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Replicating: Information Policy in Dynamic Tournaments with Sabotage
Name: Mick de Nijs Master Business Economics [Code: MSc BE] Student ID: 10253092 Specialization: Managerial Economics & Strategy Supervisor: Dhr. H. Oosterbeek Master Thesis: 15 ECTS
Abstract
Tournaments are an important and pervasive aspect of economic life. A tournament is a game in which players compete over a prize by making irreversible outlays. Sabotage is the main problem of rank-order tournaments. Previous research shows that agents that are leading in a tournament are sabotaged more strongly because they are the biggest threat. This gives rise to a dynamic concern, because an agent runs a risk of becoming the target of sabotage by being initially productive. Hence, initial effort should be weakened. This paper replicates the paper of Gürtler et al. (2013) who examine this concern. Moreover, this paper returns to their presented solution, concealing intermediate information. The results of the replication experiment of this paper strengthen the findings of Gürtler et al. (2013). Sabotage is targeted at those that are initially productive only when intermediate information is not concealed. Moreover, when intermediate information is concealed initial effort incentives are higher than when it is not concealed.
2 Statement of Originality
This document is written by Student [Mick de Nijs] who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Table of content
1. Introduction ... 4
2. Literature Review ... 7
3. Replication ... 9
3.1. Why replicate studies? ... 9
3.2. The Original Paper ... 10
3.3. Variations of conditions ... 11
4. Theoretical Analysis ... 13
4.1. Rules of the game ... 13
4.2. Sequential theoretical predictions ... 13
4.3. Simultaneous theoretical predictions ... 16
5. Methodology ... 17
5.1. Hypotheses ... 17
5.2. Experimental Design and Process ... 18
6. Results... 20 6.1. Summary statistics ... 20 6.2. Testing Hypotheses ... 24 7. Discussion ... 32 8. Appendix ... 34 8.1 Summary Statistics ... 34 8.2 Testing Hypotheses ... 35
8.3 Instructions, Answer Sheets and Survey Questions ... 36
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1. Introduction
According to Dixit (1987) tournaments, also called contests, are an important and pervasive aspect of economic life. A contest is a game in which players compete over a prize by making irreversible outlays. The player with the highest output wins the tournament. Election campaigns, rent-seeking games, R & D races, competition for monopolies and sports such as the World Soccer Cup are all contests. This irreversibility is an important aspect of contests because it implies that both winners and losers gage their bid. Players have to think over their choices because actions can’t be reversed. For example, one might choose to be inactive if effort is costly and if he perceives that his chances of winning are minimal due to his lower ability compared to his contestant. This inactivity might result in lower overall productivity if the high ability worker does not compensate by working sufficiently harder1. On the other hand, instead of being inactive the lower ability worker can choose to engage in sabotaging activities. By doing so he lowers the productivity of the (high) ability rival while not increasing productive effort himself neither. By lowering or destroying the rivals productivity a worker increases his chances of becoming on top in the tournament but decreases total productivity. Sabotage can thus be useful for an individual contestant but is overall harmful, and the main issue, for the party that launched the tournament.
This paper focusses on rank-order tournaments with a dynamic structure. According to Dechenaux et al. (2015) dynamic implies a contest in which some players can make decisions based on the actions of others. The literature about dynamic contests is relatively small compared to the literature of static tournaments. Bull et al. (1987) and Schotter and Weigelt (1992) show that the results of experimental tournaments are largely in line with the conclusions from theoretical papers, such as the seminal paper by Lazear and Rosen (1981).2 However, even
though they note that most real economic tournaments are repeated rather than one-shot tournaments and that information plays a crucial role in determining the equilibria to repeated games (Bull et al., 1987, p.7), these papers only explore static tournament settings and do not consider the impact of information on effort choice when contestants compete in a dynamic setting. Multiple dynamic contests exist; wars of attrition, sequential games, multi-stage finite horizon games and multi-stage elimination games (Dechenaux et al., 2015).
Specifically, this paper focusses on a sequential game where one can base his actions on previously observed actions of others. Rank-ordered tournaments are relative schemes that
1 His opponent dropped out, therefore it is unlikely that he will work sufficiently harder. 2 More about Lazear and Rosen (1981) in the Literature Review section.
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allow for productive effort that increases productivity and win chances. But they are also vulnerable for sabotage, that directly lower total productivity and welfare 3. Lazear (1999)
states: "There are incentives for uncooperative behaviour in any firm that awards pay, benefits, or other perquisites on the basis of some relative comparison between employees." According to the literature most of the time this sabotaging behaviour is focussed towards the most abled opponent, the biggest rival, or the person with the lead (Chen, 2003; Harbring et al., 2007; Munster, 2007). Gürtler et al. (2013) elaborated on this finding.
They note that initial effort in dynamic games should be weakened. By exerting no or weak effort initially one can hide his ability, or more general, not become a target for sabotaging activities by the others. Thus sabotage is not only directly negatively affecting productivity, but also indirectly by stimulating people to not be productive initially. Ishida (2012) states: “The possibility of sabotage (then) gives rise to a dynamic concern, similar to the Ratchet effect, because an agent runs the risk of becoming a target for sabotage by signalling his high ability and determination in early stages.”4 Note that in the paper of Gürtler and Münster (2010) this
Ratchet effect can’t occur because players’ abilities are common knowledge. In this paper they model a rank-order contest with two rounds where players are exogenously given a position. In each round players can choose to work and move themselves one rank up. Moreover, they can also sabotage an opponent to move this person one step back. The last round reflects that the most abled (favourites) are sabotaged more strongly than the least abled (underdogs). Their results show that as a consequence the possibility of sabotage decreases incentives in the first round. An important assumption is that players can observe the ranking after the first stage of the game. Otherwise, sabotage could not be focussed on the player that is leading.
According to Gürtler et al. (2013) this indirect problem of weakened initial effort can be solved by hiding intermediate information about the actions of rivals. If somebody wants to sabotage the rival with the biggest lead he can only do so if he knows who has the biggest lead. Consequently, if players know they can’t be targeted according to their initial actions then the indirect negative effect of sabotaging cannot be the reason to be initially non-productive anymore. This paper adds value by revisiting this negative effect of sabotage on initial effort. This effect is especially a problem because many (fortune 500) companies use these
3 Sabotage is sometimes referred to as destructive effort. However, sabotage does not always need to be
destructive. It can also be an activity that prevents possible gains, such as withholding valuable information from colleagues so that they can’t be efficiently productive.
4 Not only those with high ability will be targeted. If contestants don’t know the identity of their rivals they
cannot simply sabotage the most abled. They will then focus their sabotage based on information at hand, such as effort in previous periods like in Gürtler et al. (2013). In this paper identity is also not known.
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tournaments with in mind the incentivizing effect that Lazear and Rosen (1981) described, without being aware of this secondary indirect effect of sabotage (Boyle, 2001). Moreover, there is little research on this secondary effect except from the researchers that also came up with the theory, Gürtler et al. (2013). Therefore, this paper adds value as a robustness check as well. As Jonathon W. Moses, professor at NTNU, states: “Replication is the best way to check the robustness of a scientific paper, it allows us to be more certain about the findings on which our discipline builds.” This paper strives to replicate the study of Gürtler et al. “Information Policy in Tournaments with Sabotage” (2013) to support their findings on the described indirect negative effect of sabotage in dynamic rank-order tournaments. Therefore, this paper tests if initial effort is indeed lower if intermediate information is not concealed. This paper also intends to show that if intermediate information is revealed, sabotage is mostly focussed on those that work initially, and thus on those that are the biggest threat. Moreover, it also aims to show that this is not the case when information is concealed. An experiment is conducted to collect evidence for the above mentioned aims of this paper. Based on the above the research question is formulated as follows:
Can an information concealing policy in dynamic tournaments help reduce the indirect problem caused by sabotage activities?
Gürtler et al. (2013) mentions two reasons for using an experiment. One reason is that sabotage is hard to measure in field an experiment due to its nature. A second reason is because the game is a coordination game. These games have multiple equilibria in theory, an experiment gives insight to how players coordinate. Note that in the remainder of this paper the purpose of this paper is to replicate the original paper by aiming for the same hypotheses, but with some differences in the experimental design and analysis.
The experimental results confirm the hypotheses of this paper. First, sabotage is focussed towards the player that shows determination by working initially when intermediate information is revealed. Second, this does not hold when intermediate information is concealed. Third, effort levels are lower when intermediate information is revealed. This is proven by mean difference tests and probit regressions with margins. The first hypothesis is also proven by a proportion test statistic conducted with data from the strategy method.
This paper is structured as follows. The next section provides a literature review on the topic of sabotage and rank-order tournaments. The third section describes the importance of replication studies, revisits the original paper and highlights the variations of conditions from the original. The fourth section will show a theoretical analysis of a coordination game that
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shows the indirect effect of sabotage. Following this analysis, the hypotheses will be stated in section 5 together with the design and method of the experiment. Section 6 consists of the results of the experiment. In the last section a discussion will be provided. The appendix will display the some results of this paper and the paper of Gürtler et al. (2013) in tables that are structured to compare.
2. Literature review
The literature on rank-order tournaments with sabotage is fairly rich. Multiple advantages of a ranked scheme are highlighted and tested. First of all, Lazear and Rosen (1981) consider a rank-order payment scheme to sometimes be superior to individual-output based payment schemes because they, according to their theory, incentivize workers more. They show that for risk-neutral workers’ wages based upon rank induce the same efficient allocation of resources as an incentive reward scheme based on individual output. They note that it might be less costly to observe relative positions than to measure the level of each worker’s output directly. Additionally, they show theoretically that risk-averse workers actually prefer to be paid on the basis of rankings. In theory these relative payment schemes incentivize workers to be more productive. Second, another possible advantage of these relative performance schemes is that agents are compensated by ordinal rankings of performance rather than absolute measurements making it easier and cheaper (principal can set a fixed price) to incentivize them (Harbring and Irlenbusch, 2007). The possibility of setting a fixed price is especially important when the agents’ performances are not verifiable to a third party. Third, another reason why firms use relative incentive schemes is to overcome free-riding. Erev et al. (1993) conducted an experiment to test contest theory in the field. Working (picking fruits) is viewed as a voluntary contribution mechanism (VCM). The situation in which each team member is paid an equal share of total team output has a free riding equilibrium. In one of the treatments the teams of four players were split into pairs that competed against each other. This should provide incentives to work and avoid free-riding. The authors found that tournament incentives indeed lead to significantly higher output because it helps overcome the free-riding problem. A fourth important advantage of rank-order tournaments over alternative compensation schemes is that tournament incentives are not affected by common shocks (random noise that impacts all players equally), since common shocks do not change the relative ranking of players’ efforts (Wu and Roe, 2005; Wu et al., 2006; Agranov and Tergiman, 2013). As a result of filtering common shocks, rank-order tournaments reduce agents’ risk exposure, making them more
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attractive than other compensation schemes. The last three advantages are largely accepted. However, ironically, the seminal paper by Lazear and Rosen (1981) about the incentivizing effect of rank-order tournaments, is the most doubtful. Laboratory experiments find that the average effort levels in tournaments are well predicted by theory and are similar to efforts under the piece-rate scheme but with a greater variance in effort (Bull et al., 1987; Harbring and Irlenbush, 2003, 2005, 2008; Orrison et al., 2004). Gürtler et al. (2010) point out that in dynamic tournaments incentives to exert effort are reduced instead of increased. Ishida (2006) shows that with heterogeneous agents in a dynamic tournament, where costs of effort are sufficiently low that is always feasible to exert effort, any difference in productivity is due to differences in ability. If a high ability agent exerts effort in the first stages of the tournament, he becomes a threat and will be sabotaged more strongly. Hence incentives to exert effort should be weakened, which just as in Gürtler et al. (2010, 2013) contradicts the incentivizing effect of Lazear and Rosen (1981). Of course, this is due to the dynamic structure instead of the static structure in Lazear and Rosen (1981). However, Bull et al. (1987, p.7) state: “Most economic tournaments are repeated instead of static.” This should be taken into consideration when reviewing the literature. Some researchers do find significantly higher effort levels (Chen et al., 2011). Kräkel and Nieken (2015) find double the effort levels than predicted in a tournament with small productivity obligations. Findings regarding the incentive enhancing effect of tournaments are thus mixed. Note, however, that the parameters used in rank-order tournament experiments might also change the existence and, if so, the volume of the incentivizing effect. For example, larger wage spreads (difference between winning and losing or not participating) are often considered as being more incentivizing regarding effort levels (Harbring and Irlenbusch, 2009). Also, in the case of a symmetric contest it is shown that the expected individual effort decreases when the number of players increases (Konrad, 2009). This is confirmed by Sheremeta (2011). Furthermore, for rank-order tournaments the expected effort may increase, decrease or not change at all depending on the distribution of noise. Orrison et al. (2004) find that the average effort does not change in the number of players when the noise component is uniformly distributed. List et al. (2014) investigate the effect of the number of players under different distributions of noise. They design three treatments in which, depending on the noise distribution, a risk-neutral contestant’s effort should decrease, increase or remain the same. They find that, contrary to theoretical predictions, the average individual effort always decreases in the number of players. In contrast to the theory of Lazear and Rosen (1981), List et al. (2014) find that averse players exert less effort in rank-order tournaments than risk-neutral players. Overall, the evidence from lab experiments seems to favour a negative
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relationship between the number of players (group size) and individual effort levels. This statement should be taken with caution because lab experiments are sensitive to minor changes in, amongst others, the above discussed parameters. The relationship depends on the experimental design and theoretical structure.
Additionally, a field experiment by Leuven et al. (2011) also shows some evidence against the incentivizing effect of rank-order tournaments. Leuven et al. (2011) conducted a field experiment using students at the University of Amsterdam; Students could self-select into tournaments with one of three types of prizes: low (€1000), medium (€3000) and high (€5000). They showed that performance increases with the size of the prize, but that this is due to self-sorting and not due to increase of productiveness of an individual. The high ability students selected themselves into the high reward treatment. These students score better on exams than low ability students (whom selected themselves in the low treatment). Consequently, the differences in productivity might falsely lead to the conclusion that higher rewards generate higher productivity. However, it is arguable that this finding might be the result of a low number of prizes to participants’ ratio.
The mentioned papers all contribute to the literature of optimal tournament design. This paper is related to the literature of optimal tournament design considering the information policies used to reveal or conceal information about rankings in the rank-order tournament. It is a replication (with some variations, discussed in section 3.3) of the study by Gürtler et al. (2013): “Information Policy in Tournaments with Sabotage.”
3. Replication
3.1. Why replicate studies?
Because the question at hand is not extensively researched this study will somewhat replicate the study of Gürtler et al. (2013), rather than providing a new way to address the problem. Lamal (1991) says: “Replications are necessary as objectivity and self-correction distinguish the scientific method from other approaches to knowledge.” Building on, or providing external validity for, an existing scientific paper is important. As King (1995) states: “The most productive method of building on existing research is to replicate an existing finding; to follow the same path as a previous researcher and improve on methodology or data in some way. Replications provide information about the validity and reliability of the original study.”
10 3.2. The Original Paper
The key aspect of the paper of Gürtler et al. (2013) is that a principal should not reveal intermediate information to mitigate the indirect problems caused by sabotage. First, they test whether sabotage is focussed on the person that is leading if intermediate information is not concealed. Then if this is not true when intermediate information is concealed. On top of that they test whether the productivity is higher if intermediate information is concealed compared to when it is not concealed. They also test for cost effects. Ederer and Fehr (2006) show that even if information provided by the principal is cheap, it still affects the decision making of the agents. Gürtler et al. (2013) designed a laboratory experiment where three players competed over a prize in a two stage rank-order tournament. They argued that initial efforts should be weakened if information about the ranks after stage 1 is common knowledge because in stage 2 players can base their sabotage activities on this information. To test this, they used four treatments; simultaneous and sequential with and without costs of effort. For each treatment they ran two sessions. Each session consisted of 30 participants and nine rounds. The experiment took place at the Cologne Laboratory of Economic Research at the University of Cologne in August and December 2008. In total 240 students participated. In each treatment, the players first had to choose their productive effort level simultaneously. In the sequential treatments, all participants were informed about the choice of their opponents after all players had chosen their effort. No intermediate information was revealed in the simultaneous treatment. It was only possible to sabotage one of the two rivals, making it a coordination game with no unique equilibrium. Effort and sabotage choices were binary, namely 0 or 1. Final output consisted of own effort choice minus sabotage received. The player with the highest output at the end the round won prize W, others got prize L where W = 10*L. Costs of sabotage and effort were deducted from the prize at the end of the experiment. Note that both the theoretical analysis in section four, as well as the experimental design apart from the variations described in the next sub section, largely reflect the analysis of Gürtler et al. (2013). They find that subjects are sabotaged more after they work if intermediate information is not concealed. That this is not true when intermediate information is concealed and that initial productivity (effort) is higher when intermediate information is concealed compared to when it is revealed. They also find cost effects, that is, with costs the effort output is significantly lower. But the weakening effect of sabotage on effort holds with and without effort and sabotage costs. The
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results of their study can be found in the corresponding tables together with the results from this paper.
3.3. Variations of conditions
This paper differs from the original in some ways. Firstly, the experiment in this research does not allow for learning. Only one round is used instead of nine rounds as in Gürtler et al. (2013). If we allow for learning, it is reasonably arguable that after the first round, participants realize that they lost because they were focussed by sabotage activities of the others. Participants will in the further rounds base their choices on results from previous rounds instead of on choices of others in one round but different stages. When we allow for learning it becomes obvious that the results will reflect the theory. In contrast to Gürtler et al (2013) in this paper the immediate responses are measured and analysed. In the real world you might not always have the chance to adapt or change your strategy. Simply imagine a workers’ first chance of promotion. Consequently, finding the same results as in the paper that is replicated, but with only one round in the experiment, strengthens the original paper even more.
Secondly, the effect of costs of effort on effort levels is significant, therefore this paper considers only two treatments: simultaneous with costs of effort and sequential with costs of effort. Furthermore, treatments without costs of effort and sabotages resulted in less variation because it almost never happened that somebody did not exert effort or sabotage in the simultaneous treatment.
Thirdly, the design of the experiment in the original paper limits data collection. Because the experimenter places three players in a group and let this group play the game they can only measure data from the scenario that is played. Imagine that the scenario where a participant that has chosen to exert effort in the first stage and both his rivals did as well, would not take place (often). It would still be interesting to know whether in this scenario players would sabotage (as predicted). The strategy method is exploited in stage 2 of the sequential treatment to overcome the discussed limitation5. One thing to consider is that a strategy method, in contrast to a direct-response method, makes certain immoral choices, such as sabotage, easier to make. Therefore, the participants are told that the scenario that reflects the real play does affect their score, they do not know the real play at the time they make their decision. Furthermore, in this experiment participants do not know the identity of their rivals. Knowing
5 The strategy method considers all possible scenario’s. The participants are asked what they will do in different
situations. They are told that they get paid according to the real situation. They do not know which scenario reflects the real situation. This stimulates them to think carefully about every scenario.
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the identity of your opponents could influence your choice. Not knowing who you play against makes it less hard to make certain choices.
A fourth variation can be found in the design of the experiment. Gürtler et al. (2013) use a between-subject design. They ran two sessions for each of their (four) treatments. A subject was allowed in only one session and participating in one treatment, thus playing the game once. In this paper a repeated-measure or within-subject design is used. In this experiment it is arguable that a within-subject design has more explanatory power, that is, it isolates the effect of the treatment better. The choice of effort of a person can for example depend on his risk attitude, experience and intelligence (insight). By applying the within-subject design these variables remain constant during the experiment. Gürtler et al. (2013) did not use a within-subject design and had to control for risk attitude. Furthermore, it eliminates problems arising from group differences and it reduces variance. In Gürtler et al. (2013) all participants were students, therefore it is arguable that the group differences are not significant. In this study the participant pool consisted of a more diverse group, therefore the within-subject design fitted the experiment better than the between-subject design.
Furthermore, the original experiment’s subjects consisted of students only. This study used students (57%), starters (24%) and managers (19%) in the experiment. Students are generally used for experiments because they are in need of money, are relatively smart and come in numbers. However, considering the problem at hand, students generally have not experienced rank-order tournaments such as promotions yet. Their choices are thus more based on theory than experience, which makes it more obvious that the results of the experiment are in line with the theory provided. Most of the starters work for almost two years now and are going to face their first promotion. The managers provide data from the point of view of the principal (the person that launches tournaments). Thus, if results from this replication study are in line with the original taken into account this difference in the participants’ pool, this provides more evidence for the theory.
Lastly, Gürtler et al. (2013) controls for certain characteristics of the composition of the group. They control for the gender composition and study course composition. This paper in addition controls for the composition of the occupation levels of the opponents in the group.
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4. Theoretical Analysis
4.1. Rules of the game
Note that the variations of this paper compared to the original paper of Gürtler et al. (2013) does not contain variations in the rules of the game. This section is therefore similar to Gürtler et al. (2013) and here for convenience. Consider a simple dynamic game where three players compete over a prize in a ranked-order tournament that allows for sabotaging behaviour. The player with the highest output at the end of the game wins. The effort level of player i = 1, 2, 3 is 𝑒𝑖 ∈ {0, 1]. Effort increases their chance of winning as it increases their own output, whereas
player i’s sabotage level 𝑑𝑖𝑗 ∈ {0, 1] and 𝑑𝑖𝑘 ∈ {0, 1] lower (destruct) the output of rival j or k
respectively. Sabotaging both rivals is assumed to be prohibitively costly and time consuming, in other words only one rival can be sabotaged. Costs of effort and sabotage are larger than zero but relatively small to the gains of winning so that actions are not discouraged solely by their costs. We assume that 𝑀𝑎𝑥 { 𝑐𝑒, 𝑐𝑑} <
1
12(𝑊 − 𝐿). The output of player i = 1, 2, 3 equals his
productive effort minus the sum of received sabotage: 𝑄𝑖 = 𝑒𝑖 – 𝑑𝑗𝑖 – 𝑑𝑘𝑖. The player with the highest output wins prize W, the others get L (L < W). The gains of winning are thus W – L. To analyse the described problem of sabotage two versions of the game are considered; sequential and simultaneous. They differ in the timing of choices. In the sequential version players choose an initial effort level in stage 1. Then they observe the choices made by their rivals and choose a level of sabotage with this information in mind. In the simultaneous version players choose their level of effort and sabotage at the same time without having any information about the rivals. The simultaneous version thus corresponds to a setting where there is no intermediate information on rivals available, whereas the sequential version corresponds to a setting where players can base their sabotaging activities on the intermediate information about ones rivals initial actions.
4.2. Sequential theoretical predictions
The most interesting version regarding this study is the sequential version because in this version it is expected to see low/no initial productive effort due to the indirect sabotage issue discussed. Following backward induction rules the first step is to analyse stage two. Distinguish between two types of subgames; symmetric and asymmetric.
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𝑒3 = 1) or all players have chosen to not work (𝑒1 = 𝑒2 = 𝑒3 = 0). There is a univocal equilibrium
where all players sabotage each other clockwise or counter clockwise. Theoretically this means that each player sabotages each rival with probability ½. If a player deviates by not sabotaging this results in a loss. There will then be one rival that receives no sabotage and had the same initial effort as the others. This rival will have the highest output at the end of stage two, remember output equals effort minus received sabotage.
Second, consider an asymmetric game, the subgame 𝑒1 = 𝑒2 = 1, 𝑒3 = 0. This game
has an equilibrium where both productive players (1 and 2) sabotage each other and the unproductive player (3) mixes between both with equal probability. Note that there is also an equilibrium where one of the productive players gets fully sabotaged by the unproductive player (3 sabotages 1 or 2), this fully sabotaged player (1 or 2) sabotages the other productive player (1 or 2) and this other productive player mixes his sabotaging activities. There will be a different winner in each of these equilibria, but note that in every scenario an initially productive player always receives a sabotage level of at least 1. By starting of productive a player becomes the target for sabotage. Note that for a productive player (1 and 2) in this scenario sabotaging the unproductive player (3) is weakly dominated by sabotaging the other productive player (1 or 2), such that the difference between the productive and unproductive ‘rival’ disappears. It is best to sabotage your direct rival (the one that has exerted same amount of effort initially). For simplicity we assume that no player uses a weakly dominated strategy and that equal choices are treated equally (sabotage both rivals equally if they have made the same choice of effort).
The predictions for stage 2, taking the above mentioned assumptions into account, are as follows:
1) If symmetric 𝑒1 = 𝑒2 = 𝑒3, then each player sabotages each rival with probability 1/2. Expected payoffs are: 𝜋1 = 𝜋2 = 𝜋3 =1
3[𝑊 − 𝐿] + 𝐿 – 𝑐𝑑 – 𝑒 ∗ 𝑐𝑒
2) If asymmetric 𝑒1 = 1, 𝑒2 = 𝑒3 = 0, then player 2 and 3 sabotage player 1 and player 1
does not sabotage (sabotaging is costly and it doesn’t increase his win chance because his output equal 𝑄1= −1 and if he does sabotage one rival at least one of the other players will have 𝑄𝑖 = 0 and win).
Expected payoffs are: a. 𝜋1 = 𝐿 – 𝑐𝑒 b. 𝜋2 = 𝜋3 =
1
2 [ 𝑊 − 𝐿] + 𝐿 – 𝑐𝑑
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3) If asymmetric 𝑒1 = 𝑒2 = 1, 𝑒3 = 0, then player 1 and 2 sabotage each other, and 3
sabotages each rival with probability ½. Expected payoffs are:
a. 𝜋1 = 𝜋2 =1
4[𝑊 − 𝐿] + 𝐿 – 𝑐𝑑− 𝑐𝑒
b. 𝜋3 = 1
2 [ 𝑊 − 𝐿] + 𝐿 – 𝑐𝑑
Note: By sabotaging any rival, player 3’s output will be equal to the output of the rival that this player did not sabotage. Sabotaging with probability ½ means he is indifferent between sabotaging rival 1 or 2, but he cannot sabotage them both with ½ point by assumption (Section 4.1)
Remark: By working initially you are more likely to lose.
Following prediction 2) and 3) it can be seen that by putting in initial effort in the sequential game you are more likely to lose.
Now take a look at stage 1 of the game. Working is dominated by not working taking into account the mentioned assumptions. Each player predicts that if he works he will get targeted by one or both rivals and will consequently lose the game. The predictions for stage 1 are as follows:
1) 𝑒𝑖= 0 for i = 1, 2, 3 dominates 𝑒𝑖= 1 for i = 1, 2, 3. Deviating from not working to working makes you a target and results in a certain loss, whereas not working results in: a. If no player works (𝑒1 = 𝑒2= 𝑒3= 0) and there is equal or no sabotaging, then all
players have 1/3th chance of winning. Expected payoff: 1
3 [𝑊 − 𝐿] + 𝐿 − 𝑑 ∗
𝑐𝑑
b. If player 1 doesn’t work, he has 1/2 chance of winning if the other players both worked or one of the other players worked (see predictions 2 and 3 for stage 2). Expected payoff: 1
2 [𝑊 − 𝐿] + 𝐿 − 𝑐𝑑.
Remark: In both cases the expected payoff is higher than losing for sure. Losing for
sure gives the expected payoff: 𝐿 − 𝑒 ∗ 𝑐𝑒 − 𝑑 ∗ 𝑐𝑑. Not working is thus more
beneficial than working in the first stage. In short, the predictions for the sequential game are:
1) Working in stage 1 is dominated by not working.
2) Not sabotaging is dominated by sabotaging the working rival.
16 4.3. Simultaneous theoretical predictions
First, an analyses of the predictions of effort and sabotage regarding the simultaneous version will be given. In a symmetric game where 𝑒1 = 𝑒2 = 𝑒3 = 1 and each player sabotages in a circle (sabotages with probability = ½) there is an equilibrium. There is no incentive to deviate by not sabotaging because the benefits are larger when sabotaging (if relatively low sabotage costs are assumed). Also, choosing not to work results in a loss (if relatively low effort costs are assumed). This implies that productive effort should be higher in the simultaneous version, compared to the sequential version.
Working dominates not working: consider 𝑒1= 𝑒2= 𝑒3= 0 and sabotaging in a circle.
Expected payoffs for all will be equal: 1
3[𝑊 − 𝐿] + 𝐿 − 𝑐𝑑. For player i (for example player 1)
it is beneficial to deviate to 𝑒1= 1 because then the expected payoff will be: 1
2 [𝑊 − 𝐿] + 𝐿 −
𝑐𝑑− 𝑐𝑒. He wins when all players sabotage in a circle or when he is not sabotaged. Working comes at a cost. The benefits of deviating from not working to working have to be higher than the costs of working and the expected payoff that corresponds to not working. Costs of effort should thus be sufficiency low, more specifically, if 𝑐𝑒 <1
6[𝑊 − 𝐿] then working dominates
not working. Sabotaging dominates not sabotaging: consider 𝑒1= 𝑒2= 𝑒3 = 1, 𝑑1=0 and 𝑑2=
𝑑3= ?, this gives the following matrix: 𝑑3𝑖 corresponds to player 3 his sabotage decisions, 𝑑2𝑖
to player 2’s decisions. The matrix displays the chances that player 1 wins if he does not sabotage and all players work.
P1 𝒅𝟑𝟏=𝒅𝟑𝟐=0 𝒅𝟑𝟏=1 𝒅𝟑𝟐=1
𝒅𝟐𝟏=𝒅𝟐𝟑=0 1/3 0 1/2
𝒅𝟐𝟏=1 0 0 0
𝒅𝟐𝟑=1 1/2 0 1
Assume q = probability that player i= 2, 3 does not sabotage and sabotages each rival with probability 1
2(1 − 𝑞). The probability that player 1 wins if all players work and he does not
sabotage equals: 𝑃1 =1 3𝑞 2 + 2 (1 2𝑞 ∗ ( 1 2(1 − 𝑞))) + 1 ∗ ( 1 2(1 − 𝑞)) 2.
17
Now if player 1 does sabotage for any rival (for example player 2) the matrix is:
P2 𝒅𝟑𝟏=𝒅𝟑𝟐=0 𝒅𝟑𝟏=1 𝒅𝟑𝟐=1
𝒅𝟐𝟏=𝒅𝟐𝟑=0 1/2 0 1/2
𝒅𝟐𝟏=1 0 0 0
𝒅𝟐𝟑=1 1 1/3 1
The probability that player 1 wins if all players work and he does sabotage equals: 𝑃2 =1 2𝑞 2 + 1 ∗ 𝑞 ∗1 2(1 − 𝑞) + 1 2𝑞 ∗ 1 2(1 − 𝑞) + 1 3( 1 2 (1 − 𝑞) 2) + 1 ∗ ( 1 2(1 − 𝑞)) 2. If 𝑃2 −
𝑃1 > 0 then sabotaging is efficient. Solving the equation gives: 1
12(𝑞 + 1) > 0, which holds.
The benefits of sabotaging are 1
12(𝑞 + 1), thus if costs of sabotage are smaller than 1
12(𝑞 + 1)
sabotaging dominates not sabotaging. Costs of sabotage are sufficiently small in this paper: 𝑐𝑑 < 1 12(𝑊 − 𝐿) < 1 12((𝑞 + 1)(𝑊 − 𝐿)).
5. Methodology
5.1. HypothesesThe main issue displayed in this paper is that contestants might withhold themselves from exerting initial effort because they are afraid of being sabotaged due to their initial productive work. The first hypothesis tests if this fear is not misplaced. Following the above the following hypotheses are constructed:
H1: In the sequential treatment a player receives more sabotage if he exerts effort.
In the simultaneous treatment players cannot base their actions on information about the initial productive effort. It should therefore hold that effort choices and sabotage received are not depending on each other in the simultaneous treatment. The second hypothesis is as follows:
H2: In the simultaneous treatment the amount of received sabotage and initial effort exerted are independent of each other.
Taking into consideration the fear of being focussed for sabotaging activities in the sequential treatment, the third hypothesis tests if initial effort thus should be higher when intermediate information is concealed.
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H3: In the simultaneous treatment players will initially choose to be more productive compared to the sequential treatment.
5.2. Experimental Design and Process
The purpose of this experiment is to test whether initial efforts are lower if intermediate information is not concealed. Consequently, it gives insight to whether concealing information helps to mitigate the discussed problem. Results examine the external validity of the findings in Gürtler et al. (2013). The rank-order tournament of section three is implemented in a laboratory setting. In this experiment two treatments were used: simultaneous and sequential, as discussed in section 4. Two sessions are conducted, with 21 subjects per session. In a session the subjects played both treatments. In total 42 subjects participated in the experiment. Subjects did not know each other’s identity throughout the whole experiment.
The within-subject design was utilized: each participant was allowed to play one session only, but played both treatments in this session. A within-subjects design is a type of experimental design in which all participants are exposed to every treatment or condition. However, carryover effects exist when using this with-subject method. If a subject first plays the simultaneous version, this subject possibly gains knowledge about how to play the sequential method. To reduce this carryover effect a counter balance design was exploited, that is, two sessions are conducted, one starts with the simultaneous treatment whilst the other starts with the sequential treatment6. There was only one round per treatment because the main interest is the immediate response instead of the response after learning. The simultaneous treatment consisted of one stage, the sequential treatment consisted of two stages. In the second stage participants could base their sabotage decisions on the effort choices made by their rivals in the first stage. In the second stage the strategy method was applied to collect more data regarding different possible scenarios. By making a decision in stage 1 the players influence the choices made in stage 2. In other words, they set the scenario. Only data from this particular scenario can be collected when using a direct-response method. Hence, the strategy method was exploited, that is, every player was asked to make a sabotage choice for all possible scenario’s. Because of the strategy method applied in the sequential treatment the results of stage 1 never actually had to be analysed during the experiment and never had to be passed through to begin with stage 2. This reduced the duration of the experiment, which was important because rewards
6 Appendix 8.3 displays both the Dutch and English instructions for each session. One session starts with the
19 were not high.
The experiment took place in the meeting room of sports club SKV Amsterdam. Overall 42 subjects participated in the experiment, 21 per session. Most participants (57%) were students and starters (24%). Furthermore, eight senior managers (19%) also joined the experiment. The experiment was conducted on paper; no software was used during the experiment. Participants were randomly selected into groups and tagged. The experimenter handed out instructions and read them out loud7. Language was kept neutral; the word sabotage was never mentioned. Questions were asked and answered afterwards. No communication was allowed during the experiment.
Both treatments started off the same; players had to choose their productive effort level coincidental. The cost of effort was 15 points. In the sequential treatment players had to decide about their levels of sabotage corresponding to different scenario’s. They received an answer sheet with a total of four stage 1 scenario’s. This sheet remembered them of their choice in the first round. In both treatments only one of the rivals could be sabotaged, not both. It was also possible to not sabotage at all. The players had to mark their decisions on the answer sheets.8 The sabotaging options in both treatments were the same, the only difference was the timing of the choice and availability of information. The first option was to sabotage none of the rivals, the second option was to sabotage player X and the third option to sabotage player Y. The cost of sabotage was 10 points. After all participants chose their levels of sabotage. The outputs of the players in a randomly chosen group were calculated. In each session and each treatment a random group got chosen for pay-out. If randomly chosen for pay-out of one treatment it was not possible to be chosen for the pay-out of the other treatment in the same session. As can be seen in Table 1 (Appendix), for session 1 group B and group D got picked for pay-out according to the payoffs in the simultaneous and sequential treatment respectively. For session 2 the groups D and F were picked for pay-out according to the payoffs in the simultaneous and sequential treatment respectively. Output consisted of the initial effort choice minus sabotage received. The highest possible output was thus one if a player did not get sabotaged and exerted effort initially. An output of minus two was the lowest possible outcome. The player with the highest output was the winner of the tournament and received 250 points. The losers received 25 points. Any ties were broken randomly by coin tossing. Only ties between two players
7 Instructions can be found in the appendix 8.3, instructions of session 1 start with the simultaneous treatment
whereas instructions of session 2 start with the sequential treatment. This is done to match the instructions to the order of play that alters per session because of the counterbalance design.
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occurred in the randomly chosen groups as can be seen in Table 1 (*). The costs of effort and sabotage were deducted from the prize value. Show-up fees existed in the form of a free drink (worth €2.-) after the experiment. The conversion rate of points to money was 1 point to 1 eurocent. On average a subject earned €2.24, including the show-up fee as a free drink. Each session took about 15-20 minutes. Before the participants got paid according to their results they first had to answer a questionnaire. This questionnaire consisted of questions regarding participants’ gender, age, study and occupation level 9.
6. Results
6.1. Summary statistics
This section discusses the summary statistics of the experiment. Following from Table 2A one can conclude that the mean effort in the simultaneous treatment is higher than in the sequential treatment, 0.833 (SD = 0.377) versus 0.286 (SD = 0.457) respectively 10.
Table 2A. Summary statistics of the main variables; Effort and Sabotage Received.
Variable Obs Mean Std. Dev %Zero %One %Two
Effort Sequential 42 0.286 0.457 71.43 28.57 -
Effort Simultaneous 42 0.833 0.377 16.67 83.33 -
Sabotage Received Sequential 42 0.714 0.774 47.62 33.33 19.05 Sabotage Received Sequential 1 42 0.524 0.505 47.62 52.38 - Sabotage Received Simultaneous 42 0.809 0.634 30.95 57.14 11.90 Sabotage Received Simultaneous 1 42 0.690 0.468 30.95 69.05 -
Note: the label %Value shows in percentages how often a value occurred. Note that in the Effort rows the % of players choosing one equals the mean because this variable is binary. Sabotage Received “1” calculates the summary statistics if sabotage received is measured as any sabotage, thus, if at least one opponent sabotaged the player.
Consequently, in the sequential treatment the choice to not exert effort is made significantly more often than in the simultaneous treatment, 71.43% and 16.67% respectively. This suggests that Hypothesis 3 is true; effort levels are possibly higher in the simultaneous treatment compared to the sequential treatment. The mean of sabotage received in the simultaneous
9 The questionnaire can be found in appendix 8.3.
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treatment is 0.809 (SD = 0.634); with a maximum of 211. In the sequential treatment the mean
of received sabotage is 0.714 (SD = 0.774). However, in the sequential treatment it occurs more often that a player receives two points of sabotage (19.05% versus 11.90%). It also happens more often in the sequential treatment that a player receives no sabotage at all (47.62% versus 30.95%). The low mean of received sabotage in the sequential treatment and the fact that it is more spread over the possible outcomes 0, 1 and 2 can indicate that the choices are made more carefully by exploiting the information at hand. For example, if a player works, this players’ rivals both coordinate their sabotage to this player, therefore the percentage of players that receives 2 sabotage points is higher in the sequential treatment.
Table 2B shows the sabotage choices that are made during the experiment. In the simultaneous treatment most participants chose to simply sabotage player X (59.50%), that is, the next player. Only 21.40% chose to sabotage player Y.
Table 2B. Summary statistics of the sabotage choices.
Variable Observations Mean/Proportion Standard Deviation
Simultaneous No Sabotage 42 0.190 0.397 Sabotage X 42 0.595 0.497 Sabotage Y 42 0.214 0.415 Sequential No Sabotage 84 0.071 0.176 Sabotage X1 42 0.881 0.328 Sabotage Y1 42 0.809 0.397
Note: Sabotage X1 stands for how often player X is sabotaged in the scenario where X worked and Y did not. Sabotage Y1 shows this for the scenario where Y worked and X not.
Apparently, there is a preference for sabotaging player X in the simultaneous treatment, which could be due to framing in the order of the answer sheet. A mean comparison test shows that X indeed gets significantly sabotaged more than Y.12 One out of five participants choose to not sabotage when they have no intermediate information about who is the biggest threat/leader and with costs of sabotage, whereas when intermediate information is available only 7.1%
11 In the analysis below a dummy for Sabotage Received, which equals 1 if sabotaged by at least 1 rival. The
mean of sabotage received then is 0.523 (SD=0.51) in the sequential treatment and 0.690(SD=0.468) in the simultaneous treatment. Results are similar if sabotage received is a categorical variable with value 0 1 and 2.
12 The T-statistic is 3.81, the mean of Sabotaging X significantly differs from the mean of Sabotaging Y with a
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chooses not to sabotage. In the sequential treatment in the scenario where X worked and Y did not 88.10% of the participants chose to sabotage the working rival X. In the scenario where Y worked and X did not 80.90% of the subjects chose to sabotage the working rival Y. This shows evidence for Hypothesis 1; sabotage might be focussed on the working rival.
Moreover, it seems that the players anticipate that they will get sabotaged more if they work initially. In Table 2C the percentages of groups where 0 to 3 subjects worked for both treatments. The simultaneous treatment has extreme outcomes. In the simultaneous treatment the situation where all players worked occurred in seven of the 14 groups. In the other seven groups the situation where two out of three players worked occurred. It never occurred that only one or none of the players worked. In the sequential treatment, however, the situation that none of the players worked happened in 35.7% of the groups. Furthermore, in 42.8% of the groups only one player worked and in 21.4% two players worked. In contrast to the simultaneous treatment it never occurred that all players worked. This gives an indication that the players anticipate that if they work, they will get sabotaged more often in the next stage, thus they weaken their first stage productivity.
Table 2C. Percentage of groups where 0 to 3 participants chose to work.
Group % with score 0 1 2 3
Simultaneous 0% 0% 50% 50%
Sequential 35.7% 42.8% 21.4% 0%
Table 2D displays the summary statistics of the participant characteristics, obtained from the survey after the experiment. The average age of a subject is 25.78 (SD = 7.649), rounded 26 years old, with 19 being the lowest value and 56 the highest. There are more males than females participating, 64,28% are male. Most subjects are doing or did a study in the field of economics, namely 47,61%. The rest did a study in health (19%), HR (14,29%), IT (9,52%) or Law (9,52%). Only 57% of the subjects are students in this research. Furthermore, 24% are starters and 19% are managers (senior). This table also shows the opponent composition summary statistics. The composition of ones’ opponents can have an effect on the choices made. For example, it could be that if you face two managers your sabotage received will be low because managers arguably dislike sabotage. Furthermore, two females as opponents might also be less likely to sabotage as there are less competitive and more risk-averse (Croson and Gneezy, 2009). Unfortunately, there are too few opponent compositions with two managers and with one manager and one starter to be statistically useful and of added value.
23
Table 2D. Summary statistics of the participant characteristics.
Variable Obs Mean/Prop Std. Deviation Min Max
Age 42 25.786 7.649 19 56 Male 42 0.643 0 1 Study 1. Economics 2. Health 3. Hr 4. It 5. Law 42 0.476 0.190 0.143 0.095 0.095 0.505 0.397 0.354 0.297 0.297 1 5 Occupation level 1. Student 2. Starter 3. Manager (Sr.) 42 0.571 0.238 0.190 0.501 0.431 0.397 1 3 Opponent Composition 1. Male Male 2. Female Female 3. Male Female 42 0.405 0.119 0.476 0 1 Opponent Composition 1. Starter Starter 2. Starter Student 3. Manager Starter 4. Manager Student 5. Manager Manger 6. Student Student 42 0.071 0.309 0.024 0.262 0.048 0.286 0 1
24 6.2. Testing Hypotheses
The Hypotheses are analysed by using figures to show suggested evidence, followed by statistical tests to support the suggested evidence. The probit regression is used because the dependent variable Sabotage Received is a binary variable that can be either Yes (1) or No (0). Moreover, to compare results to the paper of Gürtler et al. (2013) the same type of regression should be used. Furthermore, the personalities of ones’ opponents might have an effect on the sabotage levels received, therefore controls are added for the gender composition of ones’ opponents and the composition of occupation level. Think of the dependent variable Sabotage Received as the underlying latent propensity that it is 1 (= Yes, Person is Sabotaged). In the sequential treatment it could be that some scenarios occur more often than others resulting in limited data, as explained the strategy method is used to account for this. To analyse the data from the strategy method one sample proportion tests are used.
6.2.1 Hypothesis 1: In the sequential treatment a player receives more sabotage if he exerted effort.
First, the data from the sequential treatment is analysed. Figure 1A shows that sabotage received (mutated to yes or no) is higher if the participant exerted effort in the first stage; 37% and 92% respectively13. This gives the impression that Hypothesis 1 is true; sabotage is focussed on the
working rival.
13 Here a dummy SRQ1 is used which equals 1 when the participant is sabotaged at least by one opponent. The
same results follow when Sabotage Received is 0, 1 or 2.
0.37 0.92 0 0,2 0,4 0,6 0,8 1 Mean p ro b ab b il it y o f Sab o tag e R ec eiv ed Sequential Treatment
Figure 1A. Probability of being sabotaged depending on effort
in the sequential treatment. Sabotage Received = {0,1} Yes or
No
25
The mean difference test in Table 3A shows that the mean of sabotage received is significantly higher (p-value = 0.001) if the participant chose to work in stage 1. These results are in line with Gürtler et al. (2013), who find this result with a p-value of 0.098.
Table 3A. Two sample proportion test; difference in Sabotage Received in the sequential treatment.
H0: Sabotage Received if working = Sabotage Received if not working H1: Sabotage Received if working > Sabotage Received if not working
Null hypothesis is rejected. Specifically, the mean sabotage received after working is higher than after not working initially.
Variable Mean (2) SE
Sabotage Received if work 0.917 0.800 0.0798
Sabotage Received if not worked 0.367 0.333 0.0879
Z-statistic (Fisher) 3.224
P-Value 0.001 0.098
Note: Column (2) displays the results from the fisher test of Gürtler et al. (2013); the values in their table A.3 are transformed into means/proportions to compare with the results from this paper. For example, 0.80 follows from 24 out of 30 subjects who worked got sabotaged, which is the same as the mean of sabotage received if worked.
In addition, this evidence is strengthened by the probit regression with robust standard errors in the appendix in Table 5. From the variable Dummy Effort one can see that if a participant worked in the sequential treatment in the first stage, he is significantly (p-value = 0.038) more likely to receive sabotage compared to if he did not work. These results are in line with Gürtler et al. (2013) who find this effect with a p-value below 0.001. The marginal effect of effort on Sabotage Received is 0.539*** in the sequential treatment. From not working to working regarding a player that has two male student opponents results in an increase in the probability of being sabotaged by 54 percentage points when information is not concealed. The marginal result in Gürtler et al. (2013) is 0.327*** and is in line with the marginal result from this paper but smaller. The marginal at means (constant) is displayed in the marginal test of this paper (column (3)) to add some extra information. When all variables are at their means, the probability of being sabotaged is 59%. Gürtler et al. (2013) do not exhibit this information.
In addition to this a proportion test on the data obtained from the strategy method is conducted. As can be seen in Table 3B it seems that players focus their sabotage on the working
26
rival (88% in the case that only opponent X worked and 81% in the case that only opponent Y worked). The one-sample proportion test in Table 3B confirms that sabotage is focussed on the working rival instead of the not working rival. Thus, three statistical tests where two use the same data and one uses additional data, all find significant results and confirm hypothesis 1; sabotage is focussed on the working rival.
Table 3B. One sample proportion test; effect of working on sabotage received
A participant had the chance to sabotage either player X or Y. For X1Y0RIVAL the expectation is that X will be sabotaged more than Y. For X0Y1RIVAL the expectation is that Y will be sabotaged more than X. This can be tested by constructing the following hypothesis:
H0: Proportion = 0.5 H1: Proportion > 0.5
Variable Mean/Proportion Standard Error Z-statistic P-Value
X1Y0RIVAL 0.8809 0.0499 4.94 0.000
X0Y1RIVAL 0.8095 0.0606 4.01 0.001
6.2.2 Hypothesis 2: In the simultaneous treatment the amount of received sabotage and initial effort exerted are independent of each other.
Next, the data for the simultaneous treatment is examined. Figure 1B suggests that Hypothesis 2 is true as well. The mean probabilities of being sabotaged for not working and working are closer to each other, 85.7% and 65.7% respectively. Note that in the simultaneous treatment it seems that if you don’t work the chances that you receive sabotage are higher. To test the significance of this difference a mean difference test is done and displayed in Table 3C. Results are insignificant (p-value = 0.296), thus there is no effect of effort on sabotage received if intermediate information is concealed. This insignificance follows from the fact that effort choices are not observable. It is therefore impossible to coordinate sabotage activities on the working rival. The difference in received sabotage for working and not working subjects is random and meaningless. Results from Gürtler et al. (2013) regarding their first round analyses (Fisher test p-value = 0.721) are in line with the results from this paper as can be seen in Table 3C (Column (2) displays their results). The probit regression with robust standard errors is conducted as well. A leverage against residuals squared plot shows no large outliers. Conducting a robust regression using iteratively reweighted least squares and comparing its leverage against residuals squared plot did not show large differences in the distribution of the plot. This yields that any problems about normality, heteroscedasticity, or some observations
27
that exhibit large residuals, leverage or influence are neglect able. The probit regression in Table 5 in the appendix shows that it is less likely to receive sabotage when you work, however, this effect is not significant (p-value = 0.244). This is also shown in Gürtler et al. (2013).
Table 3C. Two sample proportion test; difference in Sabotage Received in the simultaneous treatment.
H0: Sabotage Received if working = Sabotage Received if not working H1: Sabotage Received if working =/ Sabotage Received if not working
Null hypothesis is not rejected. The mean sabotage received if working and not working are not significantly different.
Variable Mean (2) SE
Sabotage Received if work 0.657 0.627 0.0802
Sabotage Received if not worked 0.857 0.550 0.1323
Z-statistic 1.044
P-Value 0.296 0.721
Note: Column (2) displays the results from the fisher test of Gürtler et al. (2013); the values in their table A.3 are transformed into means/proportions to compare with the results from this paper. For example, 0.627 follows from 32 out of 51 subjects who worked got sabotaged, which is the same as the mean of sabotage received if worked.
The marginal effect of Effort on Sabotage Received is not significant either in both studies and thus has no explanatory power. At means, there seems to be a probability of 65% of being
0.86 0.66 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Me an p ro b ab ili ty o f Sab o ta ge Rec eiv ed Simultaneous Treatment
Figure 1B. Probability of being sabotaged depending on effort
in the simultaneous treatment. Sabotage Received = {0,1} Yes or
No
28
sabotaged. The level of effort seems to have no impact on the received sabotage, confirming the second Hypothesis.
6.2.1.1 Control Variables of the probit regressions (Hypotheses 1 and 2) discussed.
Furthermore, from Table 5 it can be seen that having two female opponents significantly lowers the probability of being sabotaged in the sequential treatment compared to the reference of two male opponents. The change in probability of being sabotaged when going from two male opponents to two female opponents decreases by 68 percentage points. In contrast, Gürtler et al. (2013) find no significant effect of having two female opponents on sabotage received. If one opponent is male and the other female, this seems to not significantly affect the sabotage received as compared to the reference group in both studies. The opponent compositions regarding the occupation levels seem to suggest that students are acting more like the theory suggests and sabotage more because all dummies (with reference Opponent Student Student) have a negative effect on sabotage received. However, results are highly insignificant. Moreover, because of perfect prediction and limited data points the dummies Opponent Starter Manager and Opponent Manager Manager are omitted. Note that only 42 observations are used in this regression, that is, only the occurred scenarios are analysed. In the simultaneous treatment there is no significant effect of opponents’ gender composition nor of opponents’ occupation on sabotage received just as in Gürtler et al. (2013) 14.
Table 3D shows a regression with dependent variable Sabotage Given for both treatments. The independent variables are Age Male Study and Occupation for the simultaneous treatment and Effort Age Male Study and Occupation for the sequential method. In the sequential treatment there should be controlled for Effort because this affects the choice of sabotage according to the theory. As can be seen Age has a significant negative effect on given sabotage. Older people exert less sabotage. Important to note is that for the variable Male, there is a significant effect found in the sequential but not in the simultaneous treatment. The significance level for Male is (only) at 10% in Table 3, however, during the experiment subjects were faced by two opponents as controlled for in Table 5. Just as in Table 5, where having two female opponents resulted in less received sabotage, Table 3D also shows that females exert less sabotage in the sequential treatment. In both treatments it seems that starters exert more sabotage than students. This contradicts the suggestions from Table 5 regarding opponents’
14 Results from the replicated paper by Gürtler et al. (2013) can be found in the appendix along with the results
29
occupation levels, however, due to the insignificance the suggested negative effect of having two starters as opponents on sabotage received was not strong evidence in the first place. The significant effect of occupation level on given sabotage does highlight a critique for the original study by Gürtler et al. (2013) because they only used students in their experiment.
Table 3D. Sabotage Given depending on personal characteristics.
Variable Simultaneous Sequential
Effort - 0.114 (0.302) Age -0.439*** (0.011) -0.098** (0.037) Male 0.118 (0.135) 0.525* (0.307) Study Health HR IT Law -0.348 (0.207) -0.296 (0.199) 0.011 (0.117) -0.025 (0.121) -0.038 (0.456) 0.448* (0.225) -0.482 (0.312) -0.933* (0.532) Occupation Starter Manager 0.484*** (0.129) 0.745*** (0.219) 0.821** (0.379) 0.961 (0.661) Constant 1.718*** (0.385) 5.112*** (0.775) Observations 42 42 Adjusted R2 0.3837 0.4103
Note: The dependent variable is Sabotage Given. The reference category for Study is Economics and for Occupation the reference category is Student. ∗∗∗, ∗∗, and ∗ denote p < 0.01, p < 0.05, and p < 0.1, respectively.
30
6.2.3 Hypothesis 3: In the simultaneous treatment players will initially choose to be more productive compared to the sequential treatment.
The contestants anticipate the above positive relation between working and receiving more sabotage when intermediate information is not concealed. As can be seen in Figure 2 the mean of effort, or proportion of contestants that chose to work, is 28.57% when intermediate information is not concealed. In the simultaneous treatment, intermediate information is concealed, 83.33% of the participants chose to work initially.
The two-sample proportion test in Table 4A shows that the mean of effort in the simultaneous treatment is significantly higher than the mean of effort in the sequential treatment. The Z-statistic is 5.05, the p-value= 0.000, corresponding to the (rejected) hypothesis that the mean effort in the simultaneous treatment is not significantly higher than the mean effort in the sequential treatment. Both studies find a highly significant treatment effect on effort levels. Hypothesis 3 is confirmed, initial effort is weakened in the sequential treatment and as a result lower than the initial effort in the simultaneous treatment. There is no need for a probit regression to test the treatment effect with the control variables that Gürtler et al. (2013) used because of the within-subject design utilized in this paper. The pseudo-R2 of this paper is higher than in the replicated paper but the sample size is noteworthy smaller. The within-subject design arguably made it easier to isolate the treatment effect better.
0.83 0.29 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Me an o f E ff o rt
