Using the Coefficient of Rationality to Allow Classical Game Theory
To Handle Emotions,
Cultural Norms and NonPerfectly Rational Players
by Mark Stuckel
Abstract: Current advancements in game theory,
namely RabinÕs incorporation of fairness, have substantially improved game
theoryÕs applicability to real world interactions by recognizing that humans do
not act perfectly rationally.
However, it will be demonstrated that these improvements are
incomplete. By understanding that all human emotions affect
how rationally we act (positively or negatively), we can better grasp realworld
strategic interactions and better formulate the effects various emotions have
on them. Once this is recognized,
it will become possible to measure to what degree emotions detract or enhance a
personÕs rationality. After every
emotion and cultural norm is accounted for, we will be left with a final numerical
value called the Coefficient of Rationality (CoR). The CoR is defined as the degree to which a personÕs actions
conform to those of a perfectly rational being. The CoR should not be seen as a gauge for normative
analysis, instead it should be seen as a predictive tool which incorporates
emotions and cultural norms into GT in order to determine Nash Equilibriums for
nonperfectly rational players.
1. Introduction
The
overall purpose of this paper will be to introduce the concept of the
Coefficient of Rationality and to explain how it will allow us to use classical
game theory to generate corresponding Nash Equilibria for players who act from
emotions and cultural norms and who are not perfectly rational. Additionally, several philosophical
questions will be addressed along the way.
I will employ the following strategy:
1)
Explain
what classical game theory says about the theoretical outcome of the Ultimatum
Game
2)
Show
what actually
happens in real world Ultimatum Games.
3)
Discuss
how Rabin improved upon GT by incorporating fairness.
4)
Show
why RabinÕs model is incomplete.
5)
Provide
a better model for incorporating emotions and other cultural norms into game
theory by introducing the concept of the Coefficient of Rationality.
6)
Show
how the CoR is measured and used to find adjusted Nash Equilibria.
I: What does classical game theory say about the theoretical
outcome of the Ultimatum Game?
The
Ultimatum Game is an experimental game used in economics to model strategic
interaction. The first player
(player A) is awarded a sum of money and must divide it by making an offer to
the other player (player B).
Player B can either accept the offer or reject it. If B accepts the offer, the money is
split as dictated by A. If B
rejects the offer, neither player gets any money.
In
classical game theory, meaning that if the game were played by two perfectly
rational beings desiring only to maximize their own monetary payoff, the
resulting outcome would be player A will offer 1 cent to player B and 99 cents
to himself. The reason being that
since player B has no say in the division, his best option is to just accept
whatever positive offer is given to him. If he rejected the 1 cent he would not
be maximizing his utility since he would then be forgoing a positive gain. The Nash Equilibrium is therefore A, 99
: B, 1. A Nash Equilibrium occurs
when both players are currently playing a strategy that cannot be improved upon
by switching to a different strategy.
We will later see that the CoR will help determine adjusted Nash
Equilibria for nonperfectly rational beings that incorporate emotions,
cultural norms and other preferences.
II: What do the results from
experiments by Kahneman, Knetsch and Thaler say about the actual outcome of the Ultimatum Game?
The
conclusion reached by Kahneman, Knetsch and Thaler is that people tend to offer
fairly even splits and when an unfair split is offered (usually less than a 25%
offer) the offer is rejected.
TABLE 2 Experiment 1 Results ^{1}
Class: Psychology/ Psychology/
Commerce1
Psychology Commerce
Psychology
Mean amount offered ($) 4.76 4.47
4.21
Equal split offers (%)
81 78
63
Mean of minimum acceptable ($) 2.59
2.24
2.00
Demands > $1.50 (%)
58 59
51
Participants (IV) 43 37
35
As a result of their research, Kahneman, Knetsch and Thaler offered an even broader conclusion. They stated: ÒThe traditional assumption that fairness is irrelevant to economic analysis is questioned. Even profit maximizing firms will have an incentive to act in a manner that is perceived as fair if the individuals with whom they deal are willing to resist unfair transactions and punish unfair firms as some cost to themselves. The rules of fairness...help explain some anomalous market phenomena.Ó^{1}
Their
paper marked an important step in the improvement of game theory. By recognizing that humans do not
interact in accordance with classical game theory, he set the stage for Rabin
to mathematically formalize fairness and incorporate it GT in order to better
model real world strategic interactions.
The crucial step was to realize that most people take more than just
utility and monetary payoff into consideration when making decisions in the
Ultimatum Game (and life in general).
For example, some people are strongly influenced by what others will
think about their actions and therefore act accordingly. Others are influenced
by their deep religious beliefs or lack thereof. It will later be shown that these emotional and cultural
inclinations affect how ÒrationalÓ a person is (rational meaning maximizing
their own payoff). And by
formalizing these inclinations mathematically, it will be possible to complete
RabinÕs model by incorporating all emotions and cultural norms into GT. When this is complete, it will be
possible to use classical game theory to develop adjusted Nash Equilibria based
off of nonperfectly rational players.
But before this can be discussed, we have to first understand how Rabin
formalized just one aspect: fairness.
III: How did Rabin formalize the concept
of fairness and thus improve the realworld applicability of classical game
theory?
Firstly, Rabin reformulated Kahneman, Knetsch and ThalerÕs
view by saying, ÒPeople like to help those who are helping them, and to hurt
those who are hurting them. Outcomes reflecting such motivations are called
fairness equilibria. Outcomes are mutualmax when each person maximizes the
otherÕs material payoffs and mutualmin when each person minimizes the other's
payoffs. It is shown that every mutualmax or mutualmin Nash equilibrium is a
fairness equilibrium. If payoffs are small, fairness equilibria are roughly the
set of mutualmax and mutualmin outcomes; if payoffs are large, fairness
equilibria are roughly the set of Nash equilibria.Ó He specifically addresses the Ultimatum Game in his paper on
page 1284 (The American Economic Review, December 1993). One of his main points was to show that
in real world Ultimatum Games, classical game theory strategy did not maximize
payoffs.
To summarize briefly for clarity:
A Nash equilibrium occurs when both players are currently playing a strategy that cannot be improved upon by switching to a different strategy.^{4, 5}
Mutual max outcomes occur when, Ògiven the other person's behavior, each person maximizes the other's material payoffs.Ó^{2} [p. 1282]
^{ }
Mutual min outcomes occur when, Ògiven the other person's behavior, each person minimizes the other's material payoffs.Ó^{2}[p. 1282]^{}
^{ }
Rabin
goes beyond simply recognizing that fairness considerations affect peopleÕs
behavior and instead puts forth a method/framework to formalize fairness
mathematically to incorporate it into game theory. RabinÕs purpose was to take this new formalization and apply
it to the payoff matrix to show that people alter their behavior based on how
they are being treated. For
example, people who believe they are being treated unfairly will treat the
aggressor badly in return.
Conversely, people who feel they are being treated well will return the
favor. This fluctuation in the way
people interact is described by fairness equilibria.
With
this conceptual schema in mind, he bases his framework off of a similar idea
developed by Geanakoplos, Pearce and Stacchetti in order to formalize
fairness. The framework developed
by GPS took standard game theory and modified it to incorporate actions and beliefs when calculating
payoffs.
Rabin
dismisses the argument that this new formulation is unnecessary and that these
beliefs could somehow be incorporated by Òtransforming payoffsÓ and analyzing
it in the conventional way.
RabinÕs response is to say that if one were to try and formalize this
under classical game theory, it would inevitably lead to various
contradictions. For example, in
the Òbattle of the sexesÓ game, the standard game theory model says that each
player Òstrictly prefers to play his strategy given the equilibrium.Ó^{2} This means that there needs to be a way
to formalize the fluctuations of one person's payoffs based on:
1:
The husbandÕs strategy.
2:
The wifeÕs beliefs about what her husbandÕs strategy will be
3:
The husbandÕs belief about what his wife believes his strategy will be.
The
following formula incorporates these beliefs about fairness into GT to better
understand the desired Nash Equilibrium of the husband and wife:
U_{i }(a_{i}, b_{j},
c_{i}) = ¹_{i} (a_{i}, b_{j})
+ F_{j} (b_{j}, c_{i}). [1+f_{i} (a_{i},
b_{j})] ^{2}(page
1287, Vol. 83 No. 5)
So
in plain English we can read each of these pieces as follows:
U_{i
}= Player IÕs utility
a_{i
} = the husbandÕs or player
iÕs strategy
b_{j }= The wifeÕs or player JÕs belief
about what player IÕs strategy is going to be
c_{i}
= player iÕs belief about what the other player believes his (player i)
strategy is
¹_{i} (a_{i}, b_{j})
= player iÕs payoffs
F_{j} (b_{j}, c_{i})
= how kind player i thinks player j is being to him
f_{i}
(a_{i}, b_{j}) = how kind player i is being to j
IV: Why is incorporating fairness, on its own, into game theory
an incomplete approach?
The
short and simple answer would be to say that although RabinÕs fairness
formulation is a significant step forward in the understanding of real world
interactions by incorporating a psychological element into game theory, he
fails to see that fairness is only one human emotion or cultural trait that
affects how people interact. For
example:
1: Other human tendencies beyond
fairness affect the outcomes of the Ultimatum Game.
2:
There can be varying degrees of fairness (e.g. variations across cultures).
3: Some
people do not act fairly (see table 2).
V: What is a better way to incorporate fairness and other human
tendencies into GT?
The key step in improving upon Rabin is
to recognize that fairness is something that is not (perfectly) rational. By rational, it is meant that one
maximizes utility or pay off or expected outcome (I do not mean rational in a
larger ethical or philosophical sense).
With the perfectly rational being as a reference point, we notice that
emotions affect peopleÕs actions either positively or negatively. Instead of looking at fairness as
something by itself, we should instead look at it as something that adds or
subtracts a certain measurable quantity X from the perfectly rational level of
1.
These levels of rationality are measured
by the Coefficient of Rationality.
1: The CoR is a numerical measure of how
rational an entity is on a scale from:
a: +1 (perfectly rational; acts
as a perfectly rational being would)
b: 0 (perfectly random)
c: 1 (perfectly irrational; does exact opposite of perfectly
rational being)
0,1
1,0 0,X* 1,0
The xaxis stands for
the coefficient of rationality.
The yaxis stands for
the probability we can predict the agents actions/beliefs. (note*: the lower bound probability,
where the curve crosses the y axis, is defined as 1/the number of choices. In the Ultimatum Game, that probability
for player A is 1/101 since there are 101 amounts to offer. The probability for B in the Ultimatum
Game is 1 / 2 since he has to choose either accept of reject. The upper bound is 1, hence the
straight line across the top.)
We can
read the chart and apply it to the Ultimatum Game as follows:
1: A, 1 : B, 1 both agents are perfectly rational, CoRs of 1.
A,99 : B,1 the outcome will be as dictated by
standard game theory. It is
important to note, that the perfectly rational agent always maximizes their
outcome/payoffs regardless.
2: A, 1 : B,1 (A acts perfectly rationally, B acts perfectly
irrational.)
A, 100 : B, 0
(A will know that the most irrational thing to do as player B would be to
accept an offer 0.)
3: A, 1 : B, 1
A, 0 : B, 100 (A being perfectly irrational would offer the
lowest expected outcome which would be 0 and B being perfectly rational would
gladly accept.
4: A, 1 : B, 1
A, proposes 0 : B, 0 (he
rejects the 100 payoff. Notice
that when both players are perfectly irrational, the result is the lowest
possible outcome: neither player gets anything)
5: A, 0 : B, 0
A, 25 : B, 25 (note: for the
perfectly random ones, I took the limit of the payoffs as if the game were
played an infinite amount of times.
For example in this case, A will offer an average of 50 and B will
accept ½ of the time, thus leading to an overall pay off of 25 for both.
6: A, 1 : B, 0
A, 50 : B, 0 (Knowing that B
is perfectly random, he knows that B will accept exactly ½ the time
regardless of what A offers.
Therefore A offers 100 every time.
He has nothing to gain to by lowering his bid, and nothing to lose by
always offering 100.
7: A, 1 : B, 0
A, 0 : B, 50 (The perfectly
irrational player will always offer 0, and player B will accept the 100 half of
the time.
8: A, 0 : B, 1
A, 49: B, 49 (Player will
offer an average of 50 and player B will accept every offer except for an offer
of 100. Therefore, each player
loses that one round.
9: A, 0 : B, 1
A, 1.01 : B, 0 (Player will
offer an average of 50 and player B will reject every offer except for an offer
of 0. Therefore, each player A
wins that one round and getÕs 100.
Winning 100 out of every 101 turns equals an overall payoff of 1.01.
Now
that the extremes are covered, we can work backwards and fill in the gaps for
the other values, thus leading to some important conclusions:
1: The more rational a person is,
the more likely they will accept a low offer, and the more likely they will
offer a higher number.
2: Acting irrationally has a lower payoff
outcome than acting randomly.
3: The higher the sum of the CoRs, the
greater the expected outcome for both players.
4: The lower the sum of the CoRs, the
lower the expected outcome for both players.
5: The only times the full prize is handed out every round, is
when at least one of the players is perfectly rational.
6: The only time no money is
distributed every round, is when both players are perfectly irrational.
With
these numbers in mind, we can now view fairness as something that, all things
being equal, subtracts a certain value from a CoR of 1. The beauty of this approach compared to
RabinÕs is that now we can add in other human tendencies into the mix and
determine how they affect someoneÕs CoR.
Depending on whether they affect it positively or negatively, the new
CoR value will affect how the Nash Equilibrium is adjusted.
My
fundamental claim is that all of our emotions and cultural norms will have a
certain measurable effect on the rationality of our actions. Since this section might be
controversial, I will first address some of the philosophical implications of
this approach.
In the
extant and voluminous literature dealing with human emotions, there is much
debate over how certain traits affect a subjectÕs actions. In the previous paragraph, I have
claimed that, all things being equal, fairness would negatively affect a
personÕs expected outcome in the Ultimatum Game. However some have argued that fairness and other emotions
can also benefit a personÕs expected outcome (like Jack HirschleiferÕs On
the Emotions as Guarantors of Threats and Promises.) In his article, Hirschleifer argues that people can
sometimes improve their expected outcome by not acting self interestedly. Additionally, ÒÉ emotions can serve a
constructive role as guarantors of threats or promises in social interactionsÓ
[OEGTP, p.2]. Nevertheless, this
fact does not take away from the view I am advancing.
In the
previous paragraph, I stated that all things being equal, fairness would negatively
affect a personÕs expected outcome in the Ultimatum Game. However, if we include Òall other
things,Ó it could very well be the case, that fairness can improve a
nonperfectly rational beingÕs expected outcome.
One of
the philosophical implications the CoR will have for fields dealing with Òall
other thingsÓ(emotions, cultural norms, etc.) is that it will become clear that
the correct way to view the effects of emotions and other cultural norms will
be to view them in terms of how they will affect a personÕs CoR. Doing so will determine which emotions
positively or negatively affect a personÕs utility. In addition to this, it will also determine which emotions affect
utility the most or least in different situations. For example, fairness might equal, on average .1 for all
situations. While equaling .2 in
the Ultimatum Game and +.1 in a true bargaining situation at a street
market. Generosity might be on average
.1 and selfishness might be on average +.1. But what we can say with absolute certainty from table 2 is
that the students are not acting perfectly rationally. It then follows that their emotions and
other cultural norms as a whole are affecting their decisions and outcomes and
subsequently their CoRs. If they
were acting perfectly rationally, the experimental results would perfectly
reflect classical game theory.
Once the list of the traits and their effects is large enough, it would
be possible to add them all together and come up with average values for
different populations.
For example,
several research studies^{3} have been conducted to show how different
cultures play the Ultimatum Game differently. From the chart below, it can be observed that people in
different societies with different social and cultural norms will offer different
amounts to player B. Similarly,
(if we assume player B is perfectly rational) the farther down the list we go,
the higher the populations CoR i.e. the closer they conform to what a perfectly
rational person would offer.
ÒA bubble plot showing the distribution of UG offers for each group. The size of the bubble at each location along each row represents the proportion of the sample that made a particular offer. The right edge of the lightly shaded horizontal gray bar gives the mean offer for that group. Looking across the Machiguenga row, for example, the mode is 0.15, the secondary mode is 0.25, and the mean is 0.26.Ó ^{3}
As a
side note, before there is any confusion, I would like to make clear that the
CoR should be seen as a purely predictive tool to better find Nash Equilibria
and not as a scale with which to compare and judge right from wrong, virtuous
from nonvirtuous or good emotions from bad emotions. The CoR will be used to better assess how different people
with different norms and emotions interact with one another. It is beyond the scope of this paper to
determine whether or not game theory should or could be used for normative
analysis in fields like ethics or value theory. The CoR should not be seen as the gold standard of how one should act, but rather as a guide for
maximizing desired payoffs. And,
as we will see shortly, this includes both monetary and nonmonetary payoffs.
VI: How do we measure the CoR? And how, specifically, is it used?
By
conducting tests similar to those in table 2 we can determine that the average
person strays from perfectly rational behavior by X%. If the results showed that average amount awarded was 90% of
the total prize pool, we would say they strayed from perfectly rational
behavior by 10% and had an average CoR of .8.
CoR = 1  (% difference to perfectly
rational outcome * 2)
CoR = 1
Ð (.10*2)
CoR =
.8
We
subtract from 1 because that is the value assigned to a perfectly rational
group.
We multiply the % by two
in order to extend the spread into the negative numbers for the perfectly
irrational side.
Another
way to determine CoRs would be to use economics experiments specifically
designed to determine how close a give person compares to what a perfectly
rational person would do in the given situation. For example, you could hand them a survey that asks questions
along the lines of: Would you accept or reject an offer of 50? How about 40? 30?...1? Also, what would be the highest value
you would offer to a person who is perfectly rational? Etc, etcÉ And after
collecting enough data you could develop a bell curve that would graph the CoRs
and determine a mean, median and standard deviation. Then you would be able to find a desired Nash Equilibrium
that corresponds to player BÕs desires which also maximizes player AÕs desires,
too.
One
possible objection to this might be to arguing the following point. How does the CoR complete RabinÕs model
of incorporating fairness into the problem of measuring and formalizing
nonutility based payoffs? Rabin
seems to be saying that for most people, they do not act 100% rationally
because they Òfeel betterÓ when they act fairly. Thus fairness is a nonutility payoff that must be factored
into game theory when trying to determine and maximize ones monetary and non
monetary payoff. The CoR model
only focuses on how much the two players end up making in the end and not their
overall nonutility based payoff associated with forgoing additional monetary
gain in return for a sense of wellbeing by acting fairly.
Now,
this is a legitimate objection but I argue that it is misguided. The CoR does take into
considerations the playerÕs preferences for fairness and other nonutility
based payoffs. When the previously
mentioned survey is taken, it can be assumed that a player who refuses to offer
less than 40%, prefers this action because their emotions or cultural norms
tell him that being fair, or whatever he wants to call it, is ÒworthÓ more than
the forgone monetary gain.
One
might object to this again on the grounds that the CoR couldnÕt possibly
differentiate between a person who is very altruistic and a person who simply
just isnÕt very rational. Both
people would be assigned the same CoR.
The objector would continue, ÒBut shouldnÕt we be concerned with why people are acting a certain way?Ó
In
response to this, I would that yes, the CoR cannot differentiate between these
two cases. However, since
GT is only concerned with the ends and payoffs, the ÒmeansÓ of how we achieve
these ends does not matter. For
example, what difference does it make that a person will not offer a bid lower
than 40 because he fears person B will reject his offer and he will lose out on
the money vs. a person who will not offer less than 40 based off of a strong
moral conscience and a desire to always be fair? The purpose of the CoR is to mathematically formulate all
emotions and cultural norms into classical game theory in order to find Nash
Equilibria that are adjusted to incorporate emotions, cultural norms, and
nonutility based desires. Therefore
the reasons for peopleÕs actions arenÕt as important as the outcomes of their
actions and with this, the problem of incorporating nonutility payoffs is
solved.
Rabin
formulated fairness into game theory to better model how people interact with
one another and how fairness changed the Nash Equilibria. One of his findings was that people
tend to want to help others who are helping them and hurt others who are
hurting them. His formalization of
fairness introduced a model that fluctuated to different equilibriums depending
on how player A was treating player B.
Now
that we have the CoR value, it raises the questions, ÒOk, now what do we do
with it? Why is it
important?Ó And in response, there
are several answers. The most
important ones include:
1) By applying this value to two
individuals, we can better formulate a corresponding Nash Equilibrium based on
their CoRs.
2) The more information we know
about a particular person or population, the better we can predict how they
will respond/act.
3) This value is extremely important
because if we could find a value that predicts with great accuracy how a
population will interact with itself, then we could find the best ÒoffersÓ to
make to maximize our desired payoffs.
Additionally, by applying this framework beyond the Ultimatum Game into
the business world, or other social environments, we could better model various
strategic and not strategic interactions.
To
illustrate this last point I will now show through an example how to use the
CoR to find an adjusted NE that maximizes each playerÕs desired payoff. Let us first imagine the following
possible data for a typical Ultimatum Game.
X Nash
Equilibrium X
Offer => 
50/50 
30/70 
10/90 
Accepts offer 
B 50, A 50 
B 30, A 70 
B 10, A 90 
99% chance = 49.5avg 
75% = 52.5avg 
20% = 18 avg 

Rejects offer 
0,0 
0,0 
0,0 
** LetÕs assume that
a person with a .7 CoR will accept a 50/50 split 99% of the time, and a 30/70
split 75% of the time and a 10/90 only 20%. The CoR is what helps us determine how likely player B will
accept or reject a particular offer.**
If we put ourselves in
person AÕs position, the person making the offer, we can quickly find the offer
that maximizes our expected outcome and the offer that represents a Nash
Equilibrium. First we calculate our
own CoR (since we have the most information about ourselves). For this example I will use a CoR of 1
for the player making the offer.
Next, if we know that the average person to which we are offering a
portion of the prize has a CoR of .7, we can optimize our utility/payoff by
offering a value that maximizes what we give to ourselves and minimizes the
rejection rate. Therefore, from
this chart we can infer that optimal offer is 30, because it will return to us
an average of 52.5. Knowing player
BÕs CoR helped me to determine his acceptance rate. I cannot improve my payoff by changing my offer and player B
doesnÕt gain by rejecting.
Therefore, we are at an adjusted Nash Equilibrium that could not have
been found using classical game theory alone. The CoR was instrumental in allowing us to calculate the NE
for nonperfectly rational players by converting their emotional and cultural
inclinations into a numerical value.
This value was then used to determine their acceptance/rejection rate,
and then supply player with the knowledge of how to maximize his payoff.
VII: Application beyond the Ultimatum
Game
A
better understanding of the CoR would lead to a more unified model of how
different people with different emotions, cultural norms and preferences interact
with each other. It is not hard to
imagine the possible effects this could have on businesses, advertisers and
other fields involved in the maximization of payoffs as a result of strategic
interaction. Along these lines,
studies of this nature could change how politicians ÒmarketÓ themselves to the
electorate. This paper should
provide a solid foundation upon which future game theorists, mathematicians and
psychologists could base a coherent formulation of the human psyche, in order
to better predict strategic interactions among individuals and groups, thus
maximizing a playerÕs desired outcome.
Additionally, this paper should introduce new philosophical questions
and implications. For example, should the CoR be used to make normative
statements about which emotions or preferences are or are not rational?
VIII: Conclusion
The classical model of game theory
is insufficient for describing real world strategic interactions primarily
because it is designed to handle perfectly rational beings; humans, however,
are not perfectly rational. Rabin
improved upon this by mathematically formalizing fairness into GT. However his formalization was
incomplete because he failed to incorporate other influential emotions and
cultural norms. By expanding upon
RabinÕs fairness model using the CoR, it will now be possible to mathematically
incorporate
these emotions and cultural norms into GT in order to determine Nash
Equilibriums for nonperfectly rational players.
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by Daniel
Kahneman, Jack L Knetsch and Richard H Thaler, The Journal of Business, Vol.
59, No. 4, Part 2: The Behavioral Foundations of Economic Theory. (Oct., 1986),
pp. S285S300.
2) Incorporating
Fairness into Game Theory and Economics, by Matthew Rabin, The American Economic Review, Vol.
83, No. 5. (Dec., 1993), pp. 12811302.
3) ÒEconomic manÓ in crosscultural perspective:
Behavioral experiments in 15 smallscale societies, Joseph Henrich, Robert Boyd, Samuel
Bowles, Colin Camerer, Ernst Fehr, Herbert Gintis, Richard McElreath, Michael
Alvard, Abigail Barr, Jean Ensminger, Kim Hill, Francisco GilWhite, Michael
Gurven, Frank Marlowe, John Q. Patton, Natalie Smith, David Tracer. 2005.
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accessed February 20 Ð April 21, 2008
5) ÒGame Theory,Ó
http://plato.stanford.edu/entries/gametheory/, accessed February 20 Ð April
21, 2008
6) ÒRationality and Utility from the Standpoint of
Evolutionary BiologyÓ by Donald T. Campbell. The Journal of Business, Vol. 59, No. 4,
Part 2: The Behavioral Foundations of Economic Theory. (Oct., 1986), pp.
S355S364.
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