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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

We present a model where each of two players chooses between remuneration based on either private or team effort. Although at least one of the players has the equilibrium strategy to choose private remuneration, we frequently observe both players to choose team remuneration in a series of laboratory experiments. This allows for high cooperation payoffs but also provides individual free-riding incentives. Due to significant cooperation, we observe that, in team remuneration, participants make higher profits than in private remuneration. We also observe that, when participants are not given the option of private remuneration, they cooperate significantly less.

This paper presents a theoretical model of voluntary participation in a team effort and compares voluntary and enforced team effort in the experimental economics laboratory. To foster team effort, many firms use team incentive schemes that account for a small portion of employee income [

Team incentive schemes are typically based on profit sharing: employees are paid annual bonuses that vary with profitability defined at the overall corporate level or at the level of an individual division. Several empirical studies find evidence that profit sharing is associated with higher productivity (for an overview, see [

Putterman and Skillman [

Supporting Lin's argument, Orbell and Dawes [

Another aspect, implicit in Lin's argument, is that prior to 1958 participation was voluntary, while later on it was enforced. Enforcement could also have been one of the reasons for the failure of the labor-managed firm created in former Yugoslavia, which attracted of lot of attention in the 1960s and 1970s. In this paper, we examine the behavioral difference in voluntary

In our experiments, pairs of participants have to provide costly effort over 30 periods. In each period, each participant individually chooses an effort as an integer number between 0 and 100. Effort costs are represented by a quadratic function. In an environment where teaming is enforced, a participant's remuneration is based on the average of the participant's own effort and the effort of the participant he or she is paired with. In an environment where teaming is voluntary, each participant chooses between private or team remuneration before deciding on the effort in each period. While private remuneration is based on the participant's individual effort only, team remuneration is based on the average of the participant's own effort and the effort of his or her team member.

In the case of team remuneration, each of the two participants faces an individual incentive to take a free ride on the other's effort. The effort of each participant may be considered as a voluntary contribution to the public good

Nalbantian and Schotter [

In the experimental economics literature, we find a large number of studies on prisoner's dilemmas [

In the majority of experiments, including those by Nalbantian and Schotter, participants are told that they are members of a team or a group. They cannot choose whether to be in a group or select the group or individual group members. Exceptions are the studies by Ehrhart and Keser [

It is an important point of our investigation whether participants, when they have the choice of either private or team remuneration, will choose team remuneration at all. We have parameterized our experimental games such that in the subgame perfect equilibrium participants choose private remuneration although social efficiency would require them to choose team remuneration. Beyond the actual choice of team remuneration, we want to investigate the level of cooperative efforts and the dynamics in the decision making, which could not only affect effort but also remuneration choices.

To evaluate the robustness of our observations with respect to the choice of the remuneration mode and effort, we examine both a symmetric and an asymmetric parameterization of our game. Most public-goods experiments examine symmetric parameterizations. Asymmetry in the players' effort costs makes the definition and thus the realization of a cooperative goal more difficult [

We point out that our experiments are based on games that have a social optimum in the interior of the strategy space. This is different from the typical experiment on public-goods provision where the efficient solution lies at the upper end of the strategy space. It has been largely neglected in the literature that this design issue renders the observation of an aggregate outcome close to the efficient solution almost impossible. Thus, the specific non-linear design of our experiment is an important aspect. Despite the computational difficulties, it renders the game more realistic.

In Section 2, we present the model and its theoretical solutions. Section 3 develops behavioral predictions. Section 4 describes the experimental design. In Section 5, we present the experimental results. Section 6 concludes the article.

Our experiments with voluntary choice of the remuneration mode are based on the

Consider a game with two players

In the _{i}_{i}_{i}_{i}_{i}

In the _{i}

If at least one of the players chooses private remuneration, _{i}

Note that we assume

The effort game ends at the end of the second decision stage. Player _{i} is determined by his remuneration minus his individual cost of effort:

The subgame perfect equilibrium of the effort game can be found by backward induction. We start by considering the second decision stage in which each player chooses a profit-maximizing effort level. We have to distinguish whether private or team remuneration applies, which depends on the players' choices in the first stage.

In the case of

The resulting optimal effort

In the case

The solution is independent of the other player's effort and, thus, implies the following dominant strategy for each player

The resulting equilibrium profit for player

Consider, now, the first stage of the effort game taking the above solutions into account. If Π_{I} ** > Π_{I} *, then player _{i} ** < Π_{I} *, then player

In the case of team remuneration, the two players find themselves in a kind of prisoner's dilemma situation: their efforts represent voluntary contributions to the public good

We equally weigh both players' profits. By using different weights we would find other Pareto optimal solutions.

For each player

As _{i}_{i}_{i}′ > Π_{i}*. Thus, we have a Pareto-optimal solution for the effort game in which both players choose team remuneration and the effort _{i}

We develop a number of theoretical and behavioral predictions to be tested in the experiments. Predictions 1 and 2 are theoretical while predictions 3 to 6 are behavioral and apply only if Prediction 1 is rejected.

This follows directly from the subgame perfect equilibrium prediction derived above.

Under private remuneration, participants make an individual decision without strategic interactions. Their profit-maximizing effort can be directly read from a table in the instructions, which provides the respective cost and profit for each effort level (see Appendix).

Under team remuneration, participants are in a decision situation that is strategically equivalent to making a voluntary contribution to the provision of a public good. Over-provision relative to the dominant strategy prediction is a stylized fact [

One could argue that a participant who chooses team remuneration signals interest in cooperation. Theoretically, this kind of signaling relates to a forward induction argument [

Gächter and Thöni [

Many public-goods experiments provide evidence in favor of conditional cooperation, which implies a kind of tit-for-tat strategy [

We hypothesize that a participant chooses team remuneration if he expects to earn a higher payoff than under private remuneration. This depends on the effort level by the other participant. If team remuneration has been previously experienced, the higher the observed effort level, the more likely the team remuneration mode will be maintained. It could also be possible that noncooperative team effort by the other player may lead to a choice of private remuneration as a kind of opting out to enforce future cooperation. Hauk [

To test the above predictions we design several experimental treatments that are specified in Section 4.1. Section 4.2 describes the organization of the experiments.

In a 2 × 2 treatment design, we examine the four combinations resulting from two different parameterizations and two structural variants of the effort game. The two parameterizations are symmetric (

The two structural variants are voluntary teaming (

In the

In the

The last two columns of

In the experiments, participants played 30 repetitions, called

In the beginning of the second decision stage, in the

The computerized experiments were run at the experimental economics laboratory at CIRANO (Centre Interuniversitaire de Recherche en Analyse des Organisations) in Montréal. Participants were students from various disciplines at the University of Montreal, who had been recruited by posters into a subject pool. For each session, we invited randomly chosen participants out of this pool. None of the participants had previous experience in economic experiments.

For each of the four treatments we have eight independent observations, based on eight pairs of two participants each. This implies that we have a total of 64 participants. We conducted sessions with eight participants, each having two sessions per treatment. In the beginning of a session, the participants were randomly and anonymously assigned into four two-player groups, and, in the

Participants received written instructions (an English translation can be found in the Supplementary Files Repository, the French version is available upon request), which were also read aloud to them. Before the experiment could start, each participant had to provide correct answers to a number of questions regarding the understanding of the instructions. Participants were not allowed to communicate with each other during the entire experiment. They did not know with whom they interacted among the other participants. After the experiment, each participant was paid in private based on his or her individual earnings in the experiment plus a show-up fee. The individual earnings were converted into Canadian dollars with a factor announced in the experiment instructions. On average, participants earned 30 Canadian dollars, including the show-up fee, for a session that lasted about 90 minutes.

In this section we evaluate, based both on non-parametric data analysis and regressions, the six predictions made in Section 3 above. Each pair of participants forming a two-player group represents an independent observation in the non-parametric analysis. Unless otherwise mentioned, all non-parametric tests are two-sided. If no significance level is given, we require significance at the 10-percent level. We denote the Wilcoxon signed ranks test as Wilcoxon test and the Mann-Whitney u-test as u-test.

In the

In the

In the subgame perfect equilibrium of the

Conclusion 1:

In the

In the

Conclusion 2:

In the

Interestingly, the observed effort is not significantly different from the Pareto optimum of 50 (Wilcoxon test). In our experimental game, in contrast to most public-goods experiments, the optimum lies in the interior of the strategy space. This allows for the phenomenon that effort levels above the optimum have been chosen to the same extent as those below. If the Pareto optimum lies at the upper limit of the strategy space, participants can never err around it: deviations from the Pareto optimum are always below. This raises the concern whether it is due to this design issue that in most public-goods experiments contributions, although higher than in equilibrium, are still far below the Pareto optimum (see the related discussion on corner equilibria in [

Over all periods, the resulting average profit in team remuneration is 220.08 and significantly higher than in private remuneration, where it is 174.35 (Wilcoxon test, 10-percent significance). We observe no significant increase or decrease of profit from the first set of 15 periods to the last set of 15 periods, neither in team nor in private remuneration. The standard deviation, however, decreases from 165.34 to 81.31 in team remuneration (Wilcoxon test, 10-percent significance) and from 51.89 to 22.25 in private remuneration (Wilcoxon test, 5-percent significance).

The average profit in team remuneration is significantly below the optimal profit of 250 (Wilcoxon test, 1-percent significance). While the efforts are not significantly different from the Pareto optimum of 50, the rather large dispersion around the mean explains why the average profit is significantly below the optimum. Due to one outlier, the average profit is not significantly different from the equilibrium profit of 187.5.

In the

The resulting average profit of the low-cost players (127.26, standard deviation of 74.05) is not significantly different from the one of the high-cost players (137.1, standard deviation of 59.85) in team remuneration (Wilcoxon test). While the high-cost players' average profit is significantly above their equilibrium profit (Wilcoxon test, 5-percent significance), the low-cost players' average profit is not significantly different from their equilibrium profit (Wilcoxon test). At the same time, neither low-cost nor high-cost players' profits are significantly different from their respective joint profit-maximizing solution (Wilcoxon test): the low-cost players realize 99 percent and the high-cost players realize 86 percent of it. Note that the profit of the low-cost players tends to increase from the first set of 15 periods to the last set of 15 periods under team remuneration (Wilcoxon test, 5-percent significance). The profit of the high-cost players shows no tendency to increase or decrease under team remuneration (Wilcoxon test).

The high-cost players' average profit is significantly higher in team remuneration than in private remuneration, where it is 68.06 (Wilcoxon test, 2-percent significance). In six of the eight groups, the low-cost players' average profit is higher in team remuneration than in private remuneration. However, this difference is statistically not significant (Wilcoxon test). The low-cost players' profit under private remuneration is 112.89 on average.

Conclusion 3:

Comparing average effort in the

Enforced team effort is significantly above the equilibrium effort of 25 (Wilcoxon test, 5-percent significance) and significantly below the joint profit-maximizing effort of 50 (Wilcoxon test, 2-percent significance). Recall that, in contrast to this latter result, voluntary team effort is not significantly different from 50.

The average profit under enforced teaming is 191.73 (standard deviation of 120.56). It is significantly higher than the team equilibrium profit of 187.5 (Wilcoxon test, 5-percent significance), but lower than the joint profit-maximizing profit of 250 (Wilcoxon test, 2-percent significance). It is also lower than the average profit of 220.08 under voluntary teaming; but this difference is statistically not significant (u-test). The standard deviations of effort and profit, such as the absolute difference between the two players' effort levels are not significantly different between the two treatments.

Comparing average effort levels in the

The difference of the low-cost minus the high-cost players' effort is not significantly different from the respective value in the

The low-cost players' effort is significantly above their equilibrium effort and significantly below their joint profit-maximizing effort (Wilcoxon tests, 5-percent significance). Recalling that in voluntary teaming the low-cost players' effort is not significantly different from their joint profit-maximizing effort, we have thus got

The low-cost players' profit is 113.38 (standard deviation of 98.53) and not significantly different from the profit of 127.26 under voluntary teaming. The profit of 75.98 (standard deviation of 151.41) of the high-cost player in the

The low-cost players' profit is significantly different neither from their equilibrium profit nor from their joint profit-maximizing payoff, while the high-cost players' payoff is not significantly different from their equilibrium payoff but significantly below their joint profit-maximizing payoff (Wilcoxon test, 2-percent significance). In contrast to this, under voluntary teaming the high-cost players' payoff is not significantly different from their joint profit-maximizing payoff.

Conclusion 4:

Let us interpret participants' voluntary contributions to the public good team effort in terms of conditional cooperation, following Keser and van Winden [

In the

In the

We also use regression analysis on the change in effort to investigate conditional cooperation. We use least-squares regressions with clustering. This method takes into account that the decisions made by a participant over time may not be independent; it leads to the same coefficients as the ordinary least-squares estimates but the standard errors may be impacted by the clustering. In the regressions we investigate conditional cooperation based on the difference between the two players' effort levels in the last period they played under team remuneration. The obvious clustering variable here is simply the identification of the participant. We construct two dummy variables: the variable “Less” equals “1” when the player's effort has been more than three units smaller than the other player's effort, and it equals “0” otherwise. The variable “More” equals “1” when the player's effort has been more than three units larger than the other player's effort, and it equals “0” otherwise. The choice of more than three units of difference is arbitrary. However, analyses with other numbers around three have not changed the results. The conditional-cooperation argument suggests a positive sign of the coefficient for “Less” and a negative sign of the coefficient for “More”.

Explanatory variables also include a dummy variable “Last 5 periods”, which equals “1” if the participants played in the remuneration mode in the last five periods of the game and “0” otherwise. We expect a negative sign of this variable to account for an end-game effect [

The regression results are reported in

The results in the

These results complement the non-parametric tests of conditional cooperation, which concern the direction rather than the intensity of the reaction of the parametric estimations. Overall and particularly in the

Conclusion 5:

We analyze participants' choice of the remuneration mode with a linear probability model with clustering. Although the results are not qualitatively different with a random-effect probit model or a probit model with clustering, the linear probability model is retained for its robustness. The dependent variable “Voluntary teaming” equals “1” if the player chooses team remuneration and “0” otherwise. To account for an end-game effect, we consider the explanatory variable “Last 5 periods”, which is equal to “1” for the last five periods and “0” otherwise. We expect a negative coefficient for this variable.

We also construct the explanatory variables “Partner's effort below a strategic level” and “Partner's effort above a strategic level” based on the following hypothesis. A participant chooses team remuneration (opts in) if he expects to earn a higher payoff than under private remuneration. Assume that he chooses his dominant strategy in team remuneration and, thus, to achieve higher or equal payoff than in private remuneration, he needs a minimum effort from his team partner. In the symmetric cost situation, the partner's minimum required effort is 28. (The participant's dominant strategy in the case of team remuneration is 25. We solve the following equation to determine the partner's effort X that makes the participant indifferent to team and private remuneration: 203 = 10(25 + X)/2 − (25^{2}/10), where 203 is the (rounded) maximum profit in private remuneration.) In the asymmetric cost situation, the low-cost player requires from his partner a minimum effort of 20, while the high-cost player requires a minimum effort of 17. (The following equations are solved for X, respectively: (1) 123 = 8(20 + X)/2 − (20^{2}/10), where 123 is the low-cost player's (rounded) maximum profit in private remuneration and 20 his dominant strategy in team remuneration; (2) 98 = 8(16 + X)/2 − (16^{2}/8), where 98 is the high-cost player's maximum profit in private remuneration and 16 his dominant strategy in team remuneration.) The high-cost player's requirement is likely to be satisfied since the low-cost player's dominant strategy in team remuneration is 20 and thus above the required minimum.

We do not expect participants to be able to compute exactly those numbers and therefore create the following two binary variables. “Partner's effort above a strategic level” takes a value of “1” if the last time that team remuneration was realized the partner chose an effort larger or equal to six units above the required effort as determined above, or “0” otherwise. “Partner's effort below a strategic level” takes a value of “1” if the last time that team remuneration was realized the partner chose an effort smaller or equal to six units below the required effort as determined above, or “0” otherwise. The choice of six units around the required minimum is arbitrary. However, analyses with other numbers around six have not changed the results. Based on the above opt-in hypothesis, we expect a positive coefficient for “Partner's effort above a strategic level”. Inversely, accounting for opting out, we expect a negative coefficient for “Partner's effort below a strategic level”.

The results of the linear probability models with clustering are presented in

In the

For the high-cost player this coefficient is statistically significant but positive. This is not surprising since the high-cost players have, according to the game-theoretical solution, an interest in team remuneration that is independent of the other player's effort. This is also reflected in the relatively high and statistically significant constant for the high-cost players.

Conclusion 6:

Our experiments provide evidence in favor of Lin's [

In a symmetric cost situation, we observe that voluntary teaming implies significantly higher effort levels than enforced teaming. However, this does not come alongside a significantly higher efficiency, if we define efficiency as the realized percentage of the maximal team profit. The reason for this is that, when teaming is voluntary, participants choose effort levels above the efficient level significantly more often than when teaming is enforced. In both the voluntary and the enforced teaming environment, team effort is driven by conditional cooperation: if a player intends to change his team effort from one period to the next, he increases (decreases) it if his own effort was lower (higher) than the other player's effort.

In an asymmetric cost situation, we do not observe statistically significant differences in the effort levels of the voluntary and the enforced teaming environment. We do, however, observe higher efficiency, due to larger payoffs for the high-cost players, in the voluntary teaming environment. The principle of conditional cooperation defined above plays a minor role (only for the low-cost players when teaming is voluntary). It is not obvious for the two players in the asymmetric situation where to cooperate.

We observe that in contrast to the theoretical prediction people do build teams. They make higher efforts in teams than under private remuneration. The degree of team cooperation, however, depends on whether teaming is enforced or voluntary. We observe more cooperation in voluntary teaming than in enforced teaming. This effect is most obvious in the symmetric cost situation where it is relatively obvious to the team members, who cannot communicate other than through their decision making, where to cooperate.

The higher cooperation in voluntary teaming is in keeping with the results by Fehr and Gächter [

In our experiment there is room to “overdo” one's effort by going beyond the individual effort level that would be joint profit maximizing. We observe that participants often overdo effort in the voluntary symmetric treatment but not in the enforced symmetric treatment. Thus, simple error making cannot be the sole explanation for choosing effort levels above the joint profit-maximizing level. Another explanation could be that participants are signaling that they are interested in cooperation. A participant who expects the other to make a very low effort and who wants to send a very strong signal could have an interest in making an effort above the joint profit-maximizing level. In the bulk of experiments on voluntary contributions to finance a public good, this is excluded by design.

In the asymmetric experiments, where it is not so clear where cooperation should take place, the effort increase by voluntary teaming is not very significant. A more striking difference between voluntary and enforced teaming shows in the dispersion of the effort levels. The voluntary team efforts are much more contained around and between the subgame perfect equilibrium and the joint profit-maximizing solution than in the case of enforced teaming, where effort levels are spread out over the entire strategy space. Obviously, voluntary teaming helps participants to better coordinate than enforced teaming. Once they have agreed on team remuneration, participants have already made some investment by giving up on their higher private remuneration rate. Similar evidence has been found by Cachon and Camerer [

In our experiments, considering the game-theoretical solution, it is in particular the low-cost players who signal a commitment to attempt cooperation by their choice of team remuneration. Having made that choice, they are willing to make a somewhat higher effort than in enforced teaming. Neither in the symmetric nor in the asymmetric case do we observe a tendency that players opt out of team remuneration due to a too low effort by the other player.

Our results bear relevant implications for workforce management. Teams with a strong heterogeneity of abilities are likely to show a relatively large dispersion of efforts. Our experimental observations suggest that this dispersion can be reduced by allowing for voluntary teaming. In general, voluntary team effort will be higher than enforced team effort. The effect is likely to be the stronger the less heterogeneity there is.

Density of team effort in the

(

Parameter values and theoretical predictions for the second stage of the game.

Treatment | _{i} |
_{i} |
_{i} |
_{i} |
_{i} |
_{i} |
_{i} |
_{i}^{Min} |
_{i}^{Max} |
---|---|---|---|---|---|---|---|---|---|

1/10 | 45 | 25 | 50 | 202.5 | 187.5 | 250 | 125 | 312.5 | |

| |||||||||

1/10 | 35 | 20 | 40 | 122.5 | 104 | 128 | 64 | 168 | |

1/8 | 28 | 16 | 32 | 98 | 112 | 160 | 80 | 192 | |

_{i}_{i}_{i}_{i}_{i}_{i}_{i}^{Min}_{i}^{Max}_{i} individual cost factor.

Average effort and profit levels (standard deviation in parenthesis).

| |||||||
---|---|---|---|---|---|---|---|

Private | Team | Team | |||||

# Periods | Effort | Profit | Effort | Profit | Effort | Profit | |

16.5 | 45.27 |
174.35 |
50.10 |
220.08 |
35.68 |
191.73 | |

| |||||||

8.375 | 34.87 |
112.89 |
34.51 |
127.26 |
31.14 |
113.38 | |

8.375 | 27.22 |
68.06 |
30.14 |
137.10 |
29.32 |
75.98 |

Change in effort in the

(Least squares with clustering) | |||
---|---|---|---|

| |||

Low cost | High cost | ||

Constant | 0.1086 |
−0.2724 |
−0.7404 |

| |||

Last 5 Periods | −7.144 |
0.6909 |
−0.1753 |

Less | 5.142 |
2.453 |
3.582 |

| |||

More | −3.871 |
−1.996 |
−3.600 |

^{2} |
0.061 | 0.023 | 0.086 |

Nobs |

Significant at 5%;

Significant at 1%; ( ) Standard error.

Change in effort in the

(Least squares with clustering) | |||
---|---|---|---|

| |||

Low cost | High cost | ||

Constant | 0.6847 |
0.3266 |
2.558 |

| |||

Last 5 periods | −4.631 |
−0.5420 |
−1.516 |

| |||

Less | 4.970 |
2.487 |
−1.100 |

| |||

More | −8.180 |
−7.596 |
−5.806 |

^{2} |
0.091 | 0.098 | 0.025 |

Nobs |

Significant at 5%;

Significant at 1%; ( ) Standard error.

Choice of team remuneration in

(Linear probability model with clustering) | |||
---|---|---|---|

| |||

Low cost | High cost | ||

Constant | 0.5261 |
0.3809 |
0.5094 |

Last 5 periods | −0.1745 |
−0.0373) |
0.0575 |

Partner's effort below a strategic level | −0.0974 |
0.1454 |
0.4906 |

Partner's effort above a strategic level | 0.3220 |
0.5571 |
0.4558 |

^{2} |
0.157 | 0,339 | 0.338 |

Nobs |

Significant at 5%;

Significant at 1%; () Standard error.