Post on 24-Jun-2020
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Competition between teams vs. within a team in team production
Enrique Fatás Tibor Neugebauer LINEEX and
University Valencia University Hannover
Abstract
We report on group incentive experiments designed to study the effects of within-team
competition and between-teams competition in a voluntary contributions framework. Both settings
help to mitigate the free-rider problem. Within-team competition induces convergence to Pareto-
efficiency and promotes sustainable cooperation better than competition between teams.
JEL Classifications: C72, C92, D44, H41
Keywords: public goods, group incentives, coordination games, team production
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A little competition goes a long, long way. (Nalbantian and Schotter, 1997, p. 332)
There is a growing interest in exploiting synergies and scale effects resulting from work in teams.
No consensus has emerged so far as to the proper way of eliciting high effort levels from individual
team members. The incentives of compensation based on team output are limited by the potential
for free-riding on the efforts of other team members, and individual piece-rates provide no
cooperative incentives.
Recent experimental research has shown that the introduction of competition between
teams (Nalbantian and Schotter 1997; van Dijk, Sonneman and van Winden 2001; Bornstein,
Gneezy & Nagel 2002) and within a team (Dickinson and Isaac 1998; Dickinson 2001) significantly
increases the effort levels exerted by experimental subjects.1 In these experiments, competition was
introduced into a team production environment by a rank order tournament structure. In the
present paper we focus on the question: what competition (within a team or between teams) elicits
greater effort levels?
We report on a laboratory study that uses the framework of voluntary contributions, which
is a standard tool in experimental economics for studying team production problems. Effort and
free-riding levels are framed as contributions to a group project and to an individual project,
respectively. Into this environment we carefully introduce a comparatively low powered
tournament structure, bearing in mind that high powered incentives might have detrimental effects
on cooperation (Lazear 1989; Harbring and Irlenbusch 2003a,b,c, 2004; Harbring, Irlenbusch,
Kräkel and Selten, 2004). In the experimental treatment on within-team competition the individual
whose contribution is lowest ranked does not receive any payoff from the group project. In the
treatment on between-teams competition the members of the group whose group project is lowest
ranked do not receive any payoff from it. The incentive structure relates to the one proposed by
the literature on exclusion from the commons (???) or by the literature on ostracism (Güth, Levati,
Sutter & van der Heijden, 2004) and can be interpreted as a formal sanction mechanism on the
1 The studies on between-teams competition involve both intra-team conflict and inter-team conflict. On one hand, individual team members have incentives to free-ride on the others; on the other hand, an individual team member might be decisive in determining the outcome of the competition and therefore has incentives to contribute. There is a bunch of related literature (cf. Bornstein 1992; Bornstein, Erev and Goren 1994; Cason and Mui forthcoming; Hausken and Ortmann 2004).
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minimum effort. No irrational use of the authority to sanction is possible as observed in the
literature on informal sanctions (Fehr and Gächter, 2000; Bowles, Carpenter & Gintis, 2001;
Noussair & Tucker, 2002; Masclet, Denant-Boemont & Noussair, 2004; Nikiforakis, 2004).
Moreover, incentives in our experiment are not as competitive as in other experimental
tournaments (Bull, Schotter & Weigelt, 1986; Schotter & Weigelt, 1992) as all subjects receive the
same payoff if they contribute the same.
The introduction of these incentives induces a change in the equilibrium structure of the
team production game. In the voluntary contribution mechanism, there exists a strictly dominant
strategy to contribute nothing to the team project. Due to the incentive structure, dominance is
dissolved and a continuum of Pareto-ranked symmetric equilibria arises. In the treatment on
between-teams competition, additional asymmetric equilibria exist and the minimum team project
between the other teams defines the threshold of team project provision. In fact, individuals face
strategic uncertainty not only with respect to the contributions of their peers, but also with respect
to the behavior of the competitors in the other groups. Harsanyi and Selten’s (1988) theory of
equilibrium selection in games is applicable to our treatments. In the within-team competition
treatment Pareto-dominance and risk-dominance point into the same direction, in the between-
teams competition treatment individuals might face a trade-off between risk-dominance and
Pareto-dominance considerations.
Overall, this paper contributes to different research areas: From voluntary contributions,
team production, rank order tournaments and group incentives mechanism design over threshold
public goods to coordination games. We would summarize the main contributions of our paper as
follows. First, we introduce a relatively low powered incentive mechanism, which appears to us
akin to natural selection. Second, we compare the performance of between-teams competition and
within-team competition in team production in the laboratory. Third and finally, our experiment
involves tournaments with four teams of four subjects, and thus stands in contrast to the other
team incentives studies in the literature which involve usually only two competing teams. The
multiple teams setting is an important contribution to the experimental literature since existing
firms do use more than two work centers or departments on one hierarchical level; for instance,
XEL Communications (Banker & Lee, 2005).
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The paper is organized as follows. The following section presents the experimental design
and discusses the theoretical properties of the treatments. Thereafter, the experimental results are
reported and the conclusions are discussed.
1. Experimental design and framework
The baseline treatment, hereafter VCM, is identical to the voluntary contribution mechanism used
in Croson, Fatas and Neugebauer (forthcoming). A group of four randomly assigned experimental
subjects interacts over a time horizon of ten rounds with another, followed by another ten rounds
after a surprise restart.2 In each round, a subject is endowed with an amount of 50 Eurocents and
decides privately on how much to contribute to a group project and simultaneously on the
remainder to be contributed to an individual project. The individual payoff is the sum of the
individual project and half of the group’s contributions to the group project. More formally, let ci
denote individual i’s contribution to the group project and c-i the total contribution of the other
three subjects respectively, i’s payoff function in each round is defined by equation (1).
}4,3,2,1{,2
)50(),( ∈+
+−= −− i
cccccVCM iiiiii (1)
Since each unit contributed to the individual project yields a return of one whereas each unit
contributed to the group project yields a return of one-half, i ‘s strictly dominant strategy entails a
contribution of the entire endowment to the individual project. On the other hand, Pareto-
efficiency is achieved if all subjects contribute everything to the group project. The dominance of
the free-rider solution extends to the finitely repeated game.
The second treatment involves within-team competition, hereafter WTC. Let c denote the
lowest ranked contribution within the team, i.e., c ≤ cj ∀j, cj = c for at least one j, and ∃j: c < cj and
j ∈{1, 2, 3, 4}, i’s payoff function is defined in equation (2).
2 The surprise restart technique has been widely employed in repeated public goods experiments (Andreoni 1988; Croson 1996).
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=−
=−otherwiseVCM
ccifcccWTC
i
ii
iii,
),50(),( (2)
In WTC, every subject receives the same payoff as in VCM as long as she contributes either more
than at least one other subject or if all subjects contribute the same. Therefore, all symmetric
strategy profiles constitute Nash equilibria which can be Pareto-ranked from joint contribution of
the entire endowment to collective free-riding. The Pareto-dominant equilibrium coincides for this
game with the risk-dominant equilibrium.
The third treatment induces between-teams competition, hereafter BTC, involving four
groups of four subjects. Let Ci be the group project of i’s group (i.e., the sum of contributions of i
and the other members of i’s group), and C denotes the minimum group project between the four
groups, i.e., C ≤ Ck ∀k, C = Ck for at least one k, and ∃k: C < Ck, k ∈{1, 2, 3, 4}. The payoff of
individual i is defined in equation (3).
=−
=−otherwiseVCM
CCifcCccBTC
i
ii
iii,
),50(),,( (3)
Between groups, all symmetric group contribution vectors constitute Nash equilibria. From the
within-group viewpoint, there exist two equilibria which eventually coincide. In the first equilibrium
all subjects free-ride; in the second one the group project must weakly exceed the minimum group
project of the other groups. For a fixed minimum group project of the others C, the payoff in BTC
would be equivalent to the payoff of a subject in a public goods game with one provision point
(Marks and Croson, 1998; Croson and Marks, 1999, 2000; Broseta, Fatas & Neugebauer, 2003). For
all intermediate provision points 0 < C < 200, there exist one symmetric and an infinite number of
asymmetric equilibria if we allow for a continuous strategy space. With respect to risk dominance
considerations, for any given provision point the free-riding equilibrium is always at knife’s edge
with the other symmetric and asymmetric equilibria. In other words, (within a team) no risk
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dominant equilibrium would exist for a fixed provision point. Since there is strategic uncertainty
about the level of the provision point, the free-riding equilibrium appears less risky. However,
Harsanyi and Selten’s (1988) theory on equilibrium selection favors the Pareto-dominant
equilibrium in both BTC and WTC. In fact, the question which equilibrium will be selected in BTC
and WCT is an empirical one and we address it in our experiment.
In all three treatments, subjects received information feedback recorded in a history table
for all past rounds. In this history table, individual contributions of all group members were
presented in increasing order; individual contributions thus could not be traced to the contributor.
Subjects were informed about their own earnings both in total and subdivided by individual project
and group project. In BTC, subjects received additional information feedback about all group
projects in increasing order; the group projects of the other three groups could not be traced.
The data the results of which are reported in the present paper were generated in eight
computerized3, experimental sessions conducted in November/December 2002 at the Laboratory
for Research in Experimental Economics LINEEX; the laboratory is jointly hosted by the
University Valencia and the University Castellón. The experiment uses between-subject variation. A
total of 112 economics undergraduates participated. Subjects were inexperienced to the extent that
they had not participated in similar experiments before. The experimental sessions of VCM and
WTC each involved 24 economics undergraduates, organized into groups of four from a room of
twelve. In BTC, 64 subjects were organized into groups of four from a room of sixteen. Average
earnings in the experiment were €13.064 (VCM), €16.56 (WTC) and €14.52 (BTC), respectively.
Experiments took less than an hour to run, hence, the earnings seemed more than sufficient to
motivate participants. Before the experiment, written instructions were read, and subjects went
through four exercises. The experiment did not start until subjects had answered all questions
correctly. Thus, we are confident that the game and the incentives were understood. After the
experiment subjects were debriefed with respect to their strategies and personal characteristics in an
ex-post experimental questionnaire. Instruction sheets and exercises are appended to the paper.
3 The software was programmed in z-Tree (Fischbacher, 1999). 4 US $1 ≈ €1.
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2. The experimental results
This section is organized as follows: the data on group contributions is grossly surveyed in Figure 1
and Table 1; after having discussed these, we will turn to a more in-depth analysis of the observed
behavioral dynamics presented in Tables 2 – 4 and Figures 2 – 4. To warrant a better comparability
between the displayed figures, we scale contributions relative to the endowment, i.e., from 0% to
100%. In the analysis we distinguish between the first ten rounds (hereafter original game) and the
last ten rounds (hereafter restart game); we will direct our attention also to the impact of the
surprise restart.
--- Insert Figure 1 around here ---
What is the general picture?
Initial contributions averaged around 35 Cents in BTC and WTC, respectively; the differences
between the treatments are insignificant. By round 10, the last round of the original game, average
contributions had increased to 41.8 Cents and 46.7 Cents in WTC and BTC, respectively. In the
restart game, average contributions increased in WTC by 5% from 46.6 in round 11 to 48.5 Cents
in round 20 and decreased in BTC by 13.9% from 44.0 to 37.9 Cents, respectively. Compared to
both BTC and WTC, average contributions in VCM are significantly smaller in every round of the
original and the restart game. We observe a significant treatment effect already in the first round.
Initial contributions in the original game and in the restart game averaged around 20 Cents in VCM
and declined to 9.1 Cents by round 10 of the original game and to 5 Cents in the restart game,
respectively.
Do we observe a restart effect?
Between the last round of the original game and the first round of the restart game most subjects
increased their contributions to the group project in VCM. On average, the contribution change
induced an increase of 118% from 9.1 Cent to 19.8 Cent. Significant restart effects in VCM have
been reported earlier in the literature (Andreoni 1988; Croson 1996). In WTC and BTC we observe
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no significant restart effects; the mode observations (66.7% and 42.2%, respectively) in these
treatments involve no changes of individual contributions between rounds 10 and 11. In round 10
of WTC, all groups but one contributed 100% to the group project. Three of the four subjects who
did not contribute 100% increased and the fourth subject decreased the contribution in round 11.
Four of the subjects who contributed 100% decreased their contribution between rounds 10 and
11, and the other 16 subjects continued with a contribution of 100% of their endowment. In BTC,
29.7% and 28.1% of subjects decreased and increased their contributions between rounds 10 and
11, respectively. Half of the 28.1% of subjects who increased the contributions in that treatment
were in groups whose project was the minimum between groups in the last round of the original
game. We can only speculate why we observe a restart effect in VCM and not in WTC and BTC.
Subjects comments in the debriefings suggest that in VCM, subjects might have felt regret about
the outcome in the original game and that they tried to use the restart to try to reach at a better
outcome. In WTC and BTC, subjects’ comments suggest that they were satisfied with the outcome
of the original game and they tried to continue like this in the restart game.
Do we observe equilibrium selection?
The Pareto-efficient equilibrium strategy that involved the contribution of the entire endowment
was chosen in 65% of all individual decisions in WTC; 91.7% of participants contributed at least
once their endowment to the team project. The payoff-dominant equilibrium thus was reached 56
times (47%) in five of six groups in WTC. We observe no other equilibrium, neither in WTC nor in
the other treatments. Subjects in WTC decided contribution of the endowment significantly more
frequent than those in BTC. In BTC and VCM, 35.3% and 2.7% of subjects’ decisions (79.7% and
20.8% of subjects) involved contribution of the entire endowment, respectively. Zero contributions
occurred in 14.9% of observations in VCM and were thus significantly more frequent than in the
other treatments, where about 2% of zero contributions were recorded.
------------------ insert Table 1 about here ------------
Do we observe a trend in contributions?
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Table 2 records the results of two random effects regressions which use individual contributions as
dependent variable. Model (1) suggests regression of contributions on rounds only; model (2) uses
two additional explicatory variables: one’s contribution of the previous round, and the difference of
one’s lagged contribution and the lagged average contribution of the others; the regressions are
stratified by the independent observation. In line with earlier experimental results on voluntary
contributions, the coefficients of regression (1) indicate that contributions decline significantly in
both the original game and the restart game of VCM. In WTC contributions increase throughout
both parts of the experiment, but the trend is only significant for the original game; the increase in
the restart game is basically caused by one group who had not reached the Pareto-dominant
equilibrium in the original game. The trends in the original game and the restart game are opposing
to each other in BTC; contributions in BTC are trend-free overall, but they increase significantly in
the original game and decline significantly in the restart game. We are going to direct our attention
to this issue further below.
How can we fit contributions?
The regression model (1) provides a poor fit to the data in WTC and in BTC as is indicated by the
correlation coefficients recorded in Table 2; the fit of the dynamics in VCM is better but not
satisfactory, either. Model (2) explains the contribution of a subject in round t, cit, with the same
subject’s contribution of the previous round ci,t-1 and its difference to the lagged average
contribution of the subject’s partners, c-i,t-1/3. The regression model (2) thus can be represented by
the following equation.
cit = b0 + b1t + b2 ci,t-1 +b3 (ci,t-1 – c-i,t-1/3) + uit
i∈{1,2,..,6} (i∈{1,2,..,4} in BTC); t ∈{1,2,…,20}.5 (4)
The results of model (2) recorded in Table 2 indicate a highly significantly positive
correlation between contributions and lagged own contributions in all treatments. The result
5 Model (2) involves two missing values of lagged contributions and lagged partners’ average contributions in rounds 1 and 11. The error term uit includes an individual random error term for each independent observation.
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suggests some kind of path-dependence of contributions which would imply that subjects
contribute the more today the more they have contributed yesterday. The difference of one’s
lagged contribution to the average of the partners’ lagged contributions is significantly negatively
correlated with one’s contribution in all but the original game in BTC; apparently, some subjects in
this treatment “cheap-ride” on the other team members, as will be shown in the figures 3 and 4
below. The negative correlation of one’s contribution relative to the average contribution of the
others indicates what the literature has termed conditional cooperation; conditional cooperation in
the context of voluntary contribution means that people are willing to cooperate the more the more
others contribute.6 The contributions are adapted between rounds towards the average; the more
one’s previous contribution exceeded [fell short of] the previous average the smaller [greater] was
one’s contribution in the following round.7 The dependence of contributions on the observations
from previous rounds suggests a closer look at the adaptive dynamics between rounds; this will be
done in what follows.
------------------ insert Table 2 about here ------------
What dynamics do we observe?
Table 3 (all treatments) and Table 4 (only BTC) record the regression outcomes for the individual
adjustments between rounds. Before we turn to the outcomes of these statistical analyses, we direct
our attention to the graphical representation of the observed dynamics in Figures 2 (WTC), 3 and 4
(BTC). Figure 2 displays the individual contributions in WTC; a lower bar marks the minimum
contribution within the group for each round of the original and the restart game. To remind the
reader, subjects whose contributions in a round were both smaller than the endowment8 and
6 C.f. Croson, 1998; Sonnemans, Schram and Offerman, 1999; Ockenfels, 1999; Keser and van Winden, 2000; Fischbacher, Gächter and Fehr, 2001; Brandts and Schram, 2001; Levati and Neugebauer, 2004; Croson, Fatas and Neugebauer, in press; Neugebauer, Perote and Schmidt, 2005; Fischbacher and Gächter, 2005. 7 As the analysis includes censored data involving an upper bound on contributions at 50 Cents and a lower bound at 0 Cents (e.g., WTC contains only #134/#432 uncensored observations), a random-effects tobit model might be preferable for the estimation. Besides an adjustment of the coefficients, the random-effects tobit model involves the same conclusions as model (2); we preferred a presentation of model (2) to the tobit model due to its easy interpretability. 8 We remind the reader that the Pareto-dominant equilibrium was the only observed equilibrium in the entire experiment.
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corresponding to the lower bars in Figure 2 did not receive any payoff from the group project in
that round. In four of the six groups in WTC we observe a quick convergence to the full
contribution equilibrium. All subjects in WTC, but the one with the maximum contribution, appear
to increase their contributions between rounds in the original game. Once the equilibrium is
reached it seems to be ‘locked-in’ as eventual individual deviations from it do not affect decreasing
contributions. An exception to this is group WTC#1 (see Figure 2) as group contributions do not
reach the equilibrium in any round; the plot shows that contributions continually increased from
round to round, and thus suggests that the equilibrium would have been in-reach within a couple of
more repetitions. Besides WTC#1, not much dynamics persist in the restart game to that treatment
due to the apparent lock-in effect. When we look at averages in WTC, we must have in mind that
much of the dynamics in the restart game of WTC is represented by the behavior of the outlier
group WTC#1.
---- insert Figure 2 about here -----
Figure 3 represents the group dynamics observed in BTC; each depicted point corresponds
to one group project in some session. The lower bars mark the minimum group project between
groups in each round; the corresponding groups did not receive a payoff from their group projects
in the particular round. The initial adjustments of group projects in BTC look similar to those of
the individual contributions in WTC, though more clumsy. Almost all groups start by increasing
their group project, but the dynamic of the convergence towards the Pareto-dominant equilibrium
appear to slow down from round to round. By the restart game, three of the four BTC sessions (i.
e., including all groups except BTC#9-#12) involve decreasing minimum group projects. A
decrease of the minimum group project induces lower competitive pressure between groups,
because the threshold level of group project provision decreases for the other groups. Lower
provision points affect again the incentives to ‘cheap-ride’ within the group; we designate people as
cheap-riders if they are motivated to exert less effort than the other group members (see
contributions of BTC#3d and BTC#4b in Figure 3). Cheap riding has been observed in
experiments on threshold public goods games (cf. Isaac et al 1988).
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---- insert Figure 3 about here -----
Figure 4 plots the individual contributions of selective groups in BTC. The bars illustrate
the minimum group projects of the others (i.e., the threshold of group project provision) and the
bold squares represent the group’s project; both variables are scaled relative to the group’s
endowment. Three graphs plot the contributions of the groups BTC#2-#4 who interacted in the
first session; group BTC#4 caused the decline of the minimum group project in the restart game.
Why? - The sudden decline of the group project was caused by an apparent chain reaction; by
round 14, BTC#4 had lost the competition between groups three times in a row. In the rounds 12-
14, the most cooperative contributor of that group, BTC#4a, had experienced in every round a loss
of his endowment. BTC#4a’s zero contribution submitted in round 15 exerted an almost chaotic
appearing effect on the other group members’ contributions; thereafter, subjects alternated their
contributions between 0 and 50. Successively, the individual contributions in BTC#2-#3 also
decreased presumably upon the observation of a lower threshold of group project provision.
The fourth graph plots the individual contributions of group BTC#5 whose members
experienced a collapse of their group project in the restart game. Where did this collapse come
from? – By the beginning of the restart game, group competition had grown to an extreme in that
session; almost every Cent was contributed to the group project in all groups. Group BTC#5 lost
the first three competitions between groups in the restart game, because only three subjects
contributed the entire endowment while always one subject (with alternating identity) contributed
one to four Cents less than the endowment. In round 14, two subjects in that group contributed
less than 100 Cents, while all other groups contributed basically the entire endowment. In round
15, the other two subjects, who had lost their endowment in the former four rounds, decreased
their contributions to zero and did not contribute any further Cent thereafter. These examples
suggest that cheap-riding by some group members might have produced a foregone payoff from
the group project inducing high costs to all but particularly to the more cooperative members of
the group. Such losses might cause frustration of cooperative subjects, which can affect a collapse
of contributions within the group. Our data seem to suggest that the success of between-teams
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competition depends crucially on a team’s unified keen interest to beat another team, and that even
small deviations can affect a tremendous decline of cooperation.
---- insert Figure 4 about here ----
In this paragraph, we discuss Tables 3 and 4 which record the statistical outcomes of
individual contribution changes between rounds. The individual contribution changes between
rounds are regressed on dummy variables of lagged order statistics. We remind the reader, that after
each period subjects learned whether their contribution was maximum, second greatest, third
greatest or minimum within their group. Equation (5) represents the estimated random effects
regression model.
∆cit = b1maximumi,t-1 + b2 secondi,t-1 +b3 thirdi,t-1 +b4 minimumi,t-1 + uit
i∈{1,2,..,6} (i∈{1,2,..,4} in BTC); t ∈{1, 2,…10,..,12,..,20}.9 (4)
In equation (4), ∆cit denotes subject i’s contribution change between rounds t and t-1, i.e.,
∆cit = cit - ci, t-1; maximumi,t-1, secondi,t-1, thirdi,t-1, minimumi,t-1 denote dummies taking the value one
if the subject’s contribution was the maximum, second greatest or minimum within the group in
the previous round.10 The results recorded in Table 3 confirm our above comments to Figures 2-4;
contribution changes are more upward directed in WTC than in the other two treatments.11
---- insert Table 3 about here -----
9 Model (2) involves two missing values of lagged contributions and lagged partners’ average contributions in rounds 1 and 11. The error term uit includes an individual random error term for each independent observation. 10 If all contribute the same strictly positive amount, we designate all contributions as maxima. In case of a tie at the maximum contribution or at the minimum contribution we designate contributions maxima or minima, respectively. If not all members contribute the same, we always designate at least one contribution as maximum and at least one contribution as a minimum. If second and third greatest contributions are the same and they are strictly greater [smaller] than the minimum [maximum], we designate these contributions second greatest. 11 The contribution changes in WTC are significantly different to both BTC and VCM in the restart game and to VCM also in the original game. We obtained these results when we ran the regressions on two treatments including a treatment dummy variable.
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The model proposed in equation (4) neglects the information feedback on between teams
competition which subjects received in BTC. The regression, the results of which are recorded in
Table 4, includes four additional explicatory variables. First, a dummy variable named ‘lagged
foregone group project dummy’ is added; it takes the value one for the subjects who did not reach
the threshold of group project provision in the previous round, and the value zero otherwise.
Second, the variable ‘lagged foregone group project run’ indicates the number of times running a
subject’s group has experienced without having reached the threshold of group project provision;
the variable takes the value zero for all subjects who received a payoff from the group project in
the previous round. Third, the variable ‘lagged distance threshold from below’ measures the
amount of money a group must have contributed more to reach the threshold of group project
provision in the previous round; for all subjects who received a payoff from the group project this
variable takes the value zero. Finally, we added the variable ‘lagged distance from above’ which
measures the amount a group could have contributed less in order to just reach the threshold of
group project provision in the previous round, i.e. this variable states how much more cheap-riding
the individual group members could have exerted without losing the payoff from the group project.
As indicated in Table 4 the latter variable is the only insignificant variable for individual
contribution changes. This evidence suggests that cheap-riding, although some subjects might
eventually practice it, does not characterize the average behavior in BTC. The coefficients further
indicate that subjects who lost the between teams competition in the previous round (i.e., the
members of a group that did not reach the threshold of group project provision) increase their
contribution significantly in the next round. However, the more often a group has lost the
between-teams competition in a row the less inclined will its group members be to contribute more
in the following round. In contrast to this, it is indicated that increases of contributions within the
losing group increase with the distance from the threshold of group project provision.
---- insert Table 4 about here -----
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3. Conclusions
In this paper we have reported on experiments that introduced a team incentive mechanism, which
establishes competition in a team production environment by sanctioning the minimum effort
within a team. The experiments used a voluntary contribution mechanism setting and a framing of
standard public goods experiments; shirking was framed as a contribution to an individual project
and effort was framed as a contribution to a team project. We compared the effect of competition
on the individual contribution to the team project in two experimental treatments; on one hand, we
induced competition between teams and, on the other, we introduced competition within a team.
Our results suggest that both settings are effective at eliciting great effort levels; relative to the
benchmark of the voluntary contribution mechanism initial cooperation is significantly enhanced in
both treatments and contributions do not decline in the repeated setting. In the within-team
competition treatment, voluntary contributions to the team project converged quickly to an amount
equal to the subjects’ endowment, and there they got ‘locked in’; contribution of the entire
endowment in that treatment is both Pareto-dominant and risk-dominant. In the between-teams
competition treatment we initially observed increasing contributions but the intrinsic motivation of
subjects to increase contributions further towards the Pareto-dominant equilibrium seemed to
cease after a few rounds. After a surprise restart contributions declined significantly in the between-
teams competition setting; this decline was tremendous in two groups who were repeatedly unlucky
in the team competition. We do not exclude that the emotions of some subjects might have caused
the contributions to ‘crash’. As the between-teams competition setting appears more vulnerable to
individual members’ actions,12 the results of the within-teams competition setting seem most
encouraging with respect to successful implementation of the Pareto-efficient cooperation level in
the voluntary contribution mechanism.
We cannot be sure to which degree our results can be obtained in different team
production environments. The literature on incentive structures in work environments is
particularly concerned about collusion and sabotage activities that might be unintentionally elicited
with an incentive instrument. Although we believe that our proposed incentive mechanism is ‘low
12 Nalbantian & Schotter (1997) suggested that incentives in production should be designed to warrant that the outcomes are “relatively riskless or not ‘vulnerable’ to slight mistakes by ones colleagues.”
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powered’ (Lazear, 1989), we can imagine that it also might be susceptible to undesired motivations.
We will study these issues further.
17
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21
Figure 1. Average contribution relative of endowment
0%
25%
50%
75%
100%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
roundBTC WTC VCM
Table 1. Average contribution & p-values of two-tailed tests VCM WTC BTC p-value
VCM vs
WTC|BTC
WTC vs
BTC
Round 1a) 20.2 34.9 35.6 .000 .977
Round 10 b) 9.1 46.7 41.8 <.010 .048
Original game b) 15.9 40.9 40.5 <.010 >>.100
Round 11 b) 19.8 46.2 44.0 <.010 .105
Round 20 b) 5.0 48.5 37.9 <.010 .019
Restart game b) 14.7 46.6 42.0 <.010 .039
#zero contribution % b) .142 .019 .026 <.048 >>.100
#full contribution % b) .027 .650 .353 <.018 .076
Restart effect
- round 10 vs round 11c)
.063
.750
1
- original vs restart game c) 1 .031 .250 a) Mann-Whitney test NVCM=NWTC=24, NBTC=64. b) two sample randomization test NVCM=NWCT=6, NBTC=4 c) one sample randomization test NVCM=NWCT=6, NBTC=4; H0: #increases = #decreases
22
Table 2. Random effects regression of contributions independent VCM WTC BTC
(lagged) variable model (1) (2) (1) (2) (1) (2)
Original R2 0.097 0.475 0.041 0.410 0.001 0.269
Game constant 23.886** 3.766 35.617** 7.721* 38.234** 18.286**
(3.636) (2.446) (3.730) (3.215) (1.314) (2.605)
Round t -1.445 -0.424 0.967** 0.124 0.411** -.113
(.229) (.278) (.252) (.287) (.142) (.150)
(own contribution) 0.853** 0.822** .581**
(.070) (.075) (.064)
(difference from other’s average) -0.518** -0.385** -0.084
(.078) (.078) (.059)
Restart R2 0.169 0.377 0.002 0.326 0.032 0.456
Game constant 41.780** 14.840** 44.838** 10.106** 53.345** 7.393*
(4.140) (5.770) (3.253) (4.535) (2.667) (3.542)
Round t -1.745 -0.785** 0.113 0.124 -0.733** -.238
(.228) (.297) (.143) (.183) (.139) (.149)
(own contribution) 0.752** 0.745** .900**
(.099) (.074) (.049)
(difference from other’s average) -0.408** -0.526** -0.348**
(.090) (.083) (.052) * p<.05 ** p<.01 significance level; standard errors in parenthesis
Table 3. Random effects regression of contribution changes between rounds independent VCM WTC BTC
(lagged)
variable
coefficient
(std. error)
coefficient
(std. error)
coefficient
(std. error)
Original R2 0.238 0.173 0.089
Game (maximum dummy) -8.984** -2.793* -2.448**
(1.368) (1.093) (.640)
(second dummy) -2.750 0.846 0.143
(1.506) (2.309) (1.158)
(third dummy) 1.419 4.321 2.732*
(1.950) (2.225) (1.122)
(minimum dummy) 5.686** 10.087** 4.715**
(1.298) (1.736) (.791)
Restart R2 0.279 0.166 0.074
Game (maximum dummy) -10.515** -1.090 -3.286**
(1.841) (.620) (.604)
(second dummy) -0.979 1.400 -0.709
(2.255) (2.608) (1.093)
(third dummy) 1.061 0.556 0.366
(1.841) (2.749) (1.153)
(minimum dummy) 5.072** 11.500** 2.958**
(1.273) (1.844) (.752) * p<.05 ** p<.01 significance level
23
Table 4. Random effects regression of contribution changes in BTC Independent Original Game Restart Game
(lagged)
variable
coefficient
(std. error)
coefficient
(std. error) R2 0.196 0.120
(maximum dummy) -2.282* -3.297**
(.927) (.791)
(second dummy) -0.252 -0.999
(1.294) (1.171)
(third dummy) 2.201 0.340
(1.262) (1.219)
(minimum dummy) 4.480** 3.047**
(.997) (.894)
(lost previous competition dummy) 3.631* 3.514**
(1.522) (1.169)
(length of run of lost competitions) -2.977 -1.865**
(.530) (.365)
(distance threshold from below) 0.178** 0.079**
(.053) (.028)
(distance threshold from above) -0.018 -0.002
(.021) (.011) * p<.05 ** p<.01 significance level;
24
Figure 2. Individual contributions in WTC
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
9 10 11 12 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
13 14 15 16 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
17 18 19 20 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
21 22 23 24 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
1 2 3 4 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
5 6 7 8 MIN
25
Figure 3. Group contributions in BTC
Figure 4. Individual contributions in BTC: Groups BTC#2-#5
Figure 4. Individual contributions in BTC – Groups BTC#2 - #5
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
BTC.4a BTC.4b BTC.4c BTC.4d threshold TP4
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
BTC.5a BTC.5b BTC.5c BTC.5d threshold TP5
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
BTC.2a BTC.2b BTC.2c BTC.2d threshold TP2
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
BTC.3a BTC.3b BTC.3c BTC.3d threshold TP3
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
1 2 3 4 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
5 6 7 8 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
9 10 11 12 MIN
0
25
50
75
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
period
13 14 15 16 MIN
26
Instructions
The aim of this experiment is to study how individuals take decisions in certain contexts. The instructions are simple and if you follow them carefully you will confidentially earn an amount of money at the end of the experiment, since nobody will know the amount of money received by the rest of participants. Should you have any questions please raise your hand and ask us. It is prohibited to comunicate with the other participants during the experiment. If you violate this rule, we shall have to excluded you from the experiment.
1 The experiment consists of 10 rounds. At the beginning of the experiment you will be divided into two independent sections of 8 participants each. You will never know the identity of the members of each section.
2 In each 8 members section, there will be 2 groups of 4 participants, Group 1 and Group 2.
3 At the beginning of each round, each participant receives a lump sum payment of 50 EUROCENT. You only have to decide how much of it to assign to a collective account. The remaining part will automatically be assigned to a private account.
3 The private account payoff is equal to your assignment to this account and it does not depend on the other members’ decisions.
4 The size of the collective account payoff is determined by using the total amount of money assigned to the collective account by the group members (that is, your assignment to the collective account plus the assignments to the collective account of the other three members of your group). This total assignment to the collective account will be multiplied by two and then splitted into four equal parts among the group members.
5 Therefore, your earnings in one round will be computed as follows: Private A. Payoff + Collective A. Payoff = Individual Earning
(50 Eurocent –your assignment to the collective account) +(4
2 sum of the assignments of
the group members to the collective account)
6 The composition of the groups in the first round is ramdomly determined at the beginning of the experiment. The group with the highest total assignment to the collective account in round 1 will be named Group 1, and the other group will, therefore, be named Group 2. If both groups assign the same amount, the numbers will be ramdomly determined.
7 The composition of the groups will change according to the following mechanism: a. The member with the lowest assignment to the collective account of the
Group 1 will be moved to the Group 2 in the following round. b. The member with the highest assignment to the collective account of the
Group 2 will be moved to the Group 1 in the following round. c. If two or more subjects have the lowest assignments in the Group 1 (the
highest assignments in the Group 2), the transfer will be ramdomly determined.
8 After each round, you will receive the following information in your computer screen a. The assignments of the members of your group to the collective account in
each round, ranked from the maximum to the minimum one. But, you will not know where each assignment comes from.
b. Your earnings in each round, divided into those coming from the collective account and those coming from the private account.
c. The group you are assigned to in each round, and if your group has been changed from one round to another.
9 At the end of the experiment the total amount of money you have earned during the ten rounds will be privately paid in cash.
27
Questionaire
Choose 4 numbers between 0 and 50 and write them down: N° 1 _________________ N° 2 _________________ N° 3 _________________ N° 4 _________________ Suppose these numbers are the assignments to the collective account of your group (all the amounts are given in EUROCENT). Taking into account these assignments to the collective account, you have to calculate
the earnings of each member, by following the next steps:
Step 1: Write the sum of the assignments to the collective account: ________ Step 2: As mentioned in the instructions, each member will receive an equal part of the double of the collective account. Write the result of doubling the collective amount and dividing into 4 parts:
Collective Account Payoff = (2 x Collective Account) / 4 : ________
Step 3: The assignment to the private account is equal to the difference between the 50 EUROCENT and the individual assignment to the collective account. In order to calculate it, firstly, copy the assignments to the collective account of each member in the first column of the table below. Secondly, substract the assignment to the collective account from the inicial endowment of 50 EUROCENT and write the result in the second column of the same table. Step 4: Copy the assignments to the private account (the private account payoff) in the third column. Step 5: Copy the collective account payoff (the same payoff for each group member,
calculated in the step 2) in the fourth column. The individual payoff is the sum of the
collective account payoff (4º column) and the private account payoff (3º column). Write
this sum for each member in the fifth column.
Assignment to the Collective Account
Assignment to the Private Account
Private Account Payoff
Collective Account Payoff
Individual Payoff
1
2
3
4