DP2011-10

Impact of Ethnicities on Market Outcome:Results of Market Experiments in Kenya
Ken-Ichi SHIMOMURA
Takehiko YAMATO

March 15, 2011

Impact of Ethnicities on Market Outcome:Results of Market Experiments in Kenyaby
Ken-Ichi Shimomura andTakehiko Yamato 

Abstract
We study market exchange in the laboratory by a multiethnic experiment in Kenya. The subjectsof our experiment are of three ethnicities, Kikuyu, Luo, and Kalenjin. Our model contains two
types of consumers and two kinds of commodities, and three competitive equilibria exist. The
two equilibria with the lowest, and highest relative prices are beneficial for one type of theconsumers, and the intermediate price gives an equitable allocation. The tatonnement dynamics
however predict that relative prices diverge from the intermediate equilibrium towards thelowest equilibrium or the highest equilibrium depending on initial prices. In order to examine
how much effect the ethnicities of subjects have on the equilibrium selection, we conductedmanual experiments of pit market trading with different combinations of ethnicities of subjects.
Our result shows strong support for the convergence to the intermediate equilibrium when
Kalenjin subjects participated, whereas no such data are obtained without them. In addition, thefrequencies of transactions with Kalenjin subjects were significantly less than that with the othersubjects only, and the less frequent transactions resulted in the more efficient outcomes of theexperimental market.
Keywords: Economic Experiment, Kenya, Pit Market, Perfect Competition, Multiple Equilibria
JEL codes: C92, D51



Research Institute for Economics and Business Administration, Kobe University, 2-1 Rokkodai, Nada, Kobe
657-8501, Japan. E-mail: ken-ichi@rieb.kobe-u.ac.jp
Department of Social Engineering, Graduate School of Decision Science and Technology, Tokyo Institute ofTechnology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan. E-mail: yamato@soc.titech.ac.jp
We thank Hiroyuki Hino, Anjan Mukhurji, Syham Sunder, and Motoki Takahashi for their detailed comments anduseful suggestions. We also appreciate special supports to conduct experiments in Kenya and to compute statistics byMichiharu Masui, Joseph Onjala, Tokinao Ohtaka, Kiyotaka Takahashi, and Kohei Yoshida. This research waspartially supported by Japan International Cooperation Agency (JICA) and Grand-in-Aid for Scientific Research (B)20330036.

1

1.

Introduction

Ethnic diversity has played a central role in explaining differences in business management andlocal market performance within a country. However, results from economic experiments are
not always characterized in terms of ethnicities of subjects because there is no hypothesis of
economic behaviors or phenomena peculiar in ethnicities and it is generally difficult to haveethnically different subjects.
The purpose of our research is to conduct a laboratory experiment of an exchange
economy with different ethnicities of subjects and investigate which equilibrium is selectedfrom the multiple equilibria for the economy. The model to experiment is an exchange economy
with two types of consumers and two kinds of commodities in which three competitive
equilibria exist. One type of consumers initially own the more of the first good, and the less ofthe second good, than the other type of consumers have. The same type of consumers are all
rationed identical commodity bundles of endowment.
We choose the second good as the numeraire, the price of which is always fixed to be
oneand focus on the behavior of the relative price of the first good. There are three equilibrium
prices in our exchange model. The lowest relative price is beneficial for the type of consumers
having more of the second good, and the highest relative price is advantageous to the type of
consumers having more of the first good. The intermediate price gives a “equitable” allocation.
The tatonnement dynamics predict that relative prices go up when the first good isexcessively demanded, and go down when it is excessively supplied, in the market. According
to this dynamics, relative prices diverge from the intermediate equilibrium towards the lowest
equilibrium or the highest equilibrium depending on initial prices. It means that the market
mechanism causes an income inequality and the “invisible hand” leads the economy to an
efficient but inequitable state.
We thus have strong interest in conducting experiments of our exchange model withmultiple equilibria using two ethnic groups of subjects. We can simply conjecture that trading
outcomes will converge to the intermediate equilibrium when the two groups are of the same
ethnicity. On the other hand, when the two groups are from different ethnicities, trading
outcomes will converge to an extreme equilibrium which is beneficial for one group when theirmembers are tougher negotiators than the other group members are. One could think that
ethnically different subjects would never trade if the two ethnic groups are not getting alongwell. 1As the Washington consensus states, both developed countries and developing countries
1

In the literature of economic experiment, there are findings from international comparisons about bargaining
and market exchange (Roth et al, 1991), and public good provision (Cason et al, 2002), for which they conducted
experiments in different places separately but the subjects did not interact across countries. We thus wondered
where to conduct an experiment with subject of different ethnicities.

2are expected to have market mechanisms to warrant the minimum quality of life. We know thatin the world there are quite a few countries in which different ethnicities of people coexist.
Kenya is a well-known country having remarkable ethnic diversity. Each of the Kenyan ethnic
communities has its own culture and some of the communities have not been getting along well.
We wonder if the ethnic diversity prevents the Kenyan economy from developing smoothly.
To consider this problem, however, we are unable to take either theoretical approach or
empirical approach. We have no theoretical model of market exchange in which characteristics
or behavioral principles of different ethnicities are formulated. Whether the competitiveness of amarket under investigation is perfect or imperfect, we always assume the “anonymity” of traders
in a market. It means that every participant in the market only care for qualities and quantities ofcommodities traded, so it does not matter who buys or sells commodities. Hence, ethnicities of
the traders are regarded as nothing to do with market trades. Thus, the standard theory of market
does not work out for our interest. In addition, we would like to compare market outcomes
traded within one ethnic group with those when two different ethnic groups trade, but theexisting economies with ethnic diversity have been working for a long time and it is almost
impossible to take data to compare the two ideal market outcomes.
We have therefore decided to take the experimental approach and selected Kenya as aplace to conduct an experiment to consider the problem we are interested in. For testing ourconjecture on trading outcomes within one ethnic group and between two different ethnic group,
Kenya would be one of the best places in the world because more than 40 different ethnic
groups are present. Each group has its own background, and some groups have been historicallyin conflict. We conducted experiments in Nairobi with the three ethnic groups for subjects ofLuo, Kikuyu, and Kalenjin. The subjects are all college students originally from the three ethnic
communities, and the numbers of subjects of the same ethnicity are equal. We divided eachethnic cohort of the subjects into two groups, and assigned to them the roles of the two types ofconsumers in our economic model. We made each group to trade with the same ethnic group in
their first-round session, and with different ethnic groups in the other sessions.
Our results show that it made the variance of individual patterns of trades remarkably
smaller to conduct sessions with Kalenjin subjects than without them. In addition, the frequencyof transactions with Kalenjin subjects were significantly less than that with the other subjects
only, and the less frequent transactions resulted in the more efficient outcomes of theexperimental market. The main reason is that Kalenjin subjects quickly began to make offers of
the intermediate equilibrium only and ceased to accept other proposals although the other ethnic
groups of subjects kept making small adjustments to improve themselves upon. Thus, ourobservations tell that the bilateral trading does not cause large inequalities of income or welfare,and the participation of a non-negligible number of Kalenjin people in the experimental market
significantly facilitates the prompt decisions of negotiations at the exact point of theintermediate equilibrium.

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The problem of multiplicity of competitive equilibria in exchange economies has recently
been investigated by using laboratory markets. The example given by Gale (1963) is awell-known simple model of a two-good two-consumer exchange economy in which
consumers’ preferences are of the Leontief type.

In his model, there are three equilibria: twoof them are “extreme” (the allocations are respectively supported by the price vectors (1,0), and(0, 1)), and the other is an interior equilibrium. The Walrasian stability depends on the initialholdings of the consumers: the interior equilibrium is the only stable point in some cases, and it
is unstable and the two extreme equilibria are stable in other cases. Crockett et al. (2010)
designed and conducted an experiment of the Gale example in the double auction institution
using the MarketScape software.

Their observations surprisingly coincide with the predictions

by the Walrarian theory. The methodology of our experiment is different from theirs: ourinstitution is a manual experiment of trading a pit market while theirs is an on-line experimentof double auction.
The example by Shapley and Shubik (1977) is also a simple two-good two-consumer
exchange model of which the two consumers have strictly convex preferences linear in different
goods. Huber et al. (2009) implemented an experiment of the Shapley-Shubik example byasking the subjects to write and submit their proposal of trades only once in a period. In theirmodel, there are three equilibria which are all interior, the intermediate equilibrium is unstable,
and the two other equilibria are unstable. Their data shows that there is a tendency that
allocations converge to the intermediate equilibrium in the Edgeworth box. The methodology of
our experiment is also different from Huber et al. (2009): we told subjects to trade face–to-faceand reset holdings to the initial state at the beginning of every trading period while they used
computers for the subjects to write their offers and accept others’ offers and have the subjects tocarry over their holdings from the end of one period to the beginning of the next period until theend of one session of trade periods .
The paper is organized as follows. In Section 2, we present the model of an exchange
economy with three competitive equilibria which we used to conduct our experiment.

We alsodiscuss the Walrasian local stability of each equilibrium. In Section 3, we explain the design andprocedures of our experiment. Namely, we describe how we transformed the theoretical model
into the experiments. In Section 4, we analyze the results of the experiment to find tendencies ofthe data and effects of our scientific controls. Section 5 is for concluding remarks.

2.

An Exchange Economy with Multiple Equilibria

We consider the following exchange economy with two commodities called X and Y , andtwo types of consumers named 1 and 2. The utility functions of consumers 1 and 2 are,respectively,4

U 1 ( x1 , y1 ) = a1 min[ g1 ( x1 ), y1 ] + b1 andU 2 ( x 2 , y 2 ) = a2 min[ g 2 ( x 2 ), y 2 ] + b2 (2.1)
In the experiment, we set a1  72.77 , b1  927.23 , a2  69.2 , b2  961.98 ,g1 ( x1 )  x1 / 9.8

if x1  [0,6.2]

 10.5 x1  6.2(10.5  1/ 9.8)

if x1  [6.2,7.5]

 x1 / 9.8  1.3(10.5  1/ 9.8)

if x1  [7.5,14.9]

 10.5 x1  13.6(10.5  1/ 9.8)

otherwise;andg 2 ( x2 )  x2 / 9.1

if x2  [0,7.35]

 11.3x2  7.35(11.3  1/ 9.1)

if x2  [7.35,8]

 x2 / 9.1  0.65(11.3  1/ 9.1)

if x2  [8,17.45]

 11.3x2  16.8(11.3  1/ 9.1)

if x2  [17.45,18.45]

 x2 / 9.1  16.5(11.3  1/ 9.1)

otherwise.

Figure 1. Utility Functions of Consumers
Utility Function of Type 1 Consumer

3000
2500
2000
1500
30
25
20
Y 15
10

1000
500
5
0

0

5

10

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X

5

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UtilityUtility Function of Type 2 Consumer

2500
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1500
Utility
1000

30
25
20
Y 15
10
5

500

0

0

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10

15

20

25

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30

X

Figure 1 illustrates these utility functions. The individual endowment of consumer 1 isgiven by ( x1 , y1 )  (25,1) and the individual endowment of consumer 2 is ( x 2 , y 2 )  (5,29) .
Figure 2 displays this economy in an Edgeworth box. The solid (resp. dashed) piecewise
linear line denotes consumer 1’s (resp. consumer 2’s) offer curve, derived by varying prices andasking the consumer how much she would like to trade to maximize her utility at each price.
Notice that the offer curves are given by y1 = g1 ( x1 ) and y 2 = g 2 ( x 2 ), because the utility
maximization points are the loci of the verteces of the L-shaped indifference curves.

There arethree competitive equilibria indicated by the points of intersection of the two offer curves atwhich supply equals to demand.

Figure 2. Exchange Economy with Three Competitive Equilibria

6Consider a market excess demand function of an exchange economy. We say that acompetitive equilibrium, or simply an equilibrium, is locally stable (resp. unstable) if the market
demand function is strictly decreasing (increasing) at the equilibrium price. The intermediate
equilibrium B = (12.0132, 14.7432) is locally unstable, whereas the other two equilibrium A =(6.99771, 9.00859) and C = (15.4803, 21.1309) are locally stable. Figure 2 can be also regarded
as demonstrating symmetric equilibrium outcomes in a market with n traders on each side when
all traders of the same type take the same action.
In our experiment, subjects chose integers as trading units, not real numbers in usual
theory. Therefore, it is important to consider a discrete version of the exchange economy
corresponding to the experimental setting to make a rigorous theoretical prediction. Figure 3
shows this discrete exchange economy in an Edgeworth box. The locus of circles ( ) (resp.
multiplication signs ()) denotes consumer 1’s (resp. consumer 2’s) offer curve, which is thick,in the discrete economy. The two offer curves intersect at six points indicating competitive
equilibria: A1 = (7, 9), A2 = (8, 9), C1 = (16, 20), and C2 = (16, 21) are locally stableequilibrium points with the corresponding equilibrium price ratios p X / pY = 0.44, 047, 2.11,
2.22, respectively, while B1 = (12, 15) and B2 = (12, 16) are locally unstable points with

p X / pY = 1.08, 1.15, respectively. 2

Figure 3. Discrete Version of Offer Curves in the Exchange Economy

y1


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
25

C2,

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

C1




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


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20
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15
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A1,A2
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B2,
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B1
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 ( x, y )
0

01 0

5

10

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20

25

02

y2

x2
30

30

x1

2

The number of competitive equilibria when only integer units are allowed in trading in experimental settings
could be quite larger than that when trading units are real numbers in theory. For Shapley-Shubik (1977) exchange
economy with two goods, there are only three competitive equilibria in theory. However, there are 198 equilibria with
only integer trading units and no trading price constraint (see Masui, Ohtaka, Shimomura, Takahashi, and Yamato(2010))..

7

Moreover, we prohibited subjects from trading commodities at which the price ratio

p X / pY , the trading ratio of Y to X (= (Amount of Y)/(Amount of X)), was less than 1/4 = 0.25.
For p X / pY < 1/4, there are several competitive equilibria other than the above six equilibria.
In Figure 2, we omit these equilibria and focus on the six equilibria close to the three equilibria
in Figure 2 of the usual Edgeworth box.
Table 1 summarizes the equilibrium predictions. There are trade-off between stability and“equity” of the competitive equilibria. The equilibria A1 and A2 with low relative prices ofcommodity X, p X / pY , are beneficial for type 1 consumer having more of commodity Y, while
the equilibria C1 and C2 with high relative prices of commodity X is advantageous to type 2
consumer having more of commodity X. These four equilibria are locally stable, but not
equitable. On the other hand, the equilibria B1 and B2 with intermediate prices give allocations
that generate a negligible difference between the payoffs to the two types of consumers. We saythat the equilibrium and allocation are equitable.

In particular, each type receives the sameequilibrium payoff at B1. However, they are locally unstable.

Discrete Equilibria

Table 1: Theoretical Predictions about Discrete Equilibria

A1
A2
B1
B2
C1
C2

Allocation
Payoff
Type 1 Type 2
Walrasian Type 1 Type 2
Price(x1, y1) (x2, y2)
Stability
U1
U2(7, 9) (23, 21) 4/9=0.44
stable1582
2415(8, 9) (22, 21) 8/17=0.47
stable1582
2407(12, 15) (18, 15) 14/13=1.08 unstable 2000
2000
(12, 16) (18, 14) 15/13=1.15 unstable 2000
1931
(16, 20) (14, 10) 19/9=2.11
stable2383
1572(16, 21) (14, 9) 20/9=2.22
stable2455
1572

In a society consisting of different and conflicting ethnic groups, we conjecture thattrading outcomes when theinequitabletraders are of different ethnicities will

be an extreme andequilibrium, A1, A2, C1, or C2, which is beneficial for one type of trader who is a

tougher negotiator than the other type is. One might also think that ethnically different people
would never trade if the two ethnic groups are not getting along well. On the other hand, trading
outcomes may converge toequilibrium B1 or B2, when the two types of traders are of thesame ethnicity.

83. The Experimental Design and Procedures
3-1. Design
For testing our conjecture on trading outcomes between two ethnic groups in the previous
section, we select Kenya as a place to conduct an experiment because Kenya would be one of
the best places in the world because more than 40 different ethnic groups are present. Eachgroup has its own background, and some groups have been historically in conflict.
We conducted nine sessions at the University of Nairobi during March 2-4 of 2010. In
2008, different ethnicities of students there were in conflict due to a problem of student politics
although they were settled down when we visited. We wondered if the students sharply separate
market trades in experiment from the somewhat complex feelings with different ethnic groups.
We thus believed that the university is the Kenyan society in microcosm. Needless to say, we
are unable to conduct an experiment for every possible combination of the existing ethnicities.
We therefore choose three ethnic groups: Luo, Kikuyu, and Kalenjin. The reason why wechoose them is that these three groups of people together with Luhya actually conduct thecentral economic activities in Kenya.
The number of subjects from each of the three ethnic communities, Luo, Kikuyu, orKalenjin, was 24 for a total of 72 distinct subjects. For each ethnic group, 12 subjects played therole of type 1 consumer and 12 subjects did the role of type 2 consumer. Their roles were fixed
throughout the experiment. Twenty-four subjects participated in each session. Table 2-(a)summarizes the session names. For example, 12 Luo subjects whose roles were of type 1, and12 Kikuyu subjects whose roles were of type 2

participated in L1-Ki2 session.

Table 2. Nine Laboratory Sessions

Type 2
Luo
Kikuyu Kalenjin
Luo
L1-L2 L1-Ki2 L1-Ka2
Type 1 Kikuyu Ki1-L2 Ki1-Ki2 Ki1-Ka2
Kalenjin Ka1-L2 Ka1-Ki2 Ka1-Ka2

3/2/2010
L1-L2
AM
Ki1-Ki2
L1-Ki2PM
Ki1-L2

Table 2-(a). Session Names

3/3/2010
Ka1-Ka2

3/4/2010
L1-Ka2
Ka1-L2

Ka1-Ki2
Ki1-Ka2

Table 2-(b). Time Schedule

Each subject participated in three sessions. Table 2-(b) shows the time schedule. Eachsubject first faced participants of the same ethnic group and then those of different ethnic groups.
For example, first of all, Luo subjects of type 1 faced Luo subjects of type 2 in L1-L2 session in
the morning of the first day. Second, they participated in L1-Ki2 session with Kikuyu subjectsof type 2 in the afternoon of the first day. Finally, they met Kalenjin subjects of type 2 in
L1-Ka2 session in the morning of the third day.
The subjects were students at the University of Nairobi and Kenyatta University situated9

in major urban centers as well as at universities located in (relatively) small towns such as Moi
University, Egerton University, Mount Kenya University, Kimathi University College ofTechnology, and Jomo Kenyatta University of Agriculture and Technology. Also, the number ofmale subjects was the same as that of female subjects.
No subject had prior experiences in market experiments. The three sessions in which eachsubject participated required approximately 5 hours to complete in total. The average payoff per
subject was 5791 Ksh (One US dollar approximately exchanged for 77 Ksh in March of 2010).
The maximum payoff among the 72 subjects was 6277 Ksh, and the minimum payoff was 4502
Ksh.

3-2.

Procedures

In each session we made 12 pairs out of the 24 subjects so that there were 12 trading teams in
total, and each had two participants. Each team received two experimental procedure sheets, arecord sheet, a payoff table, and two name tags. The name tag of each subject indicated his teamname (A, B, C, …, or L), his identification number (1 or 2), and an abbreviation for his ethnicity(“L” for Luo, “Ki” for Kikuyu, or “Ka” for Kalenjin), such as “C-2-Ki”.

Six teams A, B, …,

and F played the role of type 1 consumer, and six teams G, H, …, and L played the role of type 2
consumer.
Each team was given pink cards and/or white cards in an envelope. One pink card was
one unit of commodity X, and one white card was one unit of commodity Y. We explicitly
noticed to every subject that he is not allowed to reveal any information regarding the payoff
table or the endowment of his team to any other team.
The subjects walked around a relatively large laboratory room and found a team to trade.
We prohibited any subject from giving any amount of commodity X or Y more than he held tothe team. In addition, as explained in the previous section, the trading ratio of Y to X should begreater than or equal to 1/4 = 0.25 to exclude undesirable equilibrium allocations.
We told the subjects to trade commodity X for Y or Y for X when two teams reached anagreement. After writing the trading results in their record sheets, the teams reported them to theexperimenter. The following information on the results was written on the blackboard anddisplayed publicly: the team name giving commodity X, the amount of the traded X, the teamname giving Y, the amount of the traded Y, and the trading ratio of the commodities (=Y/X).
This was the end of one trade.
We mean by a “period” the time in which subjects trade by starting from their initialholdings. The subjects had 10 minutes for each period and they were allowed to trade as manytimes as they wanted within the time limit. For the next partner, the subjects could choose any

10team as they wanted: it might be the same as or different from one of the teams they had alreadytraded. After each period, the subjects went back to their seats and the experimenter collected allcommodity cards. This was the end of the one period.
At the beginning of the next period, the subjects received the same materials as those of
the previous period. In particular, holdings of commodities were reset at the end of each period
and each team held the same endowment at the beginning of each period. After a 2-minutebreak, the next period started. We mean by a “session” a sequence of periods of experiment withthe same subjects. One session had 5 periods. The above steps were repeated 5 times. The
sessions were conducted in English.
Each subject’s earnings depended on the final payoff that his team earned in one
randomly selected period from the experiment. This period was chosen by a random device after
the experiment. Each member of the same team received the same earnings.
We distributed to each team a payoff table showing how its payoff depends on theamounts of commodities X and Y. See Table 3 (resp. Table 4) in the Appendix for the payoff
table of type 1 (type 2) in which the column denotes the amount of commodity X and the row
denotes the amount of commodity Y. We round off the decimal places of payoff values.

4.

Experimental Results

Figure 4 shows differences between the distributions of the end-of-period holdings ofcommodities X and Y over three consecutive sessions for type 1 of Luo and Kalenjin (Figure 8
in the appendix shows those for type 1 of Kikuyu). Each session has 5 periods in which 6 teamsof subjects of each type trade, so our data consist of 56 = 30 consumption bundles of

X and Yfor each type and each session. In Figure 4, the XY planes of the bases of three-dimensional
diagrams represent the possible holdings of goods

X

andY for the subjects, and theheights denote the frequencies of the holdings observed in experiment.
Figure 4(a) shows the distributions of holdings of type 1 of Luo subjects when they tradedwith type 2 of Luo subjects:

many patterns of holdings were observed and there was nopattern in which the data concentrated. Figure 4(b) shows the distributions of holdings of type 1of Kalenjin subjects when they traded with the other type of Kalenjin subjects: several patternsof holdings were attained and the data concentrated in ( x1 , y1 )  (12,15) , which is theconsumption bundle for type 1 at the intermediate equilibrium.
Figure 4(c) shows the distributions of holdings of type 1 of Luo subjects when they tradedwith type 2 of Kikuyu subjects: the patterns of holdings were less than in Figure 4(a) and the11data concentrated around (12, 15). Figure 4(d) shows the distributions of holdings of type 1 ofKalenjin subjects when they traded with type 2 of Kikuyu subjects: the patterns of holdings
were less than in Figure 4(c) and the data extremely concentrated in (12, 15).
Figure 4(e) shows the distributions of holdings of type 1 of Luo subjects when they tradedwith type 2 of Kalenjin subjects: the patterns of holdings were much less than in Figure 4(c) andthe data remarkably concentrated in (12, 15). Figure 4(f) shows the distributions of holdings oftype 1 of Kalenjin subjects when they traded with type 2 of Luo subjects: the patterns ofholdings were the least of the six diagrams of Figure 4 l and almost all of the data are (12, 15).
These observations tell that, in the sessions Kalenjin subjects participated in, most of
type1 of consumers finally had the bundle (12, 15) regardless of their ethnicities.

12

Figure 4. Distribution of End-of-Period Holdings of X and Y:
Luo Type 1 and Kalenjin Type 1(a) Session with Luo Type 1 and Luo Type 2

Luo Type 1: L1-L2.

18
16
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Y 15
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(b) Session with Kalenjin Type 1 and Kalenjin Type 2

Kalenjin Type 1: Ka1-Ka2

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(c) Session with Luo Type 1 and Kikuyu Type 2

Luo Type 1: L1-Ki2

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(d) Session with Kalenjin Type 1 and Kikuyu Type 2

Kalenjin Type 1: Ka1-Ki2

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(e) Session with Luo Type 1 and Kalenjin Type 2

Luo Type 1: L1-Ka2

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30

Frequency

X(f) Session with Kalenjin Type 1 and Luo Type 2

Kalenjin Type 1: Ka1-L2

30
25
20
Y 15
10
5
0

0

5

10

20

15

X

15

25

26
24
22
20
18
16
14 Frequency
12
10
8
6
4
2
0
30

Figure 5 shows the average distance from the intermediate equilibrium B1 consumption
bundle per subject for each ethnic group of subjects. Here the distance of each subject at eachperiod is defined as the Euclidean distance 3 between her end-of-period holdings and theconsumption bundle her type of consumer receives at B1. Figure 5-(a) indicates that average
distances are high in the Luo group, middle in the Kikuyu group, and low in the Kalenjin groupin the sessions with the same ethnicity. Figure 5-(b) demonstrates that in the sessions withdifferent ethnicities, average distances are lower in the sessions including the Kalenjin group(i.e., Sessions Ka1-Ki2, Ki1-Ka2, L1-Ka2, and Ka1-L2) than in those in the sessions consistingof the Luo and Kikuyu groups (i.e., Sessions L1-Ki and L2-Ki2). In particular, the average
distance approaches to zero as periods advance, that is, allocations converge to the intermediate
equilibrium allocation B1 in every session including the Kalenjin group.
We test the hypothesis that the mean distance per subject is equal between two ethnic
groups by pooling the data across periods with a random effects model. The pooled distancedata rejects (i) the hypothesis between each pair of Luo, Kikuyu, and Kalenjin groups at the
one-percent significant level in the first-round session with the same ethnicity and (ii) the
hypothesis between Luo and Kalenjin groups as well as that between Kikuyu and Kalenjin at the
one-percent significant level in the second-round session with different ethnicities. On the other
hand, the data fails to reject the hypothesis between Luo and Kikuyu groups in the second-roundsession with different ethnicities or that between any pair of the three groups in the third-roundsession with different ethnicities at the five-percent significant level. 4

Figure 5. Average Distances from the Intermediate equilibrium Allocation B1(a) Session with the same ethnicity

14
Average Distance

12
10

L1-L2

8

Ki1-Ki26

Ka1-Ka2

4
2
0
1

2

3

4

5

Period(b) Session with different ethnicities
3

4

The Euclidean distance between points ( a1 , a2 ) and ( b1 , b2 ) is ( a1  b1 )2  ( a2  b2 )2 .
A Wilcoxon signed rank test and a t-test give the same result as that by the panel data analysis.

16

Average Distance

6
5

L1-Ki24

Ki1-L2
Ka1-Ki23

Ki1-Ka22

L1-Ka2

1

Ka1-L201

23
Period4

5

Figure 6 shows the average number of transactions per subject for each session. The
number of transactions is high in the Luo group, middle in the Kikuyu group, and low in the
Kalenjin group in the sessions of the same ethnicity groups. In the sessions with different
ethnicities, transactions occur more often in the sessions consisting of Luo and Kikuyu subjects
than in the sessions including Kalenjin subjects in which one subject carried out only almost one
transaction on average.

Figure 6. Average Numbers of Transactions per Subject

Average Number of Trasnactions(a) Session with the same ethnicity

7
6
5

L1-L1
Ki1-Ki2

4

Ka1-Ka2
3
2
1
0
1

2

3
Period4

17

5

Average Number of Trasnactions(b) Session with different ethnicities

3.5
3

Ki1-L2
L1-Ki2
Ka1-Ki2
Ki1-Ka2
L1-Ka2
Ka1-L2

2.5
2
1.5
1
0.5
0
1

2

3
Period4

5

We test the hypothesis that the mean number of transactions per subject is equal between
two ethnic groups by pooling the data across ethnic groups with a random effects model. The
pooled transaction data rejects (i) the hypothesis between each pair of Luo, Kikuyu, andKalenjin groups at the one-percent significant level in the first-round session with the same
ethnicity and (ii) the hypothesis between Luo and Kalenjin groups as well as that between
Kikuyu and Kalenjin at the one-percent significant level in the second-round session withdifferent ethnicities. However, the data fails to reject the hypothesis between Luo and Kikuyu
groups in the second-round session with different ethnicities or that between any pair of thethree different ethnic groups in the third-round session at the five-percent significant level. 5
Next we examine a key question of whether the outcome is efficient. Here we define
efficiency as the sum of realized payoffs over all subjects as a percentage of the maximum
payoffs achievable. 6 Figure 7 demonstrates efficiency across periods in each session. Efficiency
is low in the Luo group, middle in the Kikuyu group, and high in the Kalenjin group in thesessions of the same ethnicity groups. In the sessions with different ethnicities, efficiency islower in the sessions consisting of Luo and Kikuyu subjects than in the sessions including
Kalenjin subjects. Figures 6 and 7 together suggest that there is an inverse relationship between
the number of transactions and efficiency in our experimental market.

5
6

A Wilcoxon signed rank test and a t-test provide the same result as that by the panel data analysis..
The maximum value of the sum of the payoffs of two consumer types is 4072.

18Figure 7. Efficiency(a) Session with the same ethnicity

100%

Efficiency

95%
90%
L1-L1
85%

Ki1-Ki280%

Ka1-Ka2

75%
70%
1

2

3
Period45(b) Session with different ethnicities

100%
98%

Efficiency

96%

Ki1-L294%

L1-Ki292%
90%

Ka1-Ki288%

Ki1-Ka286%

L1-Ka284%

Ka1-L282%
1

2

3
Period4

5

Why is the “Kalenjin effect” on achieving the intermediate equilibrium so strong?
Kalenjin subjects quickly began to make offers of the intermediate equilibrium only and ceased
to accept other proposals although the other ethnic groups of subjects kept making small
adjustments to improve themselves upon. Our observations tell that the bilateral trading do notcause large inequalities of income or welfare, and the participation of a non-negligible numberof Kalenjin people in the experimental market significantly facilitate the prompt decisions ofnegotiations at the exact point of the intermediate equilibrium.

19

To sum up, we observe the following:(a) CIn the sessions with Luo and/or Kikuyu subjects only, we do not observe
convergence of allocations. In the sessions with Kalenjin, however, allocations
converge to the intermediate equilibrium allocation, which is equitable but locallyunstable, as periods go on.
(b) The speed of convergence to the intermediate equilibrium B1 is remarkably fasterwith Kalenjin subjects than without them. Kalenjin subjects quickly began to makeoffers of the intermediate equilibrium only and ceased to accept other proposals.
(c) The frequency of transactions with Kalenjin subjects are significantly less than thatwith Luo and/or Kikuyu subjects only, and the less frequent transactions result in the
more efficient outcomes of the experimental market.

5.

Concluding Remarks

We have reported the organizations, implementations, observations, and statistics of ourmultiethnic experiment in Kenya. Before starting this project, we conjectured that thebackgrounds of the ethnic communities would influence the results of this series of experiments.
The conjecture is disproved in our experiment.

Our data show that the outcomes from sessions

Kalenjin subjects participate in converge to the intermediate equilibrium at least in the sensethat the average of the distance between the intermediate equilibrium and the observation goesto zero.
In our experiment, the key players are the Kalenjin subjects. We observe that it
surprisingly facilitates the fast and exact convergence to the intermediate equilibrium to get
Kalenjin into the market. We find a few remarkable differences between the two data sets: one
set contains data with Kalenjin subjects, and the other set includes no data with Kalenjin
subjects.

20References
Anderson, Christopher M., Charles R. Plott, Ken-Ichi Shimomura, and Sander Granat (2004):“Global Instability in Experimental General Equilibrium: the Scarf Example,” Journal of Economic
Theory 115, 209-249.
Bergstrom, Theodore C., Ken-Ichi Shimomura, and Takehiko Yamato (2009): “Simple Economies
with Multiple Equilibria,” The B.E. Journal of Theoretical Economics 9: Article 43.
Cason, Timothy, Tatsuyoshi Saijo, and Takehiko Yamato (2002): “Voluntary Participation and Spitein Public Good Provision Experiments: An International Comparison,” Experimental Economics 5,
133-153
Chipman, John S. (2010): “Multiple Equilibrium under CES Preferences,” Economic Theory 45,
129-145.
Crockett, Sean, Ryan Oprea, and Charles R. Plott (2010): “Extreme Walrasian Dynamics: The Gale
Example,” Mimeo, University of California at Santa Cruz.
Gale, David (1963): “A Note on Global Instability of Competitive Equilibrium,” Naval Research
Logistics Quarterly 10, 81-87.
Huber, Juergen, Martin Shubik, and Syham Sunder (2009): “Default Penalty as Disciplinary and
Selection Mechanism in Presence of Multiple Equiliria,” Cowles Foundation Discussion Paper No. 1730,
Yale University.
Roth, Alvin E., Vesna Prasnikar, Masahiro Okuno-Fujiwara, and Shmuel Zamir (1991):“Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental
Study,” American Economic Review 81, 1068-1095.
Masui, Michiharu, Tokitaka Ohtaka, Ken-Ichi Shimomura, Kiyotaka Takahashi, and Takehiko
Yamato (2010): “Discrete Exchange Economies: a Simulation Analysis,” Discussion Paper, Tokyo
Institute of Technology.
Scarf, Herbert (1960): “Some Examples of Global Instability of the Competitive Equilibrium,”International Economic Review 1, 157-171.
Shapley, Lloyd. S. and Martin Shubik (1977): “An Example of a Trading Economy with Three
Competitive Equilibria,” Journal of Political Economy 85, 873-75.
Smith, Vernon L. (1962): “An Experimental Study of Competitive Market Behavior,” Journal of
Political Economy 70, 111-137.

21

Amount of Y

30 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2862 3110 3110 3110 3110 3110 3110 3110 3110 3110 3110 3110 3110 3110 3110
29 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2862 3038 3038 3038 3038 3038 3038 3038 3038 3038 3038 3038 3038 3038 3038
28 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2862 2965 2965 2965 2965 2965 2965 2965 2965 2965 2965 2965 2965 2965 2965
27 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2862 2892 2892 2892 2892 2892 2892 2892 2892 2892 2892 2892 2892 2892 2892
26 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819 2819
25 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746 2746
24 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674 2674
23 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601 2601
22 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528 2528
21 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455 2455
20 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383 2383
19 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310 2310
18 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237 2237
17 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2098 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164 2164
16 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092 2092
15 927 935 942 950 957 964 972 1585 1970 1978 1985 1993 2000 2007 2015 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019
14 927 935 942 950 957 964 972 1585 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946 1946
13 927 935 942 950 957 964 972 1585 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873 1873
12 927 935 942 950 957 964 972 1585 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800
11 927 935 942 950 957 964 972 1585 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728 1728
10 927 935 942 950 957 964 972 1585 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655
9 927 935 942 950 957 964 972 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582 1582
8 927 935 942 950 957 964 972 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509 1509
7 927 935 942 950 957 964 972 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437 1437
6 927 935 942 950 957 964 972 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364 1364
5 927 935 942 950 957 964 972 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291
4 927 935 942 950 957 964 972 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218 1218
3 927 935 942 950 957 964 972 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146 1146
2 927 935 942 950 957 964 972 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073 1073
1 927 935 942 950 957 964 972 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
0 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927 927
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Amount of X

Payoff Table

Appendix
Table 3. Payoff Table Provided to Subjects of Type 122

30 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
29 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
28 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
27 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
26 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
25 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
24 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
23 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
22 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2422 2430 2437 2445 2453 2460 2468
21 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2384 2392 2399 2407 2415 2415 2415 2415 2415 2415 2415 2415
20 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2346 2346 2346 2346 2346 2346 2346 2346 2346 2346 2346 2346
19 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2277 2277 2277 2277 2277 2277 2277 2277 2277 2277 2277 2277
18 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2208 2208 2208 2208 2208 2208 2208 2208 2208 2208 2208 2208
17 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2138 2138 2138 2138 2138 2138 2138 2138 2138 2138 2138 2138
16 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2028 2069 2069 2069 2069 2069 2069 2069 2069 2069 2069 2069 2069
15 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000
14 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931
13 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 1862 1862 1862 1862 1862 1862 1862 1862 1862 1862 1862 1862 1862
12 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 1792 1792 1792 1792 1792 1792 1792 1792 1792 1792 1792 1792 1792
11 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 1723 1723 1723 1723 1723 1723 1723 1723 1723 1723 1723 1723 1723
10 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1587 1595 1654 1654 1654 1654 1654 1654 1654 1654 1654 1654 1654 1654 1654
9 962 970 977 985 992 1000 1008 1015 1526 1534 1541 1549 1557 1564 1572 1579 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585 1585
8 962 970 977 985 992 1000 1008 1015 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516 1516
7 962 970 977 985 992 1000 1008 1015 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446 1446
6 962 970 977 985 992 1000 1008 1015 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377 1377
5 962 970 977 985 992 1000 1008 1015 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308 1308
4 962 970 977 985 992 1000 1008 1015 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239 1239
3 962 970 977 985 992 1000 1008 1015 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170
2 962 970 977 985 992 1000 1008 1015 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
1 962 970 977 985 992 1000 1008 1015 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031
0 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962 962
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Amount of X

Table 4. Payoff Table Provided to Subjects of Type 2

23

Amount of Y

Figure 8. Distribution of End-of-Period Holdings of X and Y: Kikuyu Type 1.

(a) Session with the same ethnicity

Kikuyu Type 1: Ki1-Ki2.

30
25
20
Y 15
10
5
0

0

5

10

15

20

25

26
24
22
20
18
16
14 Frequency
12
10
8
6
4
2
0
30

X

(b) Session with Kikuyu Type 1 and Luo Type 2

Kikuyu Type 1: Ki1-L2

30
25
20
Y 15
10
5
0

0

5

10

15

20
X

24

25

26
24
22
20
18
16
14 Frequency
12
10
8
6
4
2
0
30

(c) Session with Kikuyu Type 1 and Kalenjin Type 2

Kikuyu Type 1: Ki1-Ka2

30
25
20
Y 15
10
5
0

0

5

10

15

20
X

25

25

26
24
22
20
18
16
14 Frequency
12
10
8
6
4
2
0
30