Competing to Trade when Buyers’ and Sellers’
Evaluations are Related
– An Experimental Study –
Nadine Chlaß∗‡
Werner Güth
∗
May 2007
Abstract
We enrich the bilateral trade model with one seller whose value is linearly
related to the only buyer’s evaluation (Samuelson and Bazerman 1985) by
allowing for competition. For risk neutral buyers, increasing the number of
competing symmetric sellers, promotes efficiency enhancing trade whereas
competition of buyers increases the price. In the experiment, we vary the
coefficient of linear relatedness as well as the number of competitors on both
sides. We explore whether participants (learn over the 40 rounds of play to)
realize the gains from trade at least when this is predicted.
JEL Classification: D01,D42,D43,D44,D82,L13,L15
∗
‡
Max Planck Institute of Economics, Jena, Germany.
Corresponding author. E-mail: [email protected]
1
1
Introduction
Consider the model of bilateral trade with a privately informed seller whose evaluation of the good is linearly related by a quota q ∈ (0, 1) to that one of the only
buyer (Samuelson and Bazerman 1985). Since the buyer’s evaluation v always exceeds the evaluation qv of the seller whenever, as assumed, v is positive, trade is
always efficiency enhancing. Nevertheless, when v is (expected by the buyer to be)
uniformly distributed on (0, 1) and the buyer is risk neutral, efficiency enhancing
trade is only predicted for q < 1/2 . Thus, this bilateral trade-model does not only
allow to analyze common value effects (see Kagel 1995, for a survey of common
value auction experiments), due to the linearly related evaluations of buyer and
seller, but also whether efficiency enhancing trade is only realized when consistent
with opportunism (see, for example, Chlaß et al. 2006).
Here we focus on how competition changes the result when trying to maintain most
of the structural assumptions like:
- risk neutrality of the buyers,
- linear relatedness of a seller j’s evaluation qvj and a buyer’s value vj for seller j’s
product,
- for all sellers j = 1, ..., n(≥ 2) the value vj is independently determined according
to the uniform density on (0, 1) and
- trade at price p when there exists some seller j with p > qvj .
2
The interval of parameters q, for which trade is game theoretically predicted, is
£ n ¢
0, n+1 for all numbers n of competing sellers with 1 ≤ n < ∞. Thus, trade is more
£ n ¢
easy to realize, as measured by the interval 0, n+1
for linear relatedness parameters
q, the larger the number n of potential sellers. Increasing the number of competing
buyers can thus prevent no-trade results. If, however, there is trade, competing
buyers do not profit anymore from trade.
In the experiment, we do not only vary q (see also the earlier experimental studies of
(Dittrich et al. 2005), (Güth et al. 2005), (Chlaß et al. 2006)) but also the number
of competing sellers and buyers n and m. Will participants trade more often when
both, n and/or m increase and how do they react to simultaneous variations of n
and m?
2
The Model
Let n with 1 ≤ n < ∞ denote the number of competing sellers and m with 1 ≤ m <
∞ the number of competing buyers. All (sellers) buyers are (a priori) symmetric.
More specifically, for each seller j = 1, ..., n the value vj of his sales item j, one
unit of an indivisible good, is vj for any of the m buyers i = 1, ..., m whereas seller
j himself evaluates his sales item only by qvj where 0 < q < 1. Thus, the seller’s
evaluation of his sales item and the buyers’ evaluation of it are
• linearly (cor)related and
• trade would be always efficiency enhancing.
It is assumed that for all sellers j = 1, ..., n the value vj is independently drawn
from the (open) unit interval (0, 1) according to the uniform density on (0, 1) what,
in the tradition of (Harsanyi 1967/68), expresses the commonly known beliefs of all
buyers concerning the quality of the sales items.
We first describe and solve the game with a unique buyer (m = 1), who wants to
buy at most one item, and then extend our analysis to competing buyers (m). In
case of m = 1 the market decision process is as follows:
3
• First, the only buyer i names a price pi ∈ [0, 1] .
• Then, chance determines randomly and independently vj ∈ (0, 1) for all sellers
j = 1, ..., n (≥ 2) according to a uniform density on (0, 1) .
• Learning only their own value vj but not yet the proposed price pi by buyer
i, all sellers j = 1, ..., n choose their lower price limit pj (vj ) what ends the
interaction.
If pi < pj (vj ) for all sellers j = 1, ..., n, no trade results and all interacting parties
earn 0. If, however, pi ≥ pj (vj ) for at least one seller j, the only buyer i buys at
price pi from the seller j whose price limit pj (vj ) is largest. The latter assumption
is reasonable since for each seller j = 1, ..., n
• it is a dominant strategy to set pj (vj ) = qvj and
• higher price limits pj (vj ) therefore signal reliably higher quality (vj ).
If the only buyer was randomly matched with one of the n ≥ 2 sellers rather than
according to the revealed quality, the situation would equal the case n = 1 which
has previously been discussed in the literature. In that case the only buyer i earns
Ui = vj ∗ − pi where j ∗ is the seller with pj ∗ (vj ∗ ) ≥ pj (vj ) for all j = 1, ..., n. Seller j ∗
earns Uj ∗ = pi − qvj ∗ whereas all other sellers j 6= j ∗ get 0. Due to Uj ∗ ≥ 0, if, and
only if, pi ≥ qvj , it follows that pj (vj ) = qvj is the dominant strategy for all sellers
j as claimed above.
It therefore only remains to derive the optimal price p∗i of the only buyer i. Now for
any price pi buyer i’s payoff expectation, given the dominant choices of all sellers j,
is
p
Z
Zq
[v − pi ] nv n−1 dv = n
Ui (pi ) =
£
¤
v n − pv n−1 dv
0
pi ≥qv≥0
since pi yields trade whenever pi ≥ qv for v = max {vj : j = 1, ..., n} and since the
probability distribution of v on (0, 1) is given by v n (implying the density nv n−1 ).
4
From
·
¸
1
1
pn+1
Ui (pi ) = n n
−
q
(n + 1) q n
and
0
Ui (pi ) R 0 if
it follows that
½
p∗i
=
n
Rq
n+1
n
q if n+1
>q
n
0 if q > n+1
0
since, for Ui (pi ) > 0, any price pi ≥ q will induce trade for all v ∈ (0, 1) and it
therefore does not pay to increase pi above q. The more sellers there are, i.e., the
larger n, the more likely trade results if its likelihood is measured by the length
n
n+1
of the interval of linear relatedness parameters q for which trade is predicted. Now,
consider that more buyers compete although at most one buyer will want to actually
buy one sales item. Figure a unique customer whom all sellers want to serve but
who is interested in at most one, and if so, the highest quality item. He evaluates
this latter at vj ∗ as each other buyer i = 1, ..., m whom he would compensate by vj ,
having bought seller j’s sales item. Seller j ∗ with the highest quality will, of course,
only accept prices exceeding qvj ∗ and, in case of more such price offers, the highest
price bid. Clearly, for q >
n
,
n+1
none of the buyers i = 1, ..., m (≥ 2) will want to
buy even a highest quality item following the same logic as the only buyer i in case
of m = 1. I.e. we have
p∗i = 0 for i = 1, ..., m (≥ 1) if 1 > q >
For q <
n
n+1
n
.
n+1
each of the m competing buyers will want to buy from seller j ∗ with
pj ∗ (vj ∗ ) ≥ pj (vj ) for all sellers j = 1, ..., n. Competition will thus drive the price bids
pi up to the level p∗ for which no profit for the buyers remains, i.e., to p∗ given by
Z
∗
Ui (p ) = n
1
£
¤
v n − p∗ v n−1 dv = 0
0
and thus by p∗ =
n
.
n+1
We thus have proved the general
5
Proposition. Sellers j = 1, ..., n (≥ 2) will always set their price limit pj at pj (vj )
= qvj for all vj ∈ (0, 1) and buyers i = 1, ..., m (≥ 2) will choose prices
p∗i


=

0
q
n
n+1
n
for 1 > q >
¾ n+1
if m = 1
and 0 < q <
if m ≥ 2
n
n+1
In case of m ≥ 2 buyers will thus never gain anything: if q >
trade; if q <
n
,
n+1
n
,
n+1
there is no
there is trade but buyer competition implies 0 profits for them.
Interestingly, there is no welfare effect of whether there is buyer competition or not.
Compared to that, sellers gain from buyer competition (m ≥ 2) and seller competition is welfare enhancing since the interval of relatedness parameters q yielding
trade increases with n.
Although this case is not studied here experimentally, let us briefly mention how
to allow for at most min{m, n} trades rather than only one. If k, but not the
k + 1 highest price offers pi exceed the k, but not the k + 1 lowest reservation
prices pj , exactly k trades with 0 ≤ k ≤ min{m, n} are possible. These would be
implemented if the highest price bid pi was matched with the lowest reservation
price pj , the second highest price bid with the second lowest reservation price etc.
till k trades are arranged.
The interesting question here is what determines the equilibrium trade amount k ∗
and how this depends on m(≥ 2) and n(≥ 2). Note that the sellers’ optimal reservation prices are determined as before. For k buyer i with the kth highest price bid
would therefore earn
Z
Ui (pi ) =
[x − pi ] φ(x)dx
(1)
pi ≥qx≥0
where x(v) = x(v1 , ..., vn ) is the kth highest component of v = (v1 , ..., vn ) and φ(x)
its density. If the optimal price p∗ for Ui (pi ) is 0 one would have k ∗ < k, otherwise
k ∗ ≥ k. In the latter case, one checks for k + 1, k + 2, ... for which k ∗ one has that
p∗ is positive whereas it is not for k ∗ + 1. This illustrates both possibilities and
difficulties when generalizing our analysis to allow for more than one trade.
6
3
Experimental protocol
We ran eight sessions with 32 participants each. All sessions were conducted in
the experimental laboratory of the Max Planck Institute of Economics in Jena. At
the beginning of each session, subjects were randomly assigned to visually isolated
terminals where they received a hardcopy of the German instructions (see Appendix
A. for an English translation). After reading the instructions, participants had to
answer a simple control questionnaire (see Appendix B.). Clarifying questions were
answered privately at the participant’s terminal. The experiment started after all
participants had successfully completed the questionnaire.
Relying on a 2x2x3 factorial design with
n, m ∈ {1, 3} and
q ∈ {.3, .6, .8} ,
each session was randomly partitioned in a given round either in
(ii) 4 groups with one seller and three buyers each (n = 1 and m = 3) and 4 groups
with three sellers and one buyer each (n = 3 and m = 1) or in
(ii) 4 groups with three traders on both sides (m = 3 = n) and 4 pairs with only
one trader on both sides (m = 1 = n).
In each of the constellations above the parameter q remained the same for four (two
for q = .8 only)1 rounds and was changed thereafter till having experienced all three
q levels.
1
Since no trade is predicted for all n, m constellations, we wanted to avoid frustrating participants too much.
7
More specifically, a cycle comprised 10 rounds of (i) followed by 10 rounds of (ii), each
starting out with 4 rounds of q = .4 then q = .6 and finally two rounds for q = .8.
Participants experienced two such cycles successively, i.e., they played altogether 40
rounds with varying parameters q, n and m (in a within-subjects design). To check
for ordering effects, four out of eight sessions were run in an alternating succession
of cycles. Regarding the scala of v, we chose the more intuitive interval (0,10) rather
than (0,1) in order to facilitate the experimental task.
Participants were 256 undergraduates (138 females and 118 males) at the FriedrichSchiller University in Jena, Germany. Table 1 provides an overview over subjects’
fields of study.
Natural Sciences
44
Life Sciences
61
Cultural Sciences
103
Economics
38
Informatics
10
Table 1: Nr. of participants according to fields of study
Participants were recruited by Orsee (Greiner 2004). The software was developed
with the help of z-tree (Fischbacher forthcoming). A session lasted, on average, 108
minutes (minimum: 90, maximum: 120) and average earnings were €3 for buyers,
respectively €17.5 for sellers (minimum: €-20.10 for buyers, respectively €6.5 for
sellers, maximum: €21.10 for buyers, respectively €44 for sellers). Participants were
told and agreed in the beginning to rules regarding overall losses (see the instructions
in Appendix A).
4
4.1
Results
Descriptive Data Analysis
Let us first give a general impression of market interactions. Figure 1 depicts
marginal densities of both buyers’ bids and sellers’ minimum prices for all competition intensities investigated.
8
minimum price densities
0.25
{n=1, m=1}
{n=3,m=1}
{n=3,m=3}
{n=1,m=3}
0.0
0.00
0.1
0.05
0.2
0.10
0.3
0.15
0.4
0.5
{n=1, m=1}
{n=1,m=3}
{n=3,m=3}
{n=3,m=1}
0.20
0.6
bid densities
0
Figure 1:
2
4
6
8
0
10
2
4
6
8
10
estimates2 of
marginal bid and minimum price densities for all
competition intensities investigated.
We start by examining buyers’ overall reaction to differing contexts. Do buyers
enter competition at all? And if so, does buyer competition depend on the number
of sellers? Buyers’ reaction towards an increased number of competitors is reflected
by differences between the respective bid densities for {n = 1, m = 1} and {n =
1, m = 3}. We find a distinct shift in the expected values of these densities and
a somewhat larger variance for {n = 1, m = 3}. We thus indeed observe buyer
competition.
Bids do not seem to differ between markets with a potentially symmetric competition
on both sides {n = 3, m = 3} and markets with potential buyer competition only
{n = 1, m = 3}. Thus, buyers seemingly compete without paying much attention
to whether sellers compete.
Finally, buyers themselves exert seemingly little market power. Densities for {n =
1, m = 1} and {n = 3, m = 1} do not differ in expected values. However, the
bid density for {n = 3, m = 1} shows lowest overall variance and displays two
characteristic bumps in regions of low bids, mirroring some awareness of increased
potential market power.
Regarding sellers’ behavior, densities of stated minimum prices for {n = 3, m = 1}
and {n = 1, m = 1} differ in expected values and variance. Sellers thus react to
2
Densities are derived from locally linear kernel estimates using an epanechnikov kernel function.
Bandwidth is obtained by optimizing biased cross validation (Scott and Terrell 1987), yielding
results similar to Silverman’s rule of thumb (Silverman 1986, p.48).
9
an increased number of competitors by enhancing their minimum price. Variance
turns out to be much lower for potentially higher competition {n = 3, m = 1}.
Sellers do not seem to exert much market power either, as the respective densities
for {n = 1, m = 1} and {n = 1, m = 3} almost coincide. Interestingly, the more
intense potential seller competition, the smaller overall variance in stated minimum
prices.
To summarize, both sides engage in competition though their decision variables are
affected in an opposed way. The mechanism introduced for matching buyer and
seller participants is likely to explain why. Both buyers and sellers compete for
being admitted to trade. While buyers are matched if their bid is highest, sellers
only trade if they state the minimum price closest to but below the highest bid.
Indeed, seller competition drives the expected minimum price upwards and very
closely below the buyers’ expected bid.
Having looked at both parties’ decision variables we turn to their respective earnings.
Table 2 describes the average payoffs (and their standard deviations in brackets) by
distinguishing buyers, sellers, q ∈ {0.3, 0.6, 0.8} and competition intensities n, m ∈
{1, 3}.
role
average earnings
conditional on
trade
b
s
{n, m}
q=0.3
{n = 1, m = 1} 0.40 (2.85)
{n = 1, m = 3} -0.01 (2.95)
{n = 3, m = 1} 1.30 (2.47)
{n = 3, m = 3} 0.75 (2.88)
{n = 1, m = 1} 2.27 (0.85)
{n = 3, m = 1} 1.78 (0.74)
{n = 1, m = 3} 3.27 (0.89)
{n = 3, m = 3} 3.06 (0.86)
q=0.6
-0.64 (2.75)
-1.07 (2.54)
-0.29 (2.28)
-0.56 (2.31)
1.91 (1.65)
1.58 (1.37)
2.67 (1.53)
2.32 (1.39)
q=0.8
-1.06 (2.27)
-1.73 (2.33)
-1.08 (1.96)
-1.19 (2.10)
1.59 (1.82)
1.61 (1.57)
2.40 (1.87)
1.98 (1.68)
Table 2: average earnings of buyers and sellers per market types.
We find buyers entering competition reflected by their earnings being driven to zero
for q < 0.5 - that is, where the market was profitable without competition. Severe
losses occur where competition takes place on already initially unprofitable markets
with q > 0.5. These results are in line with previous confirmations of the winner’s
10
curse where subjects do not account for the common value effect and consequently
face losses.3 Losses are furthermore increased by competition.
Sellers achieve overall positive and higher payoffs than buyers for all q. Their payoffs
vary much less than buyers’ with a marked increase in dispersion for larger q. Finally,
reflecting buyers’ increasing bids, sellers’ average payoffs increase with intensified
buyer competition and vice versa. In summary, payoffs are consistent with our
estimates of both buyers and sellers’ responses to competition.
4.2
Treatment Effects
Let us now quantify the responses described above. With an entire session providing
only one independent observation of responses, we rely on generalized mixed effect
models allowing for repeated measurements of a subject’s responses. This will permit
us to investigate the impact of all treatment variables jointly. Estimated generalized
linear mixed effect models take the following form:
1
~ + Zi~bi + Λ 2 (β, γ) ~²i with ~bi ∼ i.i.d. D(b| 0, Ψ), ~²i ∼ D(²| 0, σ 2 I40 )
~yi | ~bi = f (Xi β)
i
with ~yi {40,1} containing 40 responses j for each individual i, Xi {40,d} the individual
fixed effects observations for d variables and β~{d,1} their coefficients including one for
the intercept. Zi {40,d} finally reflects individual random effects observations, ~bi {d,1}
their coefficients and ~²i {40,1} includes an individual error term. To summarize, we
let all variables have a fixed and a random component in both intercept and slopes.
To start with modeling buyers’ responses, we tested down to a linear mixed effects
1
~ ~bi ∼ Nd (0, Ψ) and σ 2 Λ 2 (bi , γ) = σ 2 I obtaining a fit
~ = Xi β,
model with f (Xi β)
i
via restricted Maximum-Likelihood. Table 3 details the results thus obtained. The
first column displays sizes of the fixed treatment effects, followed by their standard
errors, t-statistics and significance levels. The remaining two columns provide some
3
A detailed discussion of experimental and theoretical results regarding this phenomenon can
be found in (Eyster and Rabin 2005) and (Miettinen 2006).
11
goodness-of-fit measures. Spearman’s rank correlation ρSP
ŷ,y between fitted and observed values is calculated, stepwise including all treatment variables. A difference
in ρSP
ŷ,y between two rows thus reflects the improvement in fit due to an inclusion of a
specific variable. The last column finally indicates explanatory power of a variable’s
respective random component regarding residual variation.
Intercept
q
n
m
Value
Std.Error
t-value
p-value
2.55
0.25
0.05
0.34
0.17
0.16
0.03
0.05
15.40
1.52
1.74
6.85
0.00
0.13
0.08
0.00
P
ρSP
ŷ,y
0.58***
0.63***
0.67***
0.76***
σbii
σr
0.32
0.35
0.06
0.10
Table 3: determinants of buyers’ bid.
Confirming our impression from the previous section, the evaluation parameter q
does not significantly influence buyers’ bids. The effect size reveals however some
slight bid enhancement yielding a minor improvement in ρSP
ŷ,y . Interestingly, responses to q seem to vary substantially across individuals as suggested by the large
explanatory power of its random effect component. Seller competition intensity n is
indeed found to enhance buyers’ bids. However, the effect is of moderate size and
only weakly significant. Potential buyer competition m on the other hand exerts
a highly significant and economically relevant impact, showing largest explanatory
power besides the intercept. Random components of both competition variables
contribute little to overall variation.
In summary, buyers slightly and heterogeneously react to q, weakly respond to the
number of sellers n, and engage in fierce competition.
Modeling sellers’ responses requires a number of modifications. While ~bi ∼ Nd (0, Ψ)
1
still holds, both link function and variance differ with f (·) = ln(·), and σ 2 Λi2 (bi , γ) =
f 2 (~yi |~bi , γ)I. To account for this, we derive the fit by Quasi-Maximum-Likelihood.
Table 4 displays the results thus obtained.
Confirming our impression from the previous section, sellers significantly react to
q by a notable increase in their stated minimum price. While yielding the most
important improvement in fit amongst all explanatory variables, responses to q
12
Intercept
q
n
m
v
Value
Std.Error
t-value
p-value
-0.11
0.84
0.10
0.02
0.12
0.07
0.05
0.01
0.01
0.01
-1.64
16.28
6.48
2.76
19.01
0.10
0.00
0.00
0.01
0.00
P
ρSP
ŷ,y
0.36***
0.54***
0.59***
0.60***
0.84***
σbii
σ²i
0.36
0.29
0.08
0.04
0.04
Table 4: determinants of sellers’ minimum price.
show considerable heterogeneity. This can be inferred from both a comparatively
large standard error in its fixed part and a large explanatory power of its respective
random component. The actual quality of the good v is of second largest impact
in both size and improvement of fit. Turning to competition, m as well as n turn
out significant. However, only potential competition intensity on the seller side n
shows a noticeable fixed effect and an improvement in fit. As for q, a comparatively
important explanatory power of the random component discloses heterogeneity.
In summary, sellers considerably but heterogeneously respond to their evaluation
parameter q and the number n of potential competitors. They rather consistently
react to the quality of the good v and do not seem to consider competition on the
buyer side when stating their minimum price.
5
Conclusion
We have both game-theoretically and experimentally investigated the impact of
competition in a social dilemma, namely the so-called takeover game (Samuelson/Bazerman 1985). Introducing competition on both buyer and seller side, our
enriched model predicts:
(1) seller competition to foster trade, i.e. the highest reservation price increases
with n as predicted,
(2) buyer competition to increase the price, i.e. buyers to offer higher prices when
m is large.
13
Our experimental results confirm that buyers indeed engage in competition. Price
bids are driven upwards until buyers’ profits are exhausted. Contrary to the benchmark solution, sellers compete, too, by increasing their reservation prices. This is
presumably triggered by matching the buyer with highest price bid and the seller
with highest reservation price below this price bid as traders. Results particularly
deviate from the theoretical solution for {q > 0.5, n = 1, m = 1}. Buyers make
serious losses in these markets and competition in the sense of m > 1 even increases
them.
Future work will focus on varying the matching mechanism. We particularly intend
to investigate how this affects the reservation prices of competing sellers. Could seller
competition even reduce reservation prices, in that sellers accept also unprofitable
trades? Such cutthroat competition of sellers would question sellers’ rationality
(accepting prices leading to losses being weakly dominated) but enhance efficiency
enhancing since trade is always more efficient than no trade.
References
Chlaß, N., Güth, W., and Vanberg, C. (2006), Social Learning of Effiency Enhancing
Trade With(out) Market Entry Costs, in: Papers on Strategic Interaction Nr. 36,
Max Planck Institute of Economics,Jena.
Dittrich, D.A.V., Güth, W., Kocher, M., Pezanis-Christou, P. (2005), Loss aversion and learning to bid, in: Papers on Strategic Interaction Nr. 3, Max Planck
Institute of Economics, Jena.
Eyster, E.; Rabin, M. (2005), Cursed Equilibrium, in: Econometrica, vol. 73.
Fischbacher, U. (forthcoming), z-Tree - Zurich Toolbox for Readymade Economic
Experiments, in: Experimental Economics.
Greiner, B. (2004), An Online Recruitment System for Economic Experiments, in:
Kremer, K., Macho, V. (eds.) (2004), Forschung und wissenschaftliches Rechnen
2003, GWDG Bericht 63, Ges. f. Wiss. Datenverarbeitung, Gttingen.
14
Güth, W., Normann, H-T., Nikiforakis, N. (2005) in: Vertical Cross-Shareholding
and Experimental Evidence, in: Papers on Strategic Interaction Nr. 11, Max
Planck Institute of Economics, Jena.
Harsanyi, J. (1967/68) Games with Incomplete Information Played by Bayesian
Players,in: Management Science 14.
Kagel J. (1995), Auctions: A survey of experimental research, in: J. Kagel and A.
Roth (eds.) 1995, The Handbook of Experimental Economics, Cambridge, MA:
MIT Press.
Miettinen, T. (2006), Learning Foundation and Complexity of the Cursed Equilibrium, in: Papers on Strategic Interaction Nr. 40, Max Planck Institute of Economics, Jena.
Samuelson, W. F., and M.H. Bazerman (1985), Negotiation under the winner’s
curse. Volume 3, CT: JAI Press.
Scott, D.W. and Terrell, G.R. (1987), Biased and unbiased Crossvalidation in Density Estimation, in: Journal of the American Statistical Association, Vol. 82, Nr.
400.
Silverman, B. W. (1986), Density Estimation. London: Chapman and Hall.
15
Appendix
A. Instructions4,5
Instructions
Welcome and thank you very much for participating in this experiment. For your
showing up punctually you receive €2. Please read the following instructions carefully. Instructions are identical for all participants. Communication with other
participants is to cease from now on. Please switch off your mobile phone.
If you have questions, please raise your arm - we are going to answer them individually at your seat.
During the experiment all amounts will be indicated in ECU (Experimental Currency Units). The sum of your payoffs generated throughout all rounds will be
disbursed to you in cash at the end of the experiment according to the exchange
rate: 1 ECU=0.4 Euros. As negative payoffs through single rounds are possible, you
are endowed with 4 ECU. Payoffs achieved during the experiment will be added to
this amount. An eventually negative overall payoff has to be compensated through
working at the institute. The hourly wage in this case is set at 10 Euros.
Information regarding the experiment
The experiment consists of several rounds. Participants take on different roles.
Your role is randomly determined at the beginning of the experiment and remains
the same throughout all rounds of the experiment. The role you are assigned to will
be communicated at the beginning of the first round.
4
Instructions in the experiment were written in German. The following chapter reproduces a
translation into English. Emphases like e.g. bold font, are taken from the original text. Instructions
were identical for all subjects.
5
Notation of variables do not always coincide with the paper, as we chose the first letter of the
German word (e.g. ”offer” is named ”g”) to facilitate the experimental task. Especially q, seller’s
valuation in our model, is called ”a”, letter ”q” being already used for ”quality”.
16
In each round you are randomly matched to a group of other participants equally
associated with your role. Within each round you therefore interact with different
participants unknown to you.
During each round, participants make decisions. Via their decisions, participants
affect both the own as well as the other participants’ payoffs.
On a market, groups of potential sellers and potential buyers of a good meet.
Each seller disposes of a unity of the same good, however, of a different quality
q. The quality of the good is expressed by a number between 0 and 10, randomly
drawn at the beginning of each round. 0 indicates low, 10 high quality. Each quality
between 0 and 10 occurs with the same probability. Each potential seller knows the
quality of the good in question, while potential buyers do not.
Buyers and sellers evaluate the good differently: buyers at its actual quality. Each
seller evaluates the good only at a fraction of its actual quality, that is, a ∗ q with
a < 1. This fraction a is known to both parties. For 4 successive rounds, a is fixed
at 0.3, followed by 4 rounds with a = 0.6, and 2 rounds with a = 0.8. (Do not
worry, in the beginning of each round the actual value of a is once again going to be
indicated.) The monetary value of the good is thus always higher for buyers than
for sellers.
You proceed as follows:
1. Unaware of the actual quality of the good, each buyer indicates an offer g
between 0 and 10.
2. Unaware of buyers’ offers, but aware of the actual quality q of her good, each
seller chooses a minimum price p. From this price limit on she is willing to sell the
good.
3. If at most one buyer offer exceeds one of the minimum prices stated, trade
comes about. The buyer with the highest offer buys from the seller with the highest
minimum price below that offer. Only one unit of the good is traded.
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Payoffs are derived as follows:
Buyers and sellers who are not participating in trade receive a payoff of 0 ECU.
The buyer participating in trade receives the difference between the actual quality of
the acquired good and the price payed for the acquisition. She thus receives: q − g
in ECU.
The seller participating in trade receives the offer g and delivers the good to the
buyer. Her payoff is therefore g − a ∗ q in ECU.
Group size varies throughout the experiment. The number of buyers and sellers
differs consequently. The following situations are possible:
1. Markets with 1 seller and 1 buyer.
2. Markets with 3 sellers and 1 buyer.
3. Markets with 3 sellers and 3 buyers.
4. Markets with 1 seller and 1 buyer.
We will of course inform you at the beginning of each round, which situation you
are going to encounter.
Example: The fraction at which sellers evaluate the good be 0.3. You encounter a
market with 2 sellers and 2 buyers. Buyers indicate their offers g. Unaware of these,
sellers determine their individual minimum prices p as depicted in the following
chart.
buyers’ bids
B1: g = 3.0
B2: g = 2.8
sellers’ minimum prices
S1: p = 2.5
S2: p = 2.0
quality of goods
S1: q = 5.0
S2: q = 4.2
Buyer B1 indicated the highest offer with g = 3.0. The highest minimum price
below that offer comes from seller S1 with p = 2.5. These two participants exchange
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now seller S1’s good with quality q = 5.0. Payoffs are calculated as follows: All
those participants having not been involved in trade, that is B2 and S2, receive a
payoff of 0 ECU.
Participants having been involved in trade, that is S1 and V1, obtain the following:
Buyer B1 receives the quality minus her offer, q − g = 5 − 3 = 2 in ECU. Sellers S1
gets the offer g = 3 but hands in the good evaluated at a ∗ q = 0.3 ∗ 5 = 1.5 ECU.
His payoff amounts therefore to: g − a ∗ q = 3 − 1.5 = 1.5 in ECU.
We ask for your patience until the experiment starts. Please stay calm. If you have
any questions, raise up your arm. Before the experiment starts, please answer the
following control questions.
B. Control Questions
You encounter a market with 3 buyers and 2 sellers. The fraction a at which sellers’
evaluate their good be 0.3. Below, you find the offers and minimum prices submitted
by buyers and sellers.
buyers’ bids
B1: g = 3.0
B2: g = 2.9
B3 : g = 2.5
sellers’ minimum prices
S1: p = 2.7
S2: p = 1.5
quality of goods
S1: q = 8.0
S2: q = 4.0
Question 1. Which seller participates in trade?
Question 2. Which buyer participates in trade?
Question 3. What are the respective buyer’s earnings?
Question 4. What are the respective seller’s earnings?
Question 5. What are the respective earnings of buyers and sellers who do not
participate in trade?
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