic
decision theory. The additional questions asked by me were an extension of Kahnmen’s theory to
determine the natural preference or magnitude one holds in a decision. The majority of the
demographic presented with question were an equal mix of male and females in the millenial
generation(ages 21-25). The questions that were presented in the survey were given all together
and answered one after the other. The participants are debriefed so that they know the
assumptions of the experiment are that you are attending the events on your own without the
influence of another person’s preferences***
Question 1: You are on your way to a way to see a basketball sporting event and you have a
ticket worth $20 for the event. On the way to your seats, you realize you have lost the ticket.
Would you go back to buy another ticket?
Question 2: You are on your way to a basketball sporting event and you look in your wallet and
realize you have somehow lost $20 on the way to the ticket booth. The ticket still costs $20.
Would you purchase the ticket to begin with?

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Question 3: For those that answered no to question 1, would the answer change to yes if the
event was a ballet?
Question 4: For those that said yes to question 1, would the answer change to no if the event was
a ballet?
Question 5: What if the value of the ticket and the amount of cash value lost in questions 1 was
$200 instead of $20? Would those who said yes change their answer to no?
Question 6: What if the value lost in question 2 was $200 instead of $20?
Yes No Changed Answer from Question 1
from no to yes
Changed Answer Question 2
from yes to no
Question
1
19 31
Question
2
42 8
Question
3
3
Question
4
9
Question
5
6 44
Question
5
14 36
Given the interesting data that Kahneman discovered while asking questions regarding
mental accounts and expectations, I wanted to introduce variables of preference and magnitude
in order to influence the decisions that were initially made in questions 1 and 2. Questions 3 and
4 introduce the variable of preference and how that influences the decisions of the majority
group. So if the majority of answers to question 1 were no, my goal is to essentially find out
what percentage of the the people who answered no would change their answer to yes. Overall
this analysis will allow me to determine how much the variable of natural preference influences
Kahnemen’s studies about expectations.
The results of the survey were very interesting as the questions that analyze magnitude
showed results that were not necessarily implimented in Kahneman and Tversky’s studies. For
question 1, 62% of participants decided that they would not return to buy another ticket at the
event after already being in possession of it prior to the event. For question 2, 84% of people
decided that, if they lost the $20 necessary to purchase the ticket at the door, then the evidence in
the survey convincingly shows that the majority of individuals would still initially buy a ticket at
the door. This essentially reinforces the status quo bias as individuals who already possess the
ticket, hold naturally hold more value in the possession of a unique item such as a ticket rather
than cash and do not want to lose the ticket. At the same time, individuals who do not yet possess
the ticket, do not hold as much value in their cash and are willing to essentially give up their cash
to acquire a ticket. My assumptions are that individuals look at cash as a common item that is

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used in everyday transactions while something like a ticket to an event is unique and less
involved in daily transactions.
In question 1, the majority of individuals answered no or that they wouldn’t buy another
ticket. Question 3 shows that, out of the people who answered no to question 1, 9.6% of
participants changed their answer from no to yes when the given event was changed from a
basketball game to a ballet. In Question 2, the majority of individuals answered yes or that they
would still purchase the ticket. Question 4 demonstrates that, out of the participants who
answered yes to question 2, 16.67% of inidividuals changed their answer from yes to no. This
essentially demonstrates that ,during the evaluation of a valuation of cash versus the event ticket,
the introduction of personal preference has more of an influence on the decision when the person
does not already have the ticket versus when they are already in possession of the ticket.
One of the conclusions I can draw from this data is that participants hold less value in the
preference of the event when they already have the ticket on the way to the event and then
subsequently lose the ticket. Another is that when individuals lose the money necessary to buy
the ticket on the way to the event, the type of event or preference has more of an influence on
one’s decision about whether or not they will still purchase the ticket. Unlike my initial
hypothesis, these questions essentially do not contradict Kahneman’s beliefs about mental
accounting and expectation while making uncertain decisions but it provides an extension to his
already existing study. This is because once the ticket is out of your possession after previously
having it, your personal preference does not have much of an influence on your reevaluation of
the desire for another ticket versus cash you hold. At the same time, it seems that personal
preference for the event has more of influence on the value one has towards cash during the
initial purchase of a ticket given that the money necessary to buy the ticket has previously been
lost.
Questions 5 and 6 about the influence of magnitude on decisions was included in my
survey before I had analyzed Kahneman’s own studies about magnitude and the ratio effect.
Questions 5 and 6 introduce the influence that magnitude has on decisions as well as mental
accounting and expectations. When the value of the ticket changed from $20 to $200, 88% of
people decided that they would not go back to buy another ticket for $200 if they already
possessed the ticket and lost it on upon entering the event. Question 6 demonstrates that 72%
percent of people would not purchase another ticket at the door for $200 dollars if they lost $200
before they got to the point where they needed to purchase the ticket for the event. This
essentially demonstrates that the introduction of magnitude has a strong influence on the
decisions made regarding the relative value of the ticket versus the cash one would hold. The
major difference was in the second scenario where individuals lost the money necessary to
purchase the event ticket before initially having the opportunity to. When the value of cash that
they lost was $20 before purchasing the ticket, 16% of people said they would not still purchase
the $20 ticket. On the other hand, when the participant lost $200 before purchasing the ticket, 72%
of particpants said they would not still purchase the $200 ticket at the event. The influence of
magnitude as a variable provides a great addition to Kahneman initial one question studies

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regarding mental accounting because it shows how individuals value cash differently when the
magnitude of both the ticket and the dollar amount becomes higher.
In Kahneman’s studies regarding magnitude, he essentially contradicts the neoclassical
assumption about uncertain decision making in regards to the fact that differences in decision
outcomes should not be influence the decisions that are made. The contradiction of these
assumptions arise when Kahneman and Tversky develop an understanding of the natural instict
for humans to depend on ratios when comparing the magnitude of fairly similar decisions. In
Kahnemand and Tversky’s testing for this topic, they intoduced the following question to their
participants:
Assume that a person needs to buy a calculator for $30 and a jacket for $250. The clerk at
the store informs you that the calculator and the jacket are on sale. He mentions that the
calculator now costs $20 and $240 respectively at a store located 20 minutes away. Would you
be willing to travel to the store for the jacket? Also, would you be willing to travel for the
calculator?
The results of the study show that 68% of their participants were willing to travel to the
store to get the discount for the calculator while only 29% were willing to travel for the jacket. In
both scenarios, the total amount saved by the participant is $10 dollars. Although this is true,
more people held more value in the discount that made up a larger percentage of the item’s total
cost even if the discounts on both items had the same effect on that person’s income. This
essentially shows the importance that people hold in ratios when analyzing the relative value of
two objects. Later on the paper, this psychological behavior will be applied to the relative
valuation of stocks in the financial markets.
Another one of the major neoclassical assumptions relates to the fact that future
preferences regarding a decision should not be based on infrequent emotional biases that may
occur for a short period of time. This essentially means that if the emotional behavior that is
being exhibited at the point of the decision should not be erratic and more relatable to one’s
typical emotional state of mind. Kahneman refers to the decisions that are made under an
emotional bias as the projection bias. This is further explained with the idea of delay
independence, which essentially determines that outcomes are different as the time left until the
outcome changes. This could further be explained by the idea of hyberbolic discounting, which
means that individuals will see an exponential increase in obtaining the smaller monetary reward
that occurs sooner over a larger reward that occurs later as the date the larger reward is delayed
to is closer to the current time. People are essentially less likely to wait for a larger reward as the
wait occurs closer to the present time.

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An example of projection bias is
that individuals will usually be more
likely to take $50 today rather than $100
6 months from now. Although it is a
larger reward, individuals cannot pass up
the instantaneous reward for a larger
reward later. On the other hand, if the
individual has to choose between $50 in
12 months versus $100 in 18 months,
they will likely choose to wait for the
$100 reward because they discount the
value of a wait time that is further away
at a lower rate. This study on delay
independence was tested by Ainslie and
Haendel in 1983. The reason for this level of implusiveness is caused by temporal myopia, which
essentially means that the perception of the future lacks clarity as the scenario occurs further out
in time. This causes humans to generally act irrationally and disregard the future value of the
decision-making process. The chart to the right reinforces this theory because it shows that the
utility affiliated with the smaller and sooner reward is temporarily more valuable than the larger,
later reward for a short period before the smaller reward is actually received. So essentially the
neoclassical assumptions are contradicted by the projection bias and hyberbolic discounting,
which explains the natural impulisveness that humans exhibit.
One of the additional assumptions regarding neoclassical studies of economic decisions
includes the fact that utility that has already been experienced should not significantly differe
from decision utility, predicted utility, and retrospective utility. One of the contradiction
specifically regarding the difference between experienced utility and decision utility is that
people tend to hold more value in social status and will , therefore, receive less utility when they
have to decide on experiencing a job or accomplishment that has less prestige related to others
striving towards the same goal. This feeling can occur due to extreme competition or societal
restrictions that hinder the potential opportunity to receive a reward. The next contradiction in
neoclassical assumptions is the discrepency between experienced utility and predicted utility
when analyzing the natural adaptation to the surroundings present as a result of a particular
decision. In particular, individuals will become accustomed and happy with their decision in the
future because of a human’s adaptive instincts even if the choice made was the one that
generated considerably less utility during the time of the decision. Another psychological
phenonomon when it comes to making a decision based on past experience is that individuals
tend to disregard the duration of a particularly memorable or painful experience if the end of the
experience was percieved as less painful or drastic. This essentially reinforce the contradiction of
the neoclassical assumption that is affiliated with the systematic difference between experienced
utility and retrospective utility. Remembered utility is related to the fact that the memory of an
experience over a certain period of time is remember mostly by the peak utility of the experience
and the ending utility of the experience. People tend to explain the summary of an experience
with these snippets of the peak and ending snippets of specific memories. The application of

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retrospective uitility and memory utility was finalized in its application to a clinical setting in
1996.
2.3 Introduction of Prospect Theory and Value Function
All of the previous theories led
Kahneman and Tversky to the iconic
study of Prospect Theory, which won
the nobel prize in 2002. As a part of
the study, they introduced the fact that
prospects are evaluated on the basis of
their value function. The value
function is S shaped as shown in the
chart displayed. It is convex for losses
and concave for gains. The value
function essentially demonstrates that
individuals are more risk averse for
moderate probability gains and risk
seeking for moderate probability losses.
For example, if an individual is
presented with the opportunity to win
$50 with certainty versus a 50%
probability of 100, that person will
choose to be risk averse and take the
$50. On the other hand, if the
individual is presented with a
guaranteed $50 loss versus a 50% chance of losing $100, they will generally take the risk of
losing $100. This essentially explains the steeper curve for the left side of the value function,
which indicates a loss in value. Due to the fact that individuals are not necessarily influenced by
bets that allow for equal opportunity and probability of gains and losses, the value function is
kinked at the origin. This essentially demonstrates that a person that is presented with an
economic decision will likely hold more importance or value in the negative prospect when their
reference point is the origin of the value function. The functions of decision weights treat highly
probable events as certain and highly improbable events as impossible. Although extreme events
are influenced by the decision weight that an individual places on them, the decision weight
function generally overestimates small probabilities and underweights large probabilities
Example: The following example gives a demonstration of how to value a prospect.
When the reference point is 0 and there is a 50% chance of winning 1000 dollars paired with a
50% chance of losing 1000, then the value of the prospect is negative because we hold more
value in the risk aversion or the %50 chance of losing 1000. This particular scenario assumes
that decision weights are held constant throughout the valuation of a prospect. On the other hand,

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if the reference point is -1000, then we would assign a higher value to the point of break-even
rather than that of -2000. So essentially this shows a different value towards the gain as this
scenario shows a 50% chance of losing 1000 or a %50 chance of gaining 1000 when the
reference point is already -1000 after a loss.
So as mentioned in the example, the prospect’s value is determined by the dependence it
has on reference frames, loss aversion, and the fact that a human’s sensitivity to changes in value
start to decline as one moves away from the origin reference point. This reaffirms the decision
weight function, which essentially indicates that our sensitivity to changes in probability as
individuals move from making decisions on extreme probabilities to medium probability events.
The most important improvement to the initial theories of expected utility and the neoclassical
assumptions are the changes that Kahneman and Tversky made to the reflection effect. The
revisited version of this particular reflection effect is that individuals are risk averse when they
are presented with medium to high probability gains while also being introduced to low
probability losses. At the same time, individuals become risk seeking for reasonably high
probability losses and low probability gains. Examples of the loss aversion particularly in the
stock market is that often premiums in the stock market are higher than the interest in the bond
market because individuals collectively do not want to give up the additional return on
investment. A common example of the reflection effect and an individual’s ability to overweight
low probabilities is that the lottery ticket sales start to move up as there are more people buying
the ticket and the overall prize moves up. Even though the chances of winning become less
because there is a larger eligible pool of people, individuals still seem to be inspired by the
higher prize and overweight this unlikely event.
2.4 Game Theory in Economic Decisions
Although not related to the works of
Kahneman and Tversky, it is important to
have an understanding of game theory as
it provides key assumptions regarding
decision making based on another’s
decisions that can potentially influence
your overall utility. One of the major
examples utilized to explain game theory
is the prisoner’s dilemma scenario. It is
essentially concerned with rational
individuals that are acting in self-interest
in order to try to provide the greatest
amount of utility for themselves. If you
take a look at the chart displayed, the
numbers represent the level of utility for
Player A or B. If both parties are given a
particular scenario, player A and B have
to choose from 2 options, which are that

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they are able to cooperate or defect. The following scenarios can occur as a part of this prisoner’s
dilemma example:
 Both Player A and B cooperate: As shown, this scenario would provide a utility of 3 to
both counterparties.
 Player A defects and B cooperates: Player A would receive a utility of 4 for defecting
while Player B will receive a utility of 1 for cooperating when Player A defected.
 Both Player A and B defect: Both Player A and B will receive a utility of 2.
 Player A cooperates and B defects: Player B will receive a utility of 4 while Player A will
receive a utility of 1.
The previously explained game theory utilizing the prisoner’s dilemma example was
developed by Tucker in 1955. There was an eventual extension of this theory into the experiment
that was conducted by Ross and Samuels regarding the labeling of the traditional prisoner’s
dilemma game. Their data showed that when the game was labeled “Wall Street Game”, 1/3 of
the group tested cooperated while the remaining 2/3 decided to defect. When the same game is
labeled “The Community Game”, the majority of the group tested cooperated. Essentially, this
demonstrates the how influences of the surrounding environment or society can have an impact
on the decisions regarding whether or not to cooperate in a game theory setting.
Kahneman utilizes the dictator game in 1986 to reinforce his understanding of the decisions that
individuals will make when asked to cooperate or defect with an opponent striving for similar
self-interest. His experiment was to ask individuals to split $20 between themselves and another
person. For the other counterparty, their options are to accept or reject. So the two possibilities
are that the first participant can split the $20 dollars evenly and give $10 to himself and $10 to
the other person. The other option is that the first participant can present the offer of taking $18
for himself and giving the other person $2. Based on our assumptions of game theory, one would
naturally think that the first participant would act in self-interest and attempt to offer an uneven
split to his counterparty. The only issue with this proposal is that most people would have an
inclination that their counterparty would reject that offer due to the fact that they are also acting
in their self-interest. The results are that 76% decided to split the money evenly because of their
fear about their counterparty potentially rejecting their offer due to the demonstrated lack of
altruism.
3. Application to Financial Markets
3.1 The Performance of Financial Advisors
First and foremost, one must understand Kahneman’s initial encounter with Wall Street
in order to determine some of the data that has been released regarding the influence on behavior
in the stock market. Kahneman was first introduced to Wall Street in 1984 with Amos Tversky
and Richard Thaler in order to meet with an investment manager and attempt to determine why
some individuals consistently lose or make money. One of the first observations that was
understood by both Kahneman and the financial industry was the Random Walk Theory, which
was coined by Malkiel. The central idea surrounding this theory is that a stock’s price is a

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continuous representation of the prediction regarding the future of the stock and the available
current information regarding the company’s valuation. Many academics claim that this
particular study is accurate, but Kahneman continued his curiosity regarding the reasons for
consistent profits or loss.
One of the major breakthroughs that enlightened Kahneman on the topic was extracted
from the work of Terry Odean, who previously studied under Kahneman and was a professor at
the University of California, Berkeley at the time. As a part of Odean’s experiment, he closely
followed the trade records of 10,000 brokerage accounts for a seven-year period in order to
determine the results of a particular common behavior that he noticed by investors in the
brokerage account. One of the major transactions that was being executed in these brokerage
accounts was the sale of a particular stock in order to buy a stock that the investor thought would
have more profit potential. In order to analyze the merits of this particular stock market
transaction, Odean tracked the performance of both stock, which was the one that was sold out of
and the one that was subsequently bought by the investor. The results ultimately showed that this
decision by investors was detrimental as the stock that was sold generally outperformed the new
stock that was bought by a margin of 3.3% annually.
Eventually, in Odean’s paper titled “Trading Is Hazardous to Your Wealth”, he proves
that the most active traders tend to have poor results. These result essentially have to do with the
way that investors react to changes in the market place. Usually, investors in the stock market
tend to sell out of the stocks they are gaining a profit on in order to close a transaction as a gain.
On the other hand, similar types of investors with the lack of emotional discipline will tend to
hang on to their losers with hopes that their investment will eventually break-even. The only
issue with this mindset is that stocks that have recently gained profit tend to perform better then
stocks that have recently lost profits. This can related to Kahneman’s value function as
individuals are risk seeking in the negative domain and hold more value in reaching break-even
after a loss of value rather than weighting it equal to the risk of further loss. At the same time,
both retail and institutional investors like to invest in companies that have more of a presence in
the news.
Kahneman goes on to mention during his studies of Wall Street that the majority of stock
pickers and investment funds do not have the necessary skill to beat the markets on a consistent
basis. Kahneman refers to the skill as the ability to consistently differentiate your profits year-
over-year from your competitors with the contingency that presence of luck is eliminated if the
correlation of returns over the years is significantly different from zero. Although the majority of
these funds cannot beat the markets on a regular basis, the level of skill that promotes the
importance of a financial advisor is determined by individual differences. Kahneman notes the
majority of mutual funds or approximately 66% of them underperform the market. Another key
factor to reaffirm Kahneman’s assumptions about luck is that the top performing mutual funds
every year tend to appear on the top of the leaderboard sporadically without any instance of
correlation between the year the fund was successful and the previous year’s returns.
Kahneman explains in his book “Thinking Fast and Slow” about how he was invited to
speak to a large investment firm at a social event. He essentially explains how, during this

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process, he stumbled upon the data and performance of 25 wealth managers within the firm over
an 8 year time period. He noticed that some of the upper-level managers within the firm were
providing compensation to the advisors based on the performance of the portfolio they
constructed. Based on a fairly simple statistical analysis of the data that Kahneman was given, he
performed a correlation analysis on year 1 versus all of the following years in pairs. For example,
he looked at the correlation between year 1 and year 2, year 1 and year 3, and so on. The results
were staggering to him as this process allowed him to determine that a seemingly successful
investment management firm’s performance was based more on luck and not on the skill that it
advertises.
3.2 Heuristics and Anchoring in Sales, Trading, and Real Estate
Some of the applications to the financial markets that is applicable to economic decision
making is the use of heuristics and anchoring, which increease the probability that investors will
act irrationally in the financial markets. The anchoring and adjustment heuristics has to do with
the idea that humans will commonly utilize mental shorcuts in order to make a quick judgement
or come to a conclusion given a particular scenario. These heuristics allow for humans to survive
on a daily basis without spending too much time doing extensive research before coming up with
a response to a trasitory occurrence. There are many times when these quick decisions based on
heuristics can lead to inadequate decision making. Essentially, humans anchor one of the major
pieces of information in the process of analyzing an event and then adapt according to the piece
of information to reach an ultimate decision that can be collectively deemed as rational.
Generally, the asking price on a property is a good example of utilizing heuristic thinking
based on an anchor. Usually, the strategy of a property owner looking to sell their listing will
either market the property at a selling price that is lower than the actual value of the house to
initiate a bidding war or make the selling price above the value of the house in order to try to get
a few buyers willing to pay above the property’s face value. The result is usually that the buyer
will provide a bid that is above the low asking price or a bid that is below the higher asking price.
Overall, the buyer is relying heavily on the information or anchor of the listing price. This is
usually a key factor influening the buyer’s decision and they usually adjust their perspective on
the property according to this anchor or what is considered a vital piece of information to
develop a conclusion about the listing. At the same time, no additional information has been
presented to the buyer such as the volume of buyers given the particular price. Due to the
preservation of information that the seller exhibits, it would be hard for the buyer to alter their
decision by utilizing the demand as an anchor for their adjustment heuristic. So if the listing
price is higher, the buyer may affiliate the value of the house with the listing price that is above
its intrinsic value. This is usually the reason why the proper strategy for the seller would be to set
the asking price of the property above the value of the house.
Studies show that one way to counteract a particular heuristic is determine a range of
possible options rather than one particular option or ultimatum. This allows for decision-makers
to adjust their estimates according to psychological biased. The idea of psychological pricing is
one of the major examples that is used on a daily basis. An example is when a retailer or seller
prices their product at 19.98, buyers are more likely to submit a bid for that product that is closer

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to the selling price because the decimal points or fractional currency. This is because the anchor
affiliated with this type of price is that the perception and anchor for decimals creates
adjustments by the buyer that tend to be smaller scale.
Anchoring is a concpet that is prevelant within the investment and sales community. The
anchoring and heuristics are utilized by retailers, stock brokers, car salesmen, and many other
sales professionals. An example of utilzing the effects of anchoring as a clothing retailer would
be to markup the price of your products as far as the way they are advertised on the price tag.
Once the customer comes in to try on a piece of clothing they like, a sales associate will come
over to the customer and mention that the article of clothing is on sale for approximately half the
price. Based on the effects that humans have on the fixation of anchoring their decision to a piece
of information, we will subconsciencely be influenced by the higher price and percieve the
clothing to be more valuable while portraying a higher status. Ultimately, this compels humans
to make the purchase even if the discounted price of the product is way above the amount they
were willing to spend.
In the financial markets, when stock brokers tend to give investment advice, they provide
a portrayal of a positive domain of gains. In Kahneman’s value function, individuals tend to take
the risk of losing money even if there is an equal chance of both gains and losses, which is why it
is common for investors to be easily persuaded by a stock broker or investment advisor even if
the risk-reward for the client is unfavorable. Stock brokers generally give advice to their client
on whether or not they should buy or sell a stock at a particular time. The way their sales pitch is
framed causes the client to anchor on to key pieces of information throughout the persuasion
process that leads them to a decision. An example of this in financial sales would be a stock
broker explaining that the research analysts within their firm have indicated that the stock’s
intrinsic value is drastically different than what it is selling for in the stock market. If the intrinsic
value is above the price of the stock, the broker will explain that it is the right time to buy the
stock and that it is being sold at a discount. At the same time, the client will anchor themselves to
the information provided by the analysts, which is the stock’s intrinsic value. They utilize the
heuristic regarding their inferences about the fact that the research analysts have conducted
extensive analysis to come up with the “true value” of the stock and are ,therefore, inclined to
make a quick decision that may end up being unprofitable or irrational. Also, the salesmen will
indicate the movement of the stock price and go on to frame the price’s peaks as the sole
indicator or synopsis of the price’s overall performance. Due to the broker’s motivation for
commission, this causes them to negate one of the most important factors in their investment
pitch, which is how to mitigate the downside risk affiliated with the stock or financial instrument.
This process is happening all while the broker is attempting to show the client that the particular
investment has growth potential in addition to the fact that it is trading at a discount to its
intrinsic value, as noted by the “professionals”or research analysts.
3.3 Kahneman’s Perspective of the Financial Markets
To further understand behavioral economics and decision making, it is important to
understand the results that Kahneman has enlightened individuals on when it comes to investing.
One of the ways to introduce some of the irrationalities present in the stock market, my studies

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include the following quotes and explainations regarding Kahneman’s perspective on the
financial markets:
 “Many individual investors lose consistently by trading, an achievement that a dart-
throwing chimp could not match.”First off, many traders tend to underperform the market
and are unable to match the returns of an individual that is choosing their investments
randomly. In the previous text, Kahneman proves this through his study of the skill
involved in investment advisory.
 “Few stock pickers, if any, have the skill needed to beat the market consistently, year
after year.” According to Kahneman, many stock pickers exhibit too much
overconfidence and belief that their ability to trade successful is unique to their natural
personality. Although Kahneman notes Warren Buffet as an exception, he believes the
odds of following a similar path for a traditional investor remains close to 0.
 “I actually am a believer in index funds. … if you don’t have very specific information,
which some say you’re not allowed to have, you better not kid yourself that you can pick
individual stocks.” Many of your tradional traders do not necessarily have the
information advantage that some of the professionals have. Professionals often hire
assistants or analysts to specialize in analyzing a particular stock or sector in order to gain
more information on the stock’s projected movement. Due to this premature disadvantage,
individuals are better off investing in index funds for the proper investment returns and
risk diversification.
 “For a large majority of fund managers, the selection of stocks is more like rolling dice
than like playing poker.” In Kahneman’s study of investment advisors, he provides a
measure of correlation for investment returns on a year over year basis and the data
brings him to the conclusion that the typical strong performance of a financial advisor is
attributable to luck and not skill. He explains that his thoughts about the need for
financial advisors is that their clients feel the desire to confide in them about monetary
decisions.
 “Groups tend to be more extreme than individuals.” Kahneman explains that there is a
herd mentality within the stock market and a network effect that essentially occurs. When
others notice excess demand or supply within the stock market, it causes them to
purchase or sell a stock solely based on the information about the transaction flows or
volume. This type of behavior is the reason for asset bubbles or exaggerated mispricings
of financial instruments as collective behavior is more pronounced than an indiviuals
thoughts or influence on pricing.
 “Hindsight, the ability to explain the past, gives us the illusion that the world is
understandable.” Many people when asked to recall the financial crises of 2008 are able
to explain the issues that caused the problem with great ease. This ability to recall the
past creates the illusion that investors will be able to forecast the future and better prepare
for it. The only aspect of valuation that makes sense for Kahneman in reducing
systematic risk in the financial markets is the idea of margin of safety, which essentially
provides an automatic safeguard for the macroeconomic risk that is uncertain and
unpredictable.

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 “A person who has not made peace with his losses is likely to accept gambles that would
be unacceptable to him otherwise.” This quote essentially explains that people tend to
make irrational decisions if they are prone to regret. The financial risk they may be taking
to begin with may not be worth the monetary reward or is a large proportion of their
income. Therefore, the loss of the gamble brings about the disfunctional emotion of
regret. If people thought with the mindset that they should not take a gamble that would
be regretted later, then individuals would maintain higher levels of utility while making
economic decisions with an emotionally stable and rational temperemant.
 People have “bounded self-control…. They have procrastination problems.” This quote is
a reiteration of the impulsive feelings that individuals have in the stock market. This has
to do with the natural tendency towards myopia that people having, which causes them to
reject the importance of future events in their valutation of a financial instrument. It turns
out that , if investments were held for a longer time period, most traders would be more
profitable as the returns would compound and the reward for deferring the realized gains
would be larger profits. As explained in prospect theory as a part of the value function
graph, investors will tend to sell winners early because they are risk averse in the positive
domain and hold less value in a positive prospect once their investment has gained value.
4. Application to Poker and Gambling
4.1 Behavioral Economics in Gambling
First off, it is important to intoruce some of the general applications of behavioral
economics to gambling. The identifiable forms of behavior include mood, playing with the
“house money”, gambler’s fallacy, and hot or cold streaks. The first form of behavior is mood,
which essentially draws the conclusion that mood affects one’s propensity towards risk. When an
individual is more optomistic, they exute the confidence to take a risk. On the other hand, if they
are pessemistic, then they will exhibit feelings of risk aversion. This was proven by Wright and
Bower in 1992 in their analysis of moods in the stock market. Their analysis showed results that
indicated favorable weather was correlated to positive gains in the stock market. Playing with
“house money” is another form of behavior that gamblers exhibit. This basically makes the
assumption that , when gamblers win a wager, they are more likely to have a feeling that they are
playing with money that is not theirs. Therefore, these individuals have less of a connection with
the money and tend to be more risky with the funds they just accumulated. On the other hand, if
they experience a large loss, then they instantly have the feeling that the money lost was theirs.
Therefore, the gambler becomes less confident about taking monetary risks. Another feeling that
gamblers naturally experience is gambler’s fallacy, which is the feeling that an event is less
likely to occur in the future if it has happened multiple times in a row and its occurences are
inconsistent with its associated probability. One of the instances of behavioral economics in
gambling is the feeling of a hot or a cold streak. Individuals tend to underestimate the instance of
chance in a particular outcome. In one of Tversky’s studies, he proved that basketball players
who have made more than 3 shots in a row have the confidence to believe that their high
percentage of shots made is mostly attributable to skill rather than luck. This is the reason why

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individuals believe overweight the probability of a trend in the financial markets or assume
autocorrelation between gains in different time periods.
4.2 Description of Traditional Texas Hold’em Poker
It is important to understand a basic description of Texas Hold’em Poker as it will help
with the understanding of some of the behavorial phenonomons that individuals encounter when
making economic decisions with outcomes that are uncertain. The game can mainly be broken
down into 3 particular categories, which are the setup, posting of the blinds, and betting rounds.
Poker is a game that invloves the interaction of 2-10 players seated at a table.
During the setup phase of the game, each player starts with x amount of poker chips
based on the amount of money they are willing to exhange for chips. Usually the betting that
occurs will requires the use of poker chips. Each player will be given a chance to deal out 2 cards
to all of the players at the table, which includes dealing the cards to yourself if you are the dealer.
The opportunity to be dealer or the position of the dealer will rotate clockwise around the table
so that every player has a chance to deal the cards. This dealer position will be characterized by a
dealer button, which will be passed around the table clockwise after each round to indicate who
the new dealer is during each round of play. Usually in casinos or tournaments, there will be a
dealer provided that does not participate in the game, in which case the dealer button will still
shift around the table to different players in a clockwise direction.
The second phase of the game involves posting blinds, which is broken up into small
blinds and big blinds in Texas Hold’em. Blinds are equivalent to a certain amount of chips.
Small Blinds are generally half the monetary value of big blinds. Whatever player is one position
to the left of the dealer at the table is required to post a small blind(placing chips into the middle
of the table), which is traditionally equivalent to a dollar amount of $1 for a game of medium
stakes. The big blind is required to post a dollar amount with their poker chips that is usually
twice the amount of the small blind, which usually amounts to $2. The big blind sits two
positions to the left of player who is dealing the cards and one position to the left of the small
blind. The small blind and the big blind are required to post their blinds in the pot before a round
can begin. Players who are sitting at the table and considered part of the game must post their
blinds when it is their turn. The remaining players get to start the round of play without paying
an money to start.
The third phase of the game includes the game-play and the betting rounds. As mentioned
before, each player is given two cards, which are dealt with the face side of the card down so that
no other opponent at the table can see them. Two important aspects of the game to note before
explaining the multiple rounds of betting is that the purpose of the game is to try to make the best
possible combination of a 5-card hand out of the 7 possible cards that will be available to the
players. After the 2 cards are dealt to each player, the dealer will deal 5 cards out in the middle of
the table with the face side up, which are known as community cards because everyone at the
table can utilize those cards to improve their hand. The way that the 5 cards are dealt is important

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to understaneding the game. There will first be 1 round of betting that occurs after everyone has
looked at the 2 initial cards that they are dealt in the begginning. After this round of betting, 3
cards out of the 5 cards mentioned previously will be dealt facing up in the middle of the table
for everyone to see. Since the point of the game is to put together the best combination of 5 cards,
the players must use the cards that are facing up in the middle of the table in order to put together
a hand. The first 3 cards out of the 5 total cards that will be dealt facing up in the middle of table
are known as the flop.
Once the flop is shown, players will determine whether or not the 3 cards being shown on
the table has imporved or weakened their their existing hand. The players want to see if these 3
cards have added value to the 2 cards they are holding face down. The players want to know if
their combination of 5 cards is favorable compared to their oponents. After the flop is dealt, the
betting will start with a certain player depending on where the dealer button is. The player whose
turn it is has to make a decision based on 3 options that will initiate a response from their
opponent to the left of them. The initiating actions that could be taken by the first player are to
bet, check, or fold their hand. Betting requires that the player risk a certain amount of poker
chips and place them in the pot or the middle of the table. This usually occurs if they believe that
the readily observable 5 card combination that is known to them is considered strong. This first
player, which is known as the player who is first to act, can also check. Checking is an action
that is taken that does not require betting by the player, which passes the action on to the player
on their left. This usually occurs when this person is not happy with the strength of their hand
and wants to see what actions the rest of their opponents will choose. Folding occurs when the
player gives their cards to the dealer and forfeits their participation in the rest of the hand. This
usually occurs when an opponent makes sizable bet that the folder is uncomfortable with or
when they do not have a hand that they are confident about to continue in the hand. Once the first
player makes a decision on his three options after the flop(the 3 cards facing up), then the player
to their left must respond to the first player’s actions. The second player that is asked to act will
have response options that are based on the actions of the previous player. The second player to
act can fold if the first player bets an amount that they are uncomfortable with, in which case
they cannot win the pot(the monetary value of the chips in the middle of the table. This second
player to act may also check if the first player decides that they want to check and not bet
anything. This same player could bet if the first player decided to check. This player can simply
call, which happens when the player before them bet. During a call, the second player to act must
respond by matching the amount bet by the first player to act. Otherwise they may not continue
on in the hand. The second player to act can also respond by raising, which means that they will
respond to player 1’s bet by betting an amount that is higher player 1’s bet. All of these possible
action among the players take place after the flop.
As mentioned before, there is a total of 5 cards that must be dealt facing up in the middle
of the table for the players to improve their hand with. Once the flop happens and the first 3
cards are dealt at one time, then the remaining 2 out of the 5 cards must be dealt facing up. After
the flop happens and all of the betting is concluded after the flop, 1 more card is dealt facing up.
This card is called the turn. Once the turn happens, then players go through another round of
betting and actions mentioned previously. After the turn, the final card is dealt in the middle

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facing up. This card is called the river. The river is the final card that is placed facing up in the
middle of the table. Following this card, there is one more round of betting and actions that occur
before a winner is determined by everyone showing their cards to see who has the best hand. A
winner can also be determined if ,during the rounds of betting, everyone at the table folds their
hand but one person. This usally occurs when someone makes a bet that the rest of the table has a
difficult time calling(matching the size of the bet). The following chart shows the strength of
poker hands from the best poker hands to the worst poker hands.
4.3 Poker’s Relationship to Prospect Theory and Value Function
Poker is a perfect game to test behavioral economics and some of the merits of prospect
theory as requires the ability to make decisions when there is a level of uncertainty or risk.
Similar to studies in Microeconomics, poker is a game that involves weighing the marginal costs
versus the marginal benefits of a particular scenario and then deciding how to weight the
probability of an outcome. Poker is a zero-sum game, which means that the profits you gain are
based on the rationality of you and the oponents around you. If your assestment regarding your
skill level or ability to calculate the probability of a particular hand is not an accurate
representation of reality, then your opponent will exploit some of the behavioral flaws in order to
profit. The assessment of probability that is noted within poker stategy is known as Bayesian
perspective. The most important facet of one’s strategy is to be self-aware regarding their
prospective of the potential outcomes at hand. According to neoclassical assumptions of prospect
theory, experienced players will have the emotional stability and temperemant to be able to
withstand large profits or losses without causing them to demonstrate irrational behavior.
Inexperienced poker players will often be confident and overestimate their ability in the instance
of a gain or the positive domain. On the other hand, players that are continusly incurring losses
will underestimate their abilities and believe their interpretation of the probabilities are
inaccurate. This leads one to believe that the behavioral aspects of poker are one of the more
important variables in analyzing skill as there are often contradictions to Kahneman’s value
function as well as reenforcements to his theories on positive and negative domains for some of
the more experienced players.
One of the first measures of economic decision making in poker is to measure a player’s
procilivity towards positive profits based on whether or not they use an aggressive style or
conservative style of play. Aggressive style of play is characterized as a player that initiates bets
and raises a lot in comparison to the amount of times they fold, check, or simply call the previous
bet. Aggressive players will often bet a lot in order to try to get their opponent not to continue the
remainder of the hand. Aggressive players like to win the hand of poker before the final card or
river is dealt. Essentially, these types of players will hope that their bets will get everyone else at
the table to fold. Very often, aggressive players will bluff and attempt to misrepresent the cards
they have to other players. This action is taken when the player wants their oponent to fold by
making them believe they have a strong hand even when they do not.
The other style of play is known as conservative style. These types of players will
particpate in less rounds of betting and will generally check, fold, or call more than they raise or
bet. Very often, this type of player will not participate in a hand due to the fact that they are

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waiting for the right opportunities or risk to take. These players generally wait for a strong hand
to play all the way to the river card or the final round of betting. If the opportunity does not arise,
they will simply not bet or participate. These players tend to take more calculated risk while the
variance of their gains and losses are relatively low. These players look for monetary rewards
that have a positive expected value. Even if these expected values may be lower than a skilled
aggressive player, the amount of risk assumed by these players is substantially lower.
The ratio that will be utilized to determine the style of play whether it be aggressive or
conservative is characterized by the ratio of the amount of bets and raises to the amount of
checks and calls. Players are considered passive or conservative when this ratio is below 1 while
aggressive players are characterized by agressiveness ratios above 1 or 1.5. Based on a statistical
study conducted in Ponoma college comparing the wins and losses of both styles, players tend to
be more aggressive after they have incurring a large loss than they are after gaining a large profit.
This data was retrieved by analyzing the agression ratios for a sample of players over a particular
period of time following a monetary gain or loss.
These studies reinforce the foundation of Kahneman’s prospect theory as it relates to
value function. This statistics clearly show that , when a player enter the negative domain after a
financial loss, they tend to be risk seeking. This is essentially due to the convexity of the value
curve previously mentioned in the negaitve domain of the value function. When the poker
players in this sample incurred a loss, they were holding more value in a positive prospect, which
is the urge to retrieve break-even, which is at the origin of the value function. At the same time,
these same poker players were more likely to be exhibit risk aversion when they were in the
positive domain of the value function. After gaining profit, these players essentially become
desentized to further wins. In my opinion, this creates the foundation for the common emotion of
greed in economic decisions.
One of the natural behaviorals that gamblers exhibit that is a contradiction to
Kahneman’s beliefs about prospect theory is the idea of gambler’s fallacy. Gambler’s fallacy is
the notion that an event that has occurred more than expected based on its probability will not
occur in the future trials of that event. Another study done by Ponoma College demonstrates the
merits of gambler’s fallacy versus prospect theory. Variances in a poker players wins and losses
can be determined by two types of wins. The first kind of win is cumulative in which the player
experiences several small wins throughout the course of their play to amount to a lrger gain in
the long run. The other type of win involves the instantaneous win or loss of large pots in poker.
This causes players to lose or gain a large amount in a short period of time. In order to determine
the merist of gamblers fallacy, one must look at the cumulative gains and losses experienced by
the players. The application of gamblers fallacy in cumulative gains or losses is that players will
tend to become more conservative when they are winning many times in a row due to the fact
that they believe their good fortune will eventually reverse into losses.
On the other hand, a large monetary gain or loss in poker can provide the foundation for
value function in prospect theory due to the fact that prospects are reevaluated from a different
reference frame in a negative or positive domain. The question is whether or not small
cumulative gains cause more of change in the player’s behavior than large instantaneous gains.

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According to a studies conducted at Ponoma College gathering data from 6 player poker tables,
67% of players acted more aggressive after a single big loss while only 58% of that same sample
acted more aggressive after cumulative losses. In my opinion, this shows that Kahneman’s
prospect theory provides a better understanding for the change in behavior that occurs after a win
or a loss. In my opinion, the constructs of a new value function can be introduced for cumulative
changes in gains or losses. The results of this chart would be less feelings of loss aversion at the
origin as the value curve in the negative domain would have a flatter slope. Although the
concavity would be the same, the behavior in both the negative and positive domain would be
different for this hypothetical value function for cumulative gains and losses.
5. Conclusion
In conclusion, one can determine that the merits of economic decisions from a behavioral
perspective can be validated based on the merits of prospect theory, expected utility theory, and
some of the key contradictions to neoclassical assumptions regarding decision making. My initial
hypothesis was that gains or losses would have a strong influence on our behavior in subsequent
decisions. Specifically, my beliefs were that positive monetary gains would lead to behavior that
is risk seeking while negative monetary gains would leed to risk aversions. My hypothesis was
contradicted by the foundations of value function within prospect theory. The application of
prospect theory in the financial markets and the game of poker reaffirmed reaffirmed the notable
contradiction of my initial hypothesis. Overall, behavioral economics provides emperical
evidence for the emotions that arise when making decisions with undercertainty.
6. References
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Brunnermeier. "Learning to Reoptomize Consumption at New Income Levels."
Scholar.princeton.edu. Web.
Dalla. "News :: Story Cache." Game Theory .net. Web. 16 May 2014.
"Daniel Kahneman - Biographical." Daniel Kahneman - Biographical. Web. 16 May 2014.
"Daniel Kahneman - Biographical." NobelPrize.org. Web. 16 May 2014.
"Decision Making: The Psychology of Choice." Stanford.edu. Web.

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"A Dozen Things I've Learned About Investing from Daniel Kahneman." 25iq.com. Web. 16
May 2014.
Holt, Jim. "Two Brains Running." The New York Times. The New York Times, 26 Nov. 2011.
Web. 16 May 2014.
"Judgment under Uncertainty: Heuristics and Biases." Judgment under Uncertainty: Heuristics
and Biases. Web. 16 May 2014.
Kahneman, and Tversky. "Prospect Theory: An Analysis of Decision under Risk." Princeton.edu.
Econometrica. Web.
Kahneman, Daniel. "Don’t Blink! The Hazards of Confidence." The New York Times. The New
York Times, 22 Oct. 2011. Web. 16 May 2014.
Knauff. "Result Filters." National Center for Biotechnology Information. U.S. National Library
of Medicine. Web. 16 May 2014.
Lavin, Jonathan. "Choice under Uncertainty." Stanford.edu. Web. 16 May 2014.
Marotta, John. "Behavioral Finance: Anchoring." Marotta Wealth Management. Web. 16 May
2014.
"Nobel Prize Winner: Stock Advisors Are Worthless." Forbes. Forbes Magazine. Web. 15 May
2014.
"Prisoners' Dilemma." : The Concise Encyclopedia of Economics. Web. 16 May 2014.
Redding, Joseph. "Hyperbolic Discounting." Hyperbolic Discounting (2001). Web. 15 May 2014.
<http://www.behaviorlab.org/Papers/Hyperbolic.pdf>.
Smith, Gary. "Poker Player Behavior After Big Wins and Big Losses." Pomona.edu. Web. 16
May 2014.
"Von Neumann-Morganstern Expected Utility Theory." EconPort. Web. 16 May 2014.

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