Does Fairness Constrain Profit Maximization?
New Evidence from a Dictator Monopoly Experiment1
Steven R. Beckman, Gregory DeAngelo, and W. James Smith
Kahneman et al. introduce dictator games to test whether fairness constrains profit
maximization. We show that the standard ultimatum/dictator exchange games implicitly
assume perfectly inelastic demand, an assumption that is rather special. We argue that
Kahneman’s question is best examined in a more general model of profit maximization.
This paper introduces a new experimental design based on a more general demand
specification defining a dictator monopoly. Results from initial rounds are similar to
those of standard dictator games. As rounds progress, however, dictator monopolists take
more, until they finally take it all.
JEL codes: D42, C92
Key words: dictator, monopoly, necessity, experiments
Steven Beckman, University of Colorado Denver, [email protected]*
W. James Smith, University of Colorado Denver, [email protected]
Gregory DeAngelo, Rensselaer Polytechnic Institute, [email protected]
*Corresponding Author, 2026 S. Joliet Ct., Aurora CO.
Phone: 303 315 2035
Fax: 303 315 2048
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We gratefully acknowledge helpful comments and discussion from Gary Charness, Elizabeth Hoffman and Lester
Zeager. We acknowledge the able research assistance of Eric Cao, Hannes Lang and Michelle Bongard. The paper
also significantly benefitted from the comments of participants at the Economic Science Association meetings in
Tucson and Washington D.C. and the Southern Economic Association in Washington D.C.
Introduction
Kahneman et al. (1986, p. S290) argue that fairness “might deter a profit-maximizing
agent or firm seeking to exploit some profit opportunities.” The suggestion is that the basic
microeconomic model in which firms maximize profit ignores important considerations common
in other social sciences and is (1986, p. S286) “often viewed as an embarrassment to the basic
theory that people vote, do not always free ride, and commonly allocate resources equitably to
others and to themselves when they are free to do otherwise.” The evidence for fairness is quite
strong when the results of standard dictator games are examined. As Engel (2011, p. 584)
observes, “While normally a sizeable fraction of participants does indeed give nothing, as
predicted by the payoff maximization hypothesis, only very rarely this has been the majority
choice. It is by now undisputed that human populations are systematically more benevolent than
homo oeconomicus.”
An important exception to this is Hoffman, McCabe, Shachat and Smith (1994, p. 364)
who find that, “In the Double Blind dictator treatment, over two-thirds of the first movers now
offer $0 and 84% offer $0 or $1; only 2 of 36 subjects offer $5.” They (1994, p. 371) conclude
that observed behavior is “inconsistent with any notion that the key to understanding
experimental bargaining outcomes is to be found in subjects’ autonomous, private, other
regarding preferences.” The majority of players take it all or nearly all when complete
anonymity is guaranteed.
Double Blindness plays an important role in Hoffman et al.’s result as subsequent
articles show. For example, Johanneson and Persson (2000) find that dictators will even give
something even to names drawn randomly from a phone book. Charness and Gneezy (2008)
show that knowledge of the recipients’ last name increases generosity. Aguiar et al. (2008),
1
Branas-Garza (2007), Dana, Weber and Kuang (2007), Matsui et al. (2008) among others all
provide similar variations on the social distance theme.
One interesting finding is that subjects become more self-regarding when price enters the
experiment even in a most simplified form. If one is interested in the effect of fairness on profit
maximization, why are experiments not conducted in the context of a profit maximization model,
particularly in light of the fact that Kahneman et al. point to textbook models of profit
maximization in their critique?
The standard ultimatum/dictator game is very simple. In the exchange context, for
example, in Hoffman et al. (1994, pp 352-3 and pp. 362-363), one player sets a price and the
other either accepts or rejects in the ultimatum game or simply acquiesces due “a prior
commitment to make the purchase whatever the price chosen by the seller” in the dictator
regime. What may strike some economists as unusual is that quantity demanded is never shown
to subjects and is in fact never mentioned. When price is considered, a question that is sure to
come up among economists is what then is demand and how will it be incorporated in a model of
profit maximization? Undoubtedly, the attraction of the division of a fixed sum is considerable.
As Engel (2011, p. 584) put it “The experimental paradigm has proven so powerful precisely
because it is so simple.”
The question that does not seem to have been asked, let alone, answered is does this
simplicity comes at a cost? And it does for as we show, the demand function implicit in the
standard ultimatum/dictator exchange game is one that is perfectly inelastic. And this type of
demand function is far too special to support general conclusions about profit maximization in
general or about the restraint of fairness on profit maximization in particular.
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Having said this, there is no question that the questions raised in ultimatum/dictator game
literature are important and interesting. Can be these questions be addressed in a more general
exchange framework? And what assumption in the standard ultimatum/dictator exchange
protocol must be relaxed? The fixed sum to be divided is the main problem. This is the same as
a zero-sum game. Once this assumption is relaxed, then, downward sloping demand becomes
admissible and the simple models of profit maximization can be utilized. The simplest model of
profit maximization is that of a standard monopoly. How compatible is the standard theory of
monopoly with ultimatum/dictator games? We observe that the standard model of monopoly is
only compatible with an ultimatum game. The reason is that the consumer can refuse to buy if
the price is too high in which case neither the consumer nor the monopolist gains. Can a
monopolist in the standard model take it all? The answer is “no.” What then about the dictator
game?
A recent paper by Beckman and Smith (2013) presents a model for a dictator monopoly.
Starting with a general utility function in which a consumer requires a minimum level of a good,
they show that the monopolist is able to extract all income from the consumer beyond that
necessary for the minimum consumption bundle. In short, the Beckman-Smith-type monopolist
can take it all. Will they or are they constrained by considerations of fairness?
We conducted experiments in two locations using demand derived from a translated CES
utility function (Blackorby, Boyce and Russell, 1978) and, as a contrast, completely inelastic
demand. The set of protocols allow us to examine whether social pressures, social norms
(Krupka and Weber 2013) and other-regarding preferences, or concern for economic efficiency
come into play to deter profit maximization.
3
The results turn out to be instructive. In the first round, dictator monopolists split
surpluses in proportions similar to single round dictator games and at times are even more
generous. As rounds progress, however, dictators increasingly exercise their market power much
to the detriment of buyers. By the final rounds, dictator monopolists take it all. Switching
partners in mid-game has only a small, transitory effect. Moreover, exit surveys indicate that the
monopolists, far from feeling shame, are quite happy with taking it all. Not surprisingly, the
subjects playing the role of consumers are significantly less so. These findings suggest that
social pressures, other-regarding preferences and/or a preference for economic efficiency are not
strong enough in the end to restrain profit maximization.
I.
Literature Review
Kahneman, Knetsch and Thaler (1986) provide the precursor to the dictator game in a
study that pits fairness against self-interest. Arguing that “an action that deliberately exploits the
special dependence of a particular individual is exceptionally offensive,” they conjecture that
subjects may not fully exploit their power over a defenseless subject, and subjects may well
punish anyone who does. In the first stage of the experiment, subjects are given the opportunity
to divide $20 by allocating either $10 to self and $10 to other or allocating $18 to self and $2 to
other. Of 161 students (only 30 of which were actually paid), 76% divided the $20 evenly. A
second stage explores whether subjects would split $10 evenly with someone that plays fair or
$12 evenly with someone that exploited the profit opportunity in stage one. Most choose an
even split with a fair player even though it costs self $1.
If subjects understand that there is a second stage with punishment, then generosity in the
first stage may be strategic rather than ethical. By removing the second stage, Forsythe,
Horowitz, Savin and Sefton (1994) create the canonical form of the dictator game: Player 1
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proposes a split of a monetary prize between Player 1 and Player 2. Player 2 is passive and
cannot reject the offer or retaliate in any way. Simple economic theory based on self interest
suggests that Player 1 will keep all. However, only 35% of these subjects take all and 20%
equally split the surplus.
The paper prompted a wave of follow-up experiments which demonstrate that behavior in
dictator games is sensitive to instructions, design differences and subjects’ backgrounds.
Prominent contributions include Hoffman, McCabe, Sachat and Smith (1994) who examine the
influence of procedures while Hoffman, McCabe and Smith (1996) explore the influence of
social distance between Player 1 and 2. These papers employ Double Blind procedures that
guarantee that not even the experimenter will learn of an individual dictator’s decision. The pay
method is also disguised with the same thickness in envelopes for pay and no pay outcomes,
ensuring that no one will know. Given this level of anonymity, 2/3 dictators do in fact take it all
and 84% give $1 or less. Overall, however, Engel (2011) concludes from a meta-analysis that on
average dictators offer 28% of the pie.
Even minimal knowledge of the recipient however increases generosity. Johanneson and
Persson (2000), for example, find that dictators will give something to people drawn randomly
from a phone book. Charness and Gneezy (2008) show that knowledge of recipients’ last name
increases generosity. Aguiar et al. (2008), Branas-Garza (2007), Dana, Weber and Kuang
(2007), Matsui et al. (2008) all report similar results in variations on the social distance theme.
Societal values and economic incentives also impact generosity. Henrich et al. (2005)
demonstrate the importance of cultural norms while Bolton, Katok and Zwick (1998) emphasize
attitudes regarding fairness. Generosity varies with gender and recruitment procedures (Eckel
and Grossman 1998 and 2000) as well. Even young children are altruistic (Benenson, Pascoeb
5
and Radmoreb 2007). On the other hand, dictators who earn their role are less generous (Oxoby
and Spragen 2008 and Cherry, Frykblom and Shogren 2002). Moreover, increasing the cost of
altruism reduces giving (Andreoni and Miller 2002).
Haselhuhn and Mellers (2005) report that dictators derive no pleasure from offering equal
splits but do experience joy from greed. Bardsley (2008) finds that Player 1s that give to Player
2s will take from Player 2s if the opportunity presents itself. Oberholzer and Eichenberger
(2008) add an unattractive lottery to a dictator experiment and find that, even if dictators do not
play the lottery, they still take all of the endowment.
These studies strongly suggest that self-interest is too weak to alone reliably predict
behavior? The counter argument is made succinctly by Ken Binmore (2005, p. 817)
As far as I know, nobody defends income maximization as an explanatory
hypothesis in experiments with inexperienced subjects … However, there
is a huge literature which shows that adequately rewarded laboratory
subjects learn to play income maximizing Nash equilibrium in a wide
variety of games – provided they have gained sufficient experience of the
game and the way that other subjects play.
What does the literature on market behavior suggest? There are two broad categories: those that
post prices and those that allow buyers and the seller to participate in an auction market calling out
bids and offers until a counterparty accepts (see Plott (1982) for a survey of early seminal
contributions). Posted prices tend to produce behavior more consistent with monopoly theory while
double oral auctions often exhibit prices closer to the competitive equilibrium. Otherwise the basic
structure of the experiments is the same: sellers are told the cost of producing each unit and
determine price. Buyers then decide how much to buy while consulting their demand schedule.
Only sellers know the schedule of costs and only buyers know their demand schedule. As a result,
sellers and buyers know only their own pay and not the pay of the other player. These experiments
6
generally run for a number of rounds and show considerable learning and variation across rounds as
sellers try to estimate demand and buyers attempt to under-reveal demand (see Harrison and
McKee, 1985).
What are we to make of these conflicting and shifting interpretations?
II. Ultimatum/dictator games and demand theory.
One result is clear. When exchange and price are introduced, less sharing takes place. And how
are price and exchange introduced in experiments? A prominent example is shown here in Figure 1
which is reproduced from Hoffman et al. (1994, p. 352). Prices set by the seller are reported in the
columns and the decision of the buyer in the rows. Amounts in the cells are amounts out of 10
accruing to each player. Two points merit emphasis. First, as is standard in ultimatum/dictator
games, the amount of the gain to be split is constant for all prices. Second, the quantity demanded
in the exchange never enters the game.
Figure 1: Hoffman et al.’s payoff table distributed to subjects.
The question that table naturally suggests to economists is what is the demand function implied
by the assumptions employed? To examine this question, consider the definition of the total
surplus in a market in the context of a simple monopoly (an assumption that seems to fit the context
of the game). The following proposition establishes a very simple but important point.
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Proposition 1: If the dictator and ultimatum games are viewed as a market exchange of units of
a good at a specified price where the value of the good to the buyer is higher than to the seller
then the total surplus to be divided is constant if and only if the number of units of the good is
held fixed as the price changes, that is, demand is completely inelastic.
Proof: The total surplus, TS , is the area between supply, S (Q), and demand, D(Q).
TS  
Q
0
 D(Q)  S (Q) dQ. From the fundamental theorem of calculus and the chain rule,
dTS / dP  (dTS / dQ)(dQ / dP)  ( D(Q)  S (Q))(dQ / dP)
Given  D(Q)  S (Q)   0 then dTS / dP  0  dQ / dP  0.
The assumption of a fixed surplus thus strictly restricts the structure of demand. Demand
cannot be downward sloping because, if it is, the amount to be split varies with price. But
completely inelastic demand poses an additional problem for ultimatum games. With completely
inelastic inverse demand, the buyer will never reject any price offered up to the point in which
total income is exhausted. This suggests that the standard ultimatum game is best viewed as a
decision to split a windfall gain, not as an exchange as the term is commonly understood in
microeconomic theory.
We emphasize that we understand and accept the fact that observed experimental
behavior often runs counter to accepted theory. However, it is also the case that the critique that
an economic model is flawed because it does not allow for other-regarding behavior would seem
to require a test within the model itself. This paper proposes to do so using simple monopoly
models.
How does one incorporate the important questions investigated in the standard
ultimatum/dictator games in simple monopoly models? Consider the nature of the standard
textbook model of monopoly. If a monopolist sets the price too high for any quantity, the
consumer can decline in which case neither the consumer nor the monopolist gains anything.
And this can be true for all prices (at the price where demand intersects the vertical axis). The
8
ability for the consumer to reject captures the essence of an ultimatum game. Can this type of
monopolist take it all as in a dictator game? The answer is “no” because, even at the profit
maximum, the consumer captures some surplus. What about the dictator game?
A recent theoretical paper by Beckman and Smith (2013) provides the answer.
III. A model for dictator monopoly
Beckman and Smith (1993) and Primont and Primont (1995) derive the properties of
marginal revenue for Stone-Geary and Generalized Stone-Geary utility functions.2 The main
results are that marginal revenue is: (1) always negative and monotonically upward sloping for
Stone-Geary (Cobb-Douglas-type with a minimum consumption requirement) and (2) negative
and upward sloping in the local area of the constraint and then positive and downward sloping
for other outputs in the case of Generalized Stone-Geary (CES with a minimum consumption
requirement). Drawing upon these results, Beckman and Smith (2013) investigate monopoly
behavior for demand derived from a general utility function with minimum consumption
requirements. Under very general conditions, the monopolist is shown to always maximize
profit at the minimum consumption boundary. At the profit maximizing output, the consumer
must spend all of his/her income on the minimum consumption bundle and is reduced to the
minimum utility level compatible with his/her continued existence. In short, the monopolist
takes it all. Given this property, the Beckman-Smith model provides an experimental platform
for a dictator game. The Beckman-Smith model is richer than the standard dictator exchange
game in allowing sharing of a non-constant surplus away from the global profit maximum and
preserving the right of refusal on the part of the consumer up to that boundary. Up to the
minimum, the game is, thus, an ultimatum game that then converges to a dictator game as the
2
The defining characteristic for these utility functions is minimum consumption requirements.
9
monopolist finds a price high enough to cut out all “discretionary” consumption above the
minimum.
A special case derives from the well-known TCES utility function (Blackorby, Boyce and


Russell, 1978) defined by U  ( x1  s1 )  ( x2  s2 )

1
 
where si is the subsistence requirement
for each of two goods, xi , i=1,2. Let pi and y respectively represent price and income. It is
straightforward to show that the associated demand function is: xi 
ypir 1
 si , with
 pir
i
y  y   pi si and r 
i

 1
. In effect, the cost of the subsistence bundle is subtracted from
income with utility maximized on discretionary income.
10
Figure 2: Demand, Profit and Marginal Revenue
Demand
A
120
100
Price
80
60
40
20
0
0
2
4
6
8
10
8
10
12
Quantity
B
Profit
100
Profit
80
60
40
20
0
0
2
4
6
12
Quantity
C
Marginal Revenue and Marginal Cost
20
MC
Value
10
MR
0
-10
-20
0
2
4
6
8
10
12
Quantity
-30
-40
11
If fixed costs are zero and marginal cost, c1 ' , is constant then the profit function is
( p1  c1 ' ) x1. The demand and profit functions in our example are plotted in figure 1 for r = -5,
y  130, s1  1, s2  1, p2  30, c1 '  10 . These are also the parameter values used in the
experiment. As is obvious in Panel A, demand is well behaved but starts away from the vertical
axis, due to the minimum consumption requirement. Panel B shows the profit function which is
quite different from the standard one. In particular, profit is maximized, not at the local
maximum of p1  23 , x1  3.7 and   47.4 where marginal revenue equals marginal cost, but at
the boundary of x1  1.0 where marginal revenue is negative and demand inelastic. At the
global maximum, profit is 90 at a price of 100. At this global profit max, the consumer can just
afford the subsistence bundle of (1,1); utility is reduced to its minimum value. The monopolist
in fact takes it all.
IV. Experimental Design
Our goal is to cast the dictator game in a theoretically suitable market environment to test
whether fairness and/or other factors restrain profit maximization. We use the Beckman-Smith
model to this end. We however also use a vertical demand function where one and only one unit
of the good is demanded as in the standard game both as a contrast and because it is one
admissible structure and is a special case of the Beckman-Smith model. The Beckman-Smith
model however also can capture the fact the good may provide utility in larger quantities than are
essential. Once a non-essential use for goods like salt, water or food is allowed then the
distinction between a global profit maximizing corner solution and a locally profit maximizing
interior solution becomes relevant. Perhaps behavior changes in the two environments. We thus
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conduct both sets of experiments, one with vertical demand and one with curved demand. In all
experiments, consumers must buy at least one unit.
In other respects the experiments follow the established monopoly design as closely as
possible. Rounds are repeated to allow convergence to an equilibrium in keeping with the
market convergence literature and because demand is defined for period but many periods are
possible. Sellers know the cost of production and set a price. Demand is revealed or hidden by
consumers through their purchases and monopolists imperfectly learn about demand as the
experiment proceeds. However, sellers do know that buyers must buy at least one unit and that
one unit is worth 100 cents to buyers.
We conduct a five round tutorial with linear demand, constant marginal cost and no
minimum purchase requirement to acquaint subjects with the concept of a local profit maximum
in an environment where it is also the global profit maximum. We conducted the experiments in
two locations, the University of Colorado, Denver where the primary experiments were run, and
Rensselaer Polytechnic Institute where the robustness checks are run (Denver and RPI hereafter).
In Denver, to be absolutely certain that subject behavior is a revealed preference, we show the
sellers the expected price/profit graph for the last three rounds of the experiment. If they have
converged on the local profit max, do they know about the global max? If they have converged
on the global profit max, do they know about the local max? The general idea is that we have
observed their search but we may not know if the equilibrium selected is path dependent.
At a second location, RPI, we test the robustness of our results by conducting downward
sloping demand experiments no tutorial and no revelation of the price/profit graph. This serves
as a check on whether the information may be taken as signal to the price setter either to restrain
or pursue profit maximization. At RPI, we employ one practice round. The robustness checks
13
also provide half the sellers with the round by round pay to buyers to see if this information,
common in dictator games but not monopoly experiments, affects behavior. We also link the
seller to a different buyer about half way through the experiment to see if social norms, otherregarding behavior or philanthropy require some sort of gift to a contact that is new to this
particular seller. The physical circumstances, color schemes used and subject pools are all
somewhat different adding elements to the robustness check.
In Denver 120 subjects were recruited by visits to classes in mathematics, economics,
ethnic studies and sociology. Minorities and sociology students are generally thought to be
relatively generous and we deliberately went out of our way to include them in the subject pool.
Of these 60 participate in a vertical demand experiment (30 sellers and 30 buyers) while 60
experience curved demand. At RPI 30 subjects were recruited via ORSEE in curved demand
experiments. The subjects at RPI are less likely to be minorities and more likely to be
engineering majors. All are promised a minimum pay of $5 plus whatever they earn in the
experiment.
In Denver, subjects are in one large computer room with portable partitions that preserve a
degree of privacy. At RPI, subjects congregate in a hallway and sellers are placed in one room
and buyers in another. The RPI subjects are told the experiment will last at least 12 rounds. In
fact the three sessions have 14, 15 and 13 rounds respectively and not even the laboratory
assistants know the true number of rounds. This should mitigate any end of experiment effects.
The Denver subjects know that the experiment has 16 rounds.
In contrast to Hoffman et al., we do not employ Double Blind procedures as they are not used
in market convergence studies nor seem appropriate as complete anonymity does not
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characterize actual market exchanges. In addition, we want to allow other factors that may
restrain profit maximization to come into play.
We employ a graphical user interface that allows the consumer to buy any fraction of a unit
down to 1/100.3 Each round begins with the seller selecting a price. This price is conveyed by
z-Tree to the associated buyer. Figure 2 displays the buyer’s screen. The computer draws a line
whose length is equal to demand at every integer price. The computer also draws two horizontal
lines, one at the price previously selected by the seller and one at the cost of 10. The buyer
selects the quantity by clicking his/her mouse on a quantity, and the computer draws a vertical
blue line at that quantity. The implications of the choice are then presented by color coding
demand. Demand above the price and to the left of quantity is displayed in green and represents
consumer surplus. Demand between cost and price is shown in blue and is profit to the
monopolist. The rest of demand is displayed in grey.4
The buyer is allowed to click any number of quantities and the program updates the graph
and creates a table to report the associated pay to the buyer. The buyer must buy at least one unit
and cannot buy any more units than indicated by the demand function at that price. Any click
outside the allowable range is recorded as the nearest limit. Once a final decision is made, the
buyer clicks a red button to end the stage.
3
We use version 3.2.6 of z-Tree, created by Urs Fischbacher (2007). Additional information is available at
http://www.iew.ch/ztree .
4
This is the RPI color scheme. In Denver, the monopolist profit is yellow and the unclaimed consumer surplus is
red. See the tutorial instructions for Denver.
15
Figure 2: The Buyer’s Screen
In the second round, sellers begin to see historical information. A table on the left of the
screen shows the round number, price, marginal cost, sales (to two decimal points) and profit.
On the right of the screen, a graph with profit on the vertical axis and price on the horizontal axis
displays the price/profit combination as a small green box. Half the sellers at RPI also see a
table of buyer’s points and buyer’s pay as displayed in the graph as a blue triangle to see if this
information, common in dictator games but not monopoly experiments, has an effect.
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Figure 3: The Seller’s Screen (with hypothetical prices, profits and consumer surplus)
The prices shown in figure 3 have been selected to give the reader an overall sense of the
tradeoffs possible in the experiment.5 Economic efficiency is achieved at a price of 10 with
profits equal to zero and consumer surplus at 173. The price of 22 is near the local profit
maximum and offers 47 points to the seller and 101 points to the buyer.6 While this is somewhat
less efficient with total welfare gains of 148, the efficiency is still 85% of the competitive level.
Recall that demand is calibrated assuming a close substitute with a price of 30. As the price rises
above 30 demand curves sharply and the payoffs rapidly become similar to the standard dictator
game with roughly 90 points available per round and any points to the buyer come directly from
the seller. At a price of 100, profit is 90 and consumer surplus is zero generating an efficiency of
5
6
Subjects see the display for the prices they select.
All points are converted to cash at the rate of one penny per point.
17
90/173 = 0.52, indicating that the corner solution, while globally profit maximizing, is far less
economically efficient than the interior monopoly solution.7
After completing these rounds subjects are asked how much of an additional five dollar
payment they would like.8 They are paid whatever they request. There are no ramifications
from taking the entire $5, nor are there additional benefits to leaving some amount of the $5
behind. This allows us to test the conjecture that some subjects are reluctant to take it all as
perhaps some are worried about taking money from the experimenters or are too polite to take all
that is offered (Camerer and Thaler, 1995). Hoffman et al. (1994) speculate that subjects may
attempt to increase the odds of being asked to participate in later experiments. Some of these
same motivations, politeness, an aversion to the appearance of greed and doubts about later
consequences in future experiments may also explain giving in the dictator game – a conjecture
we want to address.
Once the $5 experiment is completed, all subjects fill out a questionnaire that collects
their name, age, gender, method of recruitment and whether or not they were a seller. They are
also asked to use a seven-point scale to record their degree of irritation, contempt, anger,
surprise, envy, sadness, happiness, joy and shame. Confronting a monopolist that presses
someone to their absolute limit is likely to be a highly emotional experience. We are curious to
see if the milder experimental conditions also trigger an emotional response. On average, the
experiments last 40 to 60 minutes with payments generally in the range of $10 to $25.
7
We selected parameters of the utility function so that the monopoly corner solution has roughly half the efficiency
of the competitive equilibrium. This seems to us to divide the search space about in half, in that we could have
made the corner solution relatively more or less efficient.
8
The program displays: “Enter the pay you want. This may range from $0 to $5.00.” Following the entry, the
display reads: “Your pay will be_____ “ (The subject’s entry is displayed.) “If this is not what you want, reenter
number at left. If this is your final choice, press the button below.”
18
V. Results
Figure 4 shows median prices for the vertical and curved demand experiments in Denver
and the curved demand experiments at RPI. Several points are worth emphasizing. In the initial
rounds sellers at both RPI and Denver are quite generous. A price of 55 reflects an even split
with 45 cents going to both monopolist and buyer (55-10 for seller and 100-55 for buyer). The
RPI and Denver vertical demand experiments begin with roughly equal splits of the surplus. The
Denver curved demand produces prices that initially offer a super-fair split of the surplus with
consumers earning more than sellers. Recall from figure 3 that at a price of 30, 45 cents goes to
the seller and 78 cents goes to the buyer. The super-fair initial offers in Denver could be due to
the tutorial which deliberately steers subjects to search for the interior maximum, the higher
proportion of minority and sociology students recruited in Denver or the fact Denver sellers are
not told how much consumers are paid. Although they should know it is more than 70 cents
(100-30).
As rounds progress, prices begin to rise toward the global maximum of 100 in both
locations and in both demand conditions. They rise more slowly in Denver presumably as
subjects search more conscientiously for the local maximum. They rise quite rapidly in RPI
where no tutorial is provided. By the final rounds, profit maximization comes to dominate for all
demand functions and locations.
It is unlikely that path dependence or signaling explains the results as the Denver subjects
remain at the global maximum extracting all the surplus even after being informed of the
location and profit of the local maximum through revelation of the price – profit graph.
Supporting this contention is the fact at RPI the convergence to profit maximization is even more
19
rapid than in Denver. If any signal is present, the less rapid convergence in Denver suggests any
bias from the procedures is toward fairness and not profit maximization.
The broad pattern is consistent whether or not subjects are provided with data on buyer
surplus. In the first paid round, the median prices posted by sellers at RPI with and without
access to buyer data are 53 and 50, respectively, and in the 13th paid round both median prices
are 98. However, connecting the seller with a new buyer may result in a small gift to the buyer.
When the buyer and seller matches are changed between rounds 7 and 8 the median price falls
from 97 to 92 (the mean price falls from 83 to 74).9 Therefore, there does appear to be a gesture
of a five or ten cent gift to the new buyer although the sample size is too small to be statistically
significant. If the effect exists, it is transitory and rapidly dissipates. By round 10, the median
price rises to 99.
Figure 4: Median Prices
100
90
Denver Vertical Demand
80
RPI Curved Demand
70
60
Denver Curved Demand
50
40
30
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Round
9
These differences are not statistically significant.
20
It is traditional to analyze dictator games with histograms. These are presented for the
first and last rounds, vertical and curved demand in figure 5. (The RPI and Denver data are
merged.10) There is some clustering around an equal split of revenue in the first round but any
preference for equality vanishes by the last round. There is also evidence of searching in the
neighborhood of the local maximum of 23 in the first round in the case of curved demand. This
too all but vanishes by the last round.
Figure 5: Histograms of Prices
32
10
Curved Demand First Round
Curved Demand - Last Round
28
8
24
20
Price
Price
6
4
16
12
8
2
4
0
0
10
20
30
40
50
60
70
80
90
10
100
6
20
30
50
60
70
80
90
100
24
Vertical Demand First Round
Vertical Demand Last Round
5
20
4
16
Price
Price
40
3
12
2
8
1
4
0
0
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Turning to the $5 experiment, 77% of sellers and 83% of buyers take the full $5. For
those that do not take the full $5, the median amount taken is $4. Table 2 presents a regression
that uses first round prices as the dependent variable. The variables Vertical, Female and Denver
are dichotomous and take the value 1 if demand is vertical, the subject is female or from Denver
and zero otherwise. The variable $ Left is the amount of the $5 that the seller refuses to take.
10
Therefore the last round may be as low as 13 at RPI and is always 16 in Denver.
21
The intercept indicates that prices are near the even split in the first round but if the seller
leaves $1 of the $5 offered the price is about 13 cents lower. The vertical demand experiments
tend to have higher prices perhaps because sellers in the curved demand experiment explore the
region of prices near 30. Denver subjects tend to offer somewhat lower prices although this is
only significant at about the 6% level. Females’ reputation for being more generous in dictator
TABLE 2
Regression of first round prices
Coefficient
t-Statistic
Intercept
$ Left
Vertical
Female
Denver
52.47
-12.56
18.90
3.07
-13.84
8.09*
-2.75*
2.98*
0.55
-1.91
* indicates significance at the 1% level.
experiments is not borne out in our study. The adjusted R2 of 0.15 indicates much has been left
unexplained.11
The survey of emotions in table 3 is also revealing (see Ortony and Turner 1990 for a
standard reference). Buyers not surprisingly report significantly higher levels of anger, irritation
and jealousy, but this does not appear to cause high levels of shame among sellers. Indeed, they
report higher levels of joy and happiness. Kahneman’s observation that exploiting the special
dependence of individuals may be particularly offensive is borne out in the higher levels of buyer
irritation and anger. Sellers in contrast appear to enjoy their role. “High” levels of happiness for
11
A regression with the amount of the $5 the buyer refuses to take indicates that those subjected to high prices in the
first round take more of the $5.
22
both buyers and sellers may be due to the payment of the show-up fee as well as the
discretionary payoff.
Table 3
Survey of Emotions
7 pt. scale: 1 low, 7 high
means:
Seller
Buyer
Anger*
1.38
2.23
Contempt
2.27
2.31
Envy
1.79
2.15
Fear
1.81
1.88
Happiness*
4.50
3.17
Irritation*
1.73
3.50
Jealousy*
1.48
2.13
Joy*
3.85
2.83
Sadness
1.60
1.71
Shame
1.90
1.42
Surprise
3.29
2.63
* indicates significant difference
between buyer and seller at 5% level
A dictator monopoly has ultimate power to take it all. Will that power be tempered by
fairness, social norms, fear of retaliation etc.? The results are informative. Altruism and other
motivations beyond self-interest may well be present in initial rounds as evidenced by the low
prices initially offered by buyers in dictator experiments. If initially present, however, it
disappears by the final rounds. Along the same lines, initial sharing may reflect other
motivations such as good manners, apprehension that specific identity may be revealed, fear of
retaliation and/or a preference for economic efficiency. Again, if this is the case, these
motivations in the end do not prove strong enough to restrain the dictator monopolist who gains
experience and learning.
23
The conclusion we are able to draw is instructive. Dictator monopolies do take it all in
the end even without the protection afforded by complete anonymity. They don’t feel ashamed
of doing so. In fact, they appear quite pleased.
VI. Conclusion
Kahneman et al. (1986, p. 106) expressed the hope that other-regarding behavior “might
deter a profit-maximizing agent or firm seeking to exploit some profit opportunities.” Hoffman
et al. examine this question in Double-Blind experiments and find no evidence to support otherregarding behavior. Numerous follow-up experiments to Hoffman et al. do find that dictators
will share more even when minimal identity of the other player is provided, for example, names
drawn from a phone book or the name of charity. Moreover, when price is introduced, subjects
become less generous.
We share Kahneman’s hope of deterring the exploitation of market power, if not by
altruism, then, by other motivations. In this paper, we pose the question of whether other
possible motivations such as shame, fear of retaliation or a preference for economic efficiency
will deter full exploitation of market power. We relax the assumption of complete anonymity
afforded by Hoffman et al.’s Double Blind protocols to allow other motivations to come into
play.
The difference of this from previous studies is that we take up the question in a more
complex exchange framework more firmly founded in microeconomic theory. The reason for a
different design is that, as we show, the standard ultimatum game is not supported by any
demand function found in economic theory. The dictator game is in fact compatible with the
theory of demand but the implicit demand function has to be perfectly inelastic, an overly
24
restrictive assumption if one seeks to draw more general conclusions about profit maximization
and fairness.
The results are instructive. In initial rounds, outcomes are very similar to those found in
standard dictator games with considerable sharing of the surplus available. As rounds progress,
however, monopolists start to take more of a share; until, in the end, they take it all. Exit surveys
reveal that far from feeling shame they are quite happy to do so.
25
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28
Appendix: Instructions
The instructions combine those used for vertical and curved demand, Denver and RPI. The RPI
instructions are below with replacements as indicated for the Denver versions.
You have been asked to participate in an economics experiment. In addition to the $5 promised for your
participation you may earn an additional amount of money, which will be paid to you at the end of the
experiment.
Fundamental Concepts
In this experiment the computer links one buyer to one seller. The buyer and seller stay connected
throughout the experiment. The seller sets the price for the commodity and the buyer decides how much
to buy. After both decisions, the pay to both buyer and seller is displayed and a new round begins. Each
round is similar in that the options to each player are the same. The repetition allows sellers and buyers to
try out different strategies in an effort to determine what is best. The definition of best is left to you.
At the beginning of each round the seller is shown a history of past decisions. On the left of the screen the
history is shown as a table of prices and profits. On the right of the screen the same information is
presented in a graph with the price on the horizontal axis and the profit on the vertical axis. In the first
round, both are blank and the seller must make a decision with very little information – all the seller
knows is that the price must be a whole number no lower than the cost of production and no higher than
the maximum price the buyer can afford. Both these numbers are displayed. As rounds progress, the
table and graph displaying the profit and price histories become more informative.
Once a price is set, buyers are shown a graph displaying their pay given different purchase decisions. The
graph shows the value to the buyer on the vertical axis and the quantity on the horizontal axis. At every
possible price a line is drawn indicating the maximum purchase. As prices fall, these lines generally
become longer as lower prices allow greater purchases.
Values and Quantities
10
9
8
0
1
2
3
4
Consider the example above: the pay to the buyer for the first unit is $10, the second unit $9 and the third
unit is $8. Then at a price of $10 you will be allowed to buy no more than one unit, at $9 no more than
two units and at $8 no more than three units.
29
Your pay is calculated in the following way. If the price is $8 and you buy three units, then the first unit is
worth $10 to you, the second is worth $9 and the third is worth $8 and your pay is ($10-$8) + ($9-$8)
+($8-$8) = $2 + $1 + $0 = $3.
As a test that you understand, calculate what the pay to a buyer would be if the price was 7 and the buyer
chose to buy two units. (Values are as in the chart, the first unit is worth 10, the second, 9). Use the
space to calculate your answer.
Once the quantity is set, profits for the seller may be calculated. In our example, the price is $8, and if the
cost is $2 the seller earns $6 profit per unit. If sales equal 3 units then profit = (price –unit cost) * sales =
($8-$2)*3 = $18.
These are the fundamental concepts of the experiment. Please review them now and be sure you
understand.
 The computer links one buyer to one seller.
 The seller is told the cost of production and sets a price.
 The buyer consults a graph showing values and quantities.
 The buyer decides how much to buy.
 The pay to the buyer is the sum of the values in excess of the price that are purchased.
 The pay to the seller is (price – unit cost)*sales.
Are there any questions?
A Practice Round
The experimenter is starting the computer program now. The first round is just for practice and is not
paid. (In Denver: This sentence is replaced by a section describing a 5 round tutorial, reproduced
below.)
In this experiment buyers must buy one unit and the first unit has a value of 100. At a price of 100
buyers must buy even though they are paid nothing. As the price falls, they may want to buy more units.
At lower prices the buyer’s pay rises. How much they buy depends in part on the price compared to
another good they want. The price of this other good is 30.
(In Denver vertical demand experiment: In this experiment buyers must buy one unit and only one
unit. This unit has a value of 100. )
Each round begins with the seller entering a price. The price must be between the cost of 10 and the
buyer’s maximum of 100. Go ahead and enter a price now. Click the red button to signal you are done.
Buyers see a graph of values and quantities. If you are a buyer, click with the mouse in various places on
the graph to see how it works. Clicking to the right increases purchases up to a maximum and clicking to
the left decreases purchases to the minimum of one unit. Buyers are shown their pay in green and the pay
to the seller in blue. Gray lines are paid to no one. Click the red button when you have entered your final
choice.
30
Sellers see a table showing the price, the quantity purchased and their points. Seller’s pay in points is
calculated as the price, less the cost of 10 points, times the quantity sold. Half the sellers also see buyer’s
points.
There are at least 12 rounds. The number of additional rounds has been randomly determined before the
experiment began. (In Denver: There are 16 rounds. Beginning in round 13, sellers will be shown the
profit potential. )
We want everyone to make their own decisions so discussions with other subjects are not allowed during
the experiment. Direct questions to an experimenter.
Go ahead and begin the experiment.
The $5 experiment
Now that you have completed all rounds, the experimenter is launching another experiment. This time,
you enter the additional money you would like to be paid, up to $5. A 5 is an entry of $5. A 2.5 means
$2.50. You are paid the amount you enter.
The Questionnaire
The experimenter is launching a questionnaire. You will be asked to enter a fictitious name, gender, age,
how you were recruited and your emotional state. Once your fictitious name is entered, a payment file is
generated by the computer and printed. Each of you is released one at a time to collect your pay by
revealing the fictitious name you entered. Your real name is used on the paper receipt for pay and on the
paper consent form and is therefore never a part of the data file generated by the computer. Your name
will never be added to the data file.
The tutorial used in Denver only is below.
Introduction to the computer program
The experimenter is launching a tutorial program now. The tutorial is just for practice and is unpaid.
Each round consists of three stages. At the beginning of stage one, sellers see two blank price histories
and are asked to enter a number ranging from 5 to 65. In this tutorial, the cost of production is 5 and 65
is the most buyers can pay. Enter any whole number in this range. While the sellers are entering their
price, buyers push a meaningless button.
Buyers see a graph indicating values and quantities and are asked to click a quantity. Click anywhere in
the graph. The horizontal position clicked becomes the new quantity – unless the click is outside the
allowable range and then the quantity moves to the closest limit. The screen below shows one possibility
and will be used to explain more fully.
31
The horizontal red line at the bottom is the cost to sellers and is currently $5. The horizontal blue line is
the price set by the seller - here it is $15. The vertical blue line indicates the quantity currently selected:
25.9. The lines drawn at every price indicate the number of units you may purchase at that price. Given
the price of 15, the maximum purchase is 50. Your pay is the sum of the green lines. Red lines show the
added pay possible should you choose to increase the quantity purchased. The yellow lines indicate the
pay to the seller and calculate the area between price and cost for the goods sold. Gray lines show the
remaining parts of the value-quantity schedule that are currently paid to no one. The gray lines are paid to
buyers if the price falls and to sellers if the quantity rises.
Go ahead and click several different quantities to see how the graph changes. Click the red button to lock
in your final choice. While buyers choose quantity, sellers have a meaningless button to push.
Sellers are informed about their profit for the period and then round two begins. Sellers are shown the
price, cost, sales and profit of the first round and a graph displays price and profit. Sellers are asked to
select the price. Buyers then choose the quantity and both see their pay for the round. Continue on to
round four.
At the beginning of round four, sellers are shown the usual information plus the potential profits at every
price. The profit potentials are equal to the heights of the lines drawn at each price. This potential is
achieved if consumers buy the maximum quantity. If the buyer sets the quantity below the maximum,
profits will be below the maximum.
The tutorial has five rounds. Proceed to the end.
32
Cuts:
1. Beckman and Smith show in general that such a monopolist always maximizes profit
at the minimum consumption level and never at an interior local profit maximum. The dictator
monopolist can take all of the consumer’s income beyond that necessary for other necessities and
it is in his/her self interest to do so. At the profit maximum, the consumer’s utility is reduced to
the absolute minimum level compatible with life. A Beckman-Smith monopolist can take it all.
The question is whether he/she will? To investigate this we do not employ Double Blind
protocols as in a market/exchange setting as they are neither commonly used in market
convergence studies nor seem appropriate as complete anonymity does not characterize actual
market exchanges.
2. The complexity of the model To investigate this we do not employ Double Blind
protocols as in a market/exchange setting as they are neither commonly used in market
convergence studies nor seem appropriate as complete anonymity does not characterize actual
market exchanges.
the protocols of monopoly convergence studies.12
12
In the main, market convergence experiments assume that the monopoly is already established,
and the costs of establishment are fixed and sunk. Entry is assumed to be blocked. We defer
questions of contestability, risk preference, and the public choice question of a market in
monopoly rights to future work. Nor do we examine the case of natural monopoly (see Harrison
and McKee (1985) on the latter point) and the important issues of regulation and the strategic
interactions of an antitrust agency and cartels. All of these are important questions but beyond
the scope of this paper.
33