Working together with confident agents
Master Thesis
Tamma Pronk (6057977)
Organizational Economics
Supervisor: Jeroen van de Ven
Date: 27-06-2014
Abstract
This study investigates the effects of confident agents within teamwork. Due to the globalization and increase in gathering information in the latter years, efficient teamwork became more crucial for firms to survive. The efficiency of teamwork depends on several factors, one of them is the (over)confidence of the agents. Using data from two experiments at two primary schools, it is found that there exists a significant positive relationship between confident agents and team performance. The experiment consisted of two treatments, one where the levels of effort of both team members were complements and one where they were substitutes. Confident agents had higher levels of effort than non-confident agents in both the treatments. Also in the complements treatment, agents chose higher levels of effort when they observed an confident team member compared to the situation where they did not know the confidence level of their team mate.
Table of contents
1. Introduction ... 3
2. Literature Review ... 5
2.1 The general effects of overconfidence ... 6
2.2 Factors influencing team performance ... 8
2.3 Overconfidence within teams ... 10
2.4 Main results and hypotheses ... 14
3. Method and data ... 18
3.1 Introduction ... 18
3.2 Subjects ... 18
3.3 The experimental design ... 19
3.4 The procedure ... 21
3.5 Description of variables ... 23
3.6 Analyzing the results ... 25
4. Results and analysis ... 25
4.1 Results ... 25
4.1.1 Testing hypothesis 1 & 2 ... 25
4.1.2 Testing hypothesis 3 & 4 ... 30
4.1.3 Testing hypothesis 5 & 6 ... 32
4.1.4 Testing hypothesis 7 & 8 ... 37
4.2 Discussion ... 41 4.2.1 Potential problems ... 41 4.2.2 Limitations ... 42 5. Conclusion ... 46 References ... 48 Appendix 1 ... 49 Appendix 2 ... 50 Appendix 3 ... 51 Appendix 4 ... 52 Appendix 5 ... 53 Appendix 6 ... 55
1. Introduction
There is a growing debate about the consequences of overconfident people for the individual and social welfare. Overconfidence does make a difference in various kinds of situations. These overconfident individuals overestimate their own skills, which results in a different decision made in many situations, compared to individuals who do not overestimate their skills. Dunning et al. (1990) mentioned that social behaviour is genuinely based on
predictions that people make about the peers’ behaviour and the personal confidence level with which people make their predictions. It starts at primary school, where confident children most of the times become the popular ones. When those children become older, their obtained skills become more important. For example, the ones with strong mathematical skills become more confident in situations where they can take advantage of these skills, like in tournaments with mathematical exercises. Also, in the working environment overconfidence plays an important role in several ways. It starts with the hiring process; individuals who are less confident will mostly not get the job. The overconfident ones are the individuals who take more risk when convincing the employer that they are the most capable person for the specific job. Therefore, the overconfident individuals genuinely fulfil the high positions (Goel and Thakor, 2008).
Due to the fact that in the past years the world has faced an increase in globalization and gathering of knowledge, modern businesses have to deal with more complex technologies and fiercer market competition. For these modern businesses to survive and develop, the efficiency of teamwork has become crucial. Therefore, it is interesting to investigate which factors influence the efficiency of teamwork. Teamwork depends on the individual levels of effort of the agents within the team. Each agent’s marginal contribution also depends on the level of effort of the other agents. Consequently, it makes sense that agents choose different levels of effort when facing different kinds of team members. Confident team members could therefore influence the levels of effort of other team members and as a result, also influencing the total team output. In real life, many situations occur where non-confident individuals have to work together in teams with overconfident people. These non-confident individuals are people who do not overestimate their own skills. In teamwork, these latter agents are less certain about the fact that their contribution is higher than their costs of effort compared to overconfident agents. It is interesting to investigate how these non-confident workers decide on their level of effort when they work together with a overconfident individual. On the one hand, they could be extra motivated to exert effort, because they know the other is certain of his abilities and therefore also exerts a lot of effort. On the other hand, they could become
lazy if they observe that the other team member is overconfident, because they expect the other to do all the necessary work and this therefore results in ‘free-riding’.
In the existing literature, several studies investigated the effects of overconfident agents on the individual level of effort and total team output. In these studies, they investigated these effects within teams where levels of effort from different individuals complement each other. It was therefore optimal for agents who observed a team member who probably would exert a lot of effort, to also exert a lot of effort. On the other hand, situations exist where the levels of effort from individuals within teams substitute each other. Within firms this situation exists a lot in teams. There, the effort of some agents may
compensate for the lack of effort of other team members. It could even be the case that these extra effort renders their work superfluous. These situations exist when team success requires just one ‘eureka’ task, the success is dependent on one agent to come with the solution. An example is a group working on an anagram task. When this ‘eureka’ moment has taken place, exerting more effort does not result in extra benefits, but only in extra cost of effort (Kerr and Bruun, 1983). Therefore, when facing a confident team member, who probably will exert a lot of effort due to his confidence, it is less optimal to also exert lots of effort compared to the situation with complementing levels of effort. The extra benefits from exerting effort are less and the extra costs are higher in teams with substitute levels of effort. On the other hand, the fear of being overruled could result in agents also exerting effort. It is therefore interesting to investigate how other agents react when they face confident team members in teams with substitute levels of effort. Another important difference is the fact that in this study, confidence is measured instead off overconfidence, as in the existing literature. Overconfidence is the comparative term of confidence. In other words, overconfident
individuals overestimate their skills with a wider range than confident individuals. In real life, in situations where several agents have to work together, it is also unknown if the other team mates are overconfident. The only thing they could observe is the confidence of other agents about their skills. Overconfidence is observable after a certain time period, because then the actual performance of this confident agent could be compared to the predicted performance. Therefore, in this study, confidence is used, because this is the variable that could be
measured in a short time period and is more in line with the real life situations. The fact that the other (first) team mate is confident or not should have enough effects on the levels of effort. Also, most of the existing studies investigated the effects of overconfident agents on infinite team outputs. In other words, in these studies the team outputs did not have a limit. The higher the levels of effort of all agents, the higher the total team output. In this study,
team output is measured with targets. Exerting more effort than is needed for the target, does not result in more benefits for the agents. Therefore, this study tries to investigate if agents exert the optimal level of effort, given the confidence level of their team mate, or if other factors are more important instead off the maximization of their utility. Due to the fact that this study also investigates the effects of confident agents in teams with substitute levels of effort and team outputs with targets, this study is a contribution to the existing literature. Based on the above, the research question of this study will be as follows: To what extent do confident people have an effect within teamwork?
Results have shown that confident agents had significantly more good solutions than the non-confident agents. In the treatment where levels of effort were complementary, the second players had a higher number of good solutions when they faced a confident team member compared to the situation where they played first. In fact, not all the strategic decisions where the most optimal ones. However, the total team performance was
significantly higher when the first agent was confident, compared to the teams where the first agent was not.
This study has the following structure. The related literature and the hypotheses based on these studies are discussed in paragraph 2. First, the studies are mentioned where situations and outcomes are described in the case that overconfidence is an important factor. Second, the necessity of teamwork is explained. Furthermore, some factors which influence the efficiency of teamwork are mentioned. Finally, the studies where the effect of overconfident individuals on team performance/output is investigated are discussed. The methodology of this research is discussed in paragraph 3. This contains the design of the experiment, the tested model and the statistics which were provided to answer the research question. In the follow-up paragraph, the main results are represented, analyzed and discussed. The conclusion and answer on the research question are described in the final paragraph.
2. Literature Review
In this paragraph, the related literature about overconfident individuals and team performance is discussed. Firstly, the effects of overconfident individuals are described in different
situations, in general. Secondly, the most common factors which influence the efficiency of teamwork are discussed. Furthermore, the studies where the effects of overconfident
2.1 The general effects of overconfidence
As mentioned in the introduction, overconfidence plays a role in different kinds of situations. Overconfidence is simply explained as individuals who tend to overestimate their own skills (Gervais and Goldstein, 2004). In all kinds of situations, overconfidence could change the way people behave and make decisions. Besides the change in behaviour of overconfident people, the behaviour of people they interact with could also change.
In the past years, researchers in psychology have shown that overestimation of own skills does exist. Individuals tend to base their performance perceptions partly on their own skills’ preconceived notions. Unfortunately, these notions are often not in line with objective performance. This results in individuals making judgments about their own performance level that often does not correlate with their actual accomplishment (Dunning et al., 2003).
Examples in real life of these subjective perceptions are the following. Svenson (1981) showed that most people overestimate their driving skills. This empirical paper used Swedish and US subjects, most of which regarded themselves as drivers with above average skills and also less risky than the average driver within the group. Half of the subjects regarded
themselves to be in the safest 20 or 30 percent of drivers in the group. In the US group of subjects, 93% regarded themselves as drivers with above median driving skills, in the Swedish group, this percentage was 69%. Also the empirical paper of Dunning et al. (2003) mentioned some situations where people tend to overestimate their skills. For example, subjects who participated in tests where they had to think logically, write grammatically and spot funny jokes, regarded themselves to perform above average in these tests compared to the group. Actually, their perceived percentile ranking compared to their peers was 40 to 50 points higher than the real percentile ranking. Also Dunning et al. (1990) discussed the overestimation of own skills. Their subjects perceived themselves to have a 75% accuracy level, just between chance (50%) and perfection (100%). Actually, their real performance level seemed to be closer to chance than to perfection. They also showed a difference appears in the overestimation of own skills in difficulty of tasks. Overconfidence seemed to occur more frequently in relatively difficult tasks compared to the relatively easy tasks.
These overestimations started to attract interest when looking at economic relevant situations. This is because the economic consequences are twofold; it results in both costs and benefits (Vialle, Santos-Pinto & Rullière, 2011; Wickhorst, 2010). The negative consequence of (over)confidence is the daring behaviour it fosters, resulting in risky decisions within many economic situations. On the other hand, positive effects do occur as well, because it could result in self-esteem utility. It is also proven that (over)confidence does result in an increased
motivation and therefore higher levels of effort (Wickhorst, 2010). Ludwig, Wichardt & Wickhorst (2011) mentioned that despite the different effects on eventual outcomes, it can be concluded that overconfident individuals, who overestimate their own skills, tend to exert more effort than individuals who are unbiased.
When looking at the effects of overconfidence in economic relevant situations, many researchers have shown these costs and benefits of overconfidence. In the stock market, increased overconfidence results in an increase in the trading volume, an increase in volatility and a bigger bubble. This could be explained, because overconfidence firstly results in more diverged beliefs. Therefore, the trading volume will increase. Second, overconfidence results in a higher option component of the price, resulting in an increase in volatility. Furthermore, these latter changes will result in market participants driving stock prices above their true values, hence resulting in a bigger bubble in the market (Scheinkman & Xiong, 2003). In the start-ups of new business, overconfidence could result in high failure rates. To determine which effects of overconfidence could increase the failure-rate, it is interesting to investigate the main drivers to start new firms. Koellinger, Minniti & Schade (2007) investigated which factors were the main drivers for individuals to start a new business. They concluded that individuals determine their future prospects of a new business by taking a subjective view of situations, including confidence in their own skills as the major driver. Hence, this explains the high failure rate. Because, the subjective view of individuals sometimes rule the objective view, this results in decisions that are not well thought through, and therefore resulting in bad and risky decisions. Excess market entry could also be explained by overconfidence. The empirical study of Camerer and Lovallo (1999) is in line with the latter statement. They investigated whether optimistic biases could plausible and predictably influence economic behavior in one particular setting – entry into competitive games or markets. They
hypothesized that due to overconfidence and competitive blind spots, many entry decisions seemed to be mistakes. Their results confirmed their hypotheses, because overconfidence significantly increased the tendency to enter more frequently. Bernardo & Welch (2001) mentioned that overconfident individuals are the ones to undertake ventures that might not be undertaken by the more rational individuals. In their article, they mentioned a study where 81% of the entrepreneurs believed with at least 70% certainty that their firms would succeed, while in real life about 75% of new ventures does not exist anymore after five years. Also, they showed that entrepreneurs had a higher level of confidence in answering questions compared to managers, while in reality their accuracy level was equal. They also gave a new explanation for the overconfidence under entrepreneurs: entrepreneurs are more likely to
explore their environment and therefore less likely to copy their peers. The benefits of
overconfidence seemed to occur in situations where individuals apply for new jobs. In the top level of management, the higher positions are mostly taken by overconfident individuals. Goel and Thakor (2008) mentioned that due to selection, overconfident managers end up at the top levels. This is because they overestimate their own skills, therefore regarding themselves as the ones taking the right decisions and having the right prospects. The latter, results in these individuals taking excessive risk. This results in higher variations in outcomes and therefore relatively more positive outcomes than individuals who do not take a lot of risk. Those risk-averse managers move to the middle positions and excessive risk taking
individuals will have the high positions.
2.2 Factors influencing team performance
Due to the global changes in the past years, firms have to find new ways of running the organization. Like mentioned in the introduction, modern businesses have to deal with more complex technologies and fiercer market competition. For these modern businesses to survive and develop, the efficiency of teamwork has become crucial. This efficiency of teamwork is crucial, because teamwork nowadays exists in most of the organizations. The purpose of teamwork is that the common output of several agents working together is higher than a situation where the same agents produce output individually. When agents work together, they each choose their level of effort independently, resulting in a common output. For each agent, the marginal contribution to the common output level depends on the levels of effort of their team workers (Xun et al, 2011). During teamwork, the effort decisions of the team members are unobservable. As a result, moral hazard problems are prevalent. Also, for organizations it is hard to monitor the effort decisions. Because team members often make decisions based on self-interest, it is hard for organizations to make sure these agents make decisions that are in line with the organization’s objectives (Gervais and Goldstein, 2004). Many factors exist within teams which influence the total team output. Therefore, it is
interesting to investigate which factors within teams will result in the perceived outcomes for firms.
For teams to be efficient, total team output has to be higher than a situation where these same agents produce output individually. Vialle, Santos-Pinto & Rullière (2011) mentioned that team production outperforms a situation where individuals work alone, when the inputs of different workers (skills or efforts) are complementarities. Actually, total team
output is not automatically higher than situations where agents work alone. This is because teamwork faces different threats and factors which influence the total team output. One threat for teamwork is the free-ride effect. The free-ride effect occurs when agents could benefit from the input and effort of others, without paying for the costs of benefit. This happens when effort is unobservable and every team member will get a share of the total team output.
Because in some situations these free-ride decisions are in fact rational decisions, teamwork could result in inefficient social outcomes. On the other hand, there are also situations where agents might not free-ride. This could occur when they have some behavioural concerns, like fairness or equality concerns. In this view, free-riding does not result in an increase in utility, because it violates cooperative social norms and will not result in more fairness or equality. An agent with these altruistic feelings often provides higher levels of effort than the optimal levels of effort. Besides these behavioural concerns, also peer pressure could solve the free-riders problem. If team members have the opportunity to monitor each other and also punish the ones who do not act cooperatively, then outcomes will be more cooperative. The latter will only be attained when these monitor costs are lower than the extra attained benefits. Besides the fear of punishment, agents could also reject free-riding because they prefer social approval. In their article, Vialle, Santos-Pinto & Rullière (2011) mentioned a study where the latter is proven. The individual levels of effort of agents significantly increased due to team competition.
Gervais and Goldstein (2004) also investigated the behavioural considerations within teams. Within their article, they mentioned several other studies to give a clear overview of the existing literature. They mentioned that within teams where the inputs of agents are complementarities, altruistic agents can increase the team output, resulting in Pareto improvements. Also, teams with altruistic agents seemed to survive in the long run. The article of Gervais and Goldstein (2004) is in line with the article of Vialle, Santos-Pinto & Rullière (2011), because they also claimed that peer pressure will result in agents exerting more effort. In both the articles, their explanation for this result was the increase in costs for agents who did not act cooperatively when they were monitored.
Madrid, Canas & Ortega-Medina (2007) investigated the effects of team competition and team cooperation on the performance levels of children in class. The empirical study incorporated three instructional interventions: (1) standard teacher-led instruction, (2) cooperative team peer tutoring and (3) competitive team peer tutoring. Results showed that team cooperation and team competition resulted in an increase in correct responding
correct responding was in the condition with cooperative team peer tutoring. There, the score increased from 12% before the program started to 92.8% after the program finished. For the competitive team peer tutoring this increase was 13% to 80.2% and in the standard sessions, 14% to 36.2%.
Besides the altruistic and peer pressure effects, also group size seemed to influence the effort decisions within teams. Kerr and Bruun (1983) mentioned that group size resulted in a drop down of motivation for certain tasks. This result is due to the fact that when the group size increases, it is more difficult to identify the contribution of each group member. Therefore, an increase in group size decreases the praise for working hard.
2.3 Overconfidence within teams
Besides peer pressure, altruistic feelings and group size, confidence could also affect the efficiency of teamwork. Overconfident team members could affect the team output, because their own levels of effort could be different from the levels of effort of non-confident agents and they could change the effort decision of their team mates. Dunning et al. (1990)
mentioned that people tend to predict their behaviour on predictions about their peers’ behaviour and about the confidence of their own predictions. The following studies investigated the relationship between overconfident individuals and team performance.
Gervais and Goldstein (2004) wrote a theoretical paper and investigated the effects of overconfidence within a team model. In their model, the levels of effort across team members were complementarities. Therefore, if one agent increases his/her level of effort, it is optimal for the other team member to also increase the level of effort, because their effort is therefore more valuable. The overconfident agents, who overestimate their own marginal product, will chose high levels of effort. This is because these agents justify at an earlier stage the extra costs of effort than non-biased agents. Overconfident agents think their effort is valuable and are therefore willing to make higher costs of effort than non-biased agents, because they predict their extra value to be higher than their costs. The fact that these overconfident agents chose higher levels of effort, also reduces the free-rider problem. This is because, like
mentioned before, the levels of effort are complementarities. For the other, non-biased, agent is it therefore optimal to also increase the level of effort if they observe their overconfident teammate to do so, because their effort becomes more valuable now. As a result,
overconfident agents will help to increase the chance of team success. Gervais and Goldstein (2004) also mentioned that besides the free-rider problem, also the coordination problems are
solved due to these biased agents. Due to their extreme self-perception, thinking that their contribution is higher than their costs, the other team member will chose a high level of effort as well which fosters cooperation within the team. This extreme self-perception has nothing to do with the concerns for others or any other consideration for their team members.
Furthermore, this indicates that the incentives for agents to cooperate with each other are not the willingness to cooperate, but because cooperation is optimal when some agents believe they are skilled. The biased, overconfident agents will in fact benefit from his/her
overinvestment in effort, because their teammates also increase their levels of effort and therefore total performance does increase. The latter only holds when the overconfidence bias is not too extreme, because then the overinvestment will be too high resulting in higher costs than benefits. Besides the fact that overconfident agents misinterpret their contribution to team output, they also have the chance to make wrong predictions about the eventual larger team output. Biased agents believe the team output to increase due to their own skills, due to their extra contribution, instead of the higher levels of effort of their other teammates due to complementarities. After noticing the realized performance, agents learn about their abilities over time. In fact, learning about their actual ability is slowed down due to the self-attribution bias. Therefore, the effects of overconfidence are longer-lasting, resulting in relatively higher benefits. Based on the information above, Gervais and Goldstein (2004) made some
conclusions. First, it can be concluded that overconfidence will result in higher team performance when complementarities exist. These complementarities are responsible for making overconfidence useful (for both the agents as team performance) and making it persists (due to the slower learning of biased agents). It can also be concluded that
overconfidence will solve the free-riding and coordination problems and will make all agents within the team better off. They showed that a team consisting of one overconfident agent and one rational agent outperformers a team where both agents are rational.
An extension to the paper of Gervais and Goldstein (2004) is the study of Wickhorst (2010). This paper is again not empirical, but a theoretical paper. He investigated in a same way the effects of overconfident agents within teams; he also used a mathematical model to test his predictions.What is new in his model is the fact that he made the assumption that in general, everybody knows that overconfidence exists. The agents are however not completely informed about the team members’ confidence. In this model, the agents have a certain bias awareness, they are aware of the fact that overconfidence does exist and they know the chance that the existing literature does assign to probability of their team member being
results of Gervais and Goldstein (2004). The existence of the bias awareness did result for all types of agents in a higher level of effort. This is because they anticipated their team member to exert more effort because he/she could be overconfident; therefore they expect the optimal level of effort to increase, due to the increased marginal productivity. Also, in this model the higher levels of effort had a positive effect for all types of agents as well as for the principal, due to the mitigated coordination problems.
Ludwig, Wichardt & Wickhorst (2011) also discussed the effects of overconfidence in a theoretical paper. They analyzed a team model where effort choices were
complementarities.Their results are quite the same as the result of both the articles mentioned above; overconfidence in teams enhanced team productivity, due to the increase in levels of effort of both agents. They also concluded that the extra benefits of overconfidence were higher when the overconfident agents were unaware of the bias of other people. On the other hand, for the unbiased agents, it is optimal to be aware of the overconfidence of their
teammate. These latter two statements could be explained in the following way. First, for the unbiased agent it is optimal to be aware of the bias of the other agent, because he/she will increase his/her levels of effort, due to synergy effects. On the other hand, for the
overconfident (biased agent) it is optimal to be unaware of the other’s bias, because their levels of effort are already above the individual optimum (due to their bias). Actually, when this biased agent would observe this it would lead to a further (suboptimal) increase of their levels of effort.
Vialle, Santos-Pinto & Rullière (2011) investigated the effects of agents’ overconfidence (their beliefs about their skills) on their contribution of effort, team
performance and payoffs. They also explained why overconfident agents do help solving the free-riders problem. Overconfident agents solve the free-riders problem if the following statements hold: (1) if skills and effort have a positive effect on team performance, (2) if skills and effort are complements and (3) if agents’ effort choices are complements. These
statements automatically result in agents to provide more effort when their beliefs about their effort contributions are positively biased. Because the other team mates will also exert more effort due to the complement levels of effort, overconfidence can result in a Pareto
improvement of agents’ payoffs. To investigate if their predictions are true, they did an experiment. Their subjects had to solve as many problems as they can, while making predictions about their own skills before and afterwards. This resulted in four different
groups: (1) overconfident subjects, (2) under confident subjects, (3) high-skill subjects and (4) unbiased, low-skill subjects. Before subjects made effort choices in each round, they were
told about the belief of skill of their teammate. Results showed that overconfident subjects had higher levels of effort than unbiased low-skill subjects and subjects who faced
overconfident team members also exerted more effort than the ones who faced an unbiased low-skilled subject. As a result, overconfidence did result in Pareto improvements of subjects’ payoffs.
Both Gervais and Goldstein (2004), as Wickhorst (2010,) as Ludwig, Wichardt & Wickhorst (2011) and Vialle, Santos-Pinto & Rullière (2011) concluded that the levels of effort of overconfident agents were higher, therefore also the levels of effort of the unbiased agents (due to complement levels of effort) and the total team output. However, there are some differences between these studies. The study of Ludwig, Wichardt & Wickhorst (2011) is innovative, because they made a distinction between the effects of overconfident agents when agents were aware of the others’ bias and when agents were unaware of the others’ bias. They investigated how individual payoffs are affected by the awareness of the biases and how they developed to the optimal individual payoffs. Where Vialle, Santos-Pinto & Rullière (2011) used an experiment to investigate the effects of overconfidence within teams, Ludwig, Wichardt & Wickhorst (2011) analyzed a model. They created a model where the
overconfidence of agents was taken into account, with 1 overconfident and 1 rational agent and also with the variable if they could observe the bias of the other or not. Furthermore, they also investigated the effects in teams with two overconfident agents or with two rational agents. In all models variations with the awareness of biases were incorporated. The paper of Wickhorst (2010) is also innovative, because it extended the model of Gervais and Goldstein (2004). Instead of telling each participant if their team mate is confident or not, they made the assumption that it is a widespread phenomenon that individuals could be overconfident. Gervais and Goldstein (2004) and Wickhorst (2010) also based their conclusions on the assumptions they made within their mathematical model. A mathematical model is a helpful tool in providing theoretical predictions. Due to mathematical models, researchers are able to make accurate predictions for a large body of data. Although mathematical models face some problems due to the fact that the individuals’ behaviour is hard to predict and very complex, they are useful tools to analyze the behaviour of individuals. In many situations they provide more precise predictions than is the case when verbal descriptions are used. Mathematical models also make the viability of the hypotheses made about the behaviour decisions of people clear.Another characteristic is that it helps point out factors which otherwise have been unobserved and on the other hand it helps identify shortcomings (Mazur, 2006). On the contrary, this could be a threat for the validation and reliability of the results. All the latter
mentioned studies based their conclusions on the assumptions, conditions and propositions of their model, so not with real people. This could be a threat, because people in real life do not always make the optimal decisions. They could be biased due to several factors or make mistakes. Some people are not risk averse, or have fairness and equality concerns. Therefore, experiments are useful to see if the theoretical predictions are in line with the decisions that individuals make in real life. Vialle, Santos-Pinto & Rullière (2011) are original, because they made use of an experiment to prove their predictions. By using a mathematic model (based on a theoretical framework), they made their hypotheses. To investigate these hypotheses, they did an (computerized) experiment to get their results. Their experiment consisted of two treatments. The two treatments differed in the provided information. In one treatment only the beliefs about their teammates’ skills were told, in the other treatment both the beliefs about their skills and their actual skills were told. The effects of overconfidence on effort proved to be stronger in the treatment where only the beliefs about their skills were told. Due to the design of their experimental model, the chance that social preferences played a role instead of self-confidence is diminished. Social preferences like peer pressure, cooperative social norms and reciprocity are unlikely to have an effect on the effort choices. The only social preference which is not ruled out due to their experiment model is altruism. Besides these latter social preferences, all studies mentioned in this paragraph could extend their study in several ways. A first extension could be the examination of risk averse or loving agents. Another extension could be to investigate the effect of confidence on the levels of effort of agent within a
treatment where levels of effort are substitutes. The studies mentioned in this paragraph all used team models where levels of effort were complementarities. According to Vialle, Santos-Pinto & Rullière (2011), this choice is crucial, because otherwise agents would make effort decisions regardless the level of effort of their team members. Also, within firms it is crucial for teams to have complementary levels of effort; otherwise positive externalities cannot exist. Without complementary effort choices within teamwork in firms, it would lead to a
production level beneath the individual production level. Actually, in this study both
complementary and substitute levels of effort are investigated. If the existing literature is right about their predictions, this would result in different outcomes between the two treatments.
2.4 Main results and hypotheses
The purpose of this study is to investigate the effects of confident team members within a team. The theoretical background contained literature about overconfident people, but the fact
that the other (first) team mate is confident or not should have enough effects on the levels of effort. In this paragraph, first the general effects of overconfident individuals are discussed. Overestimates in the economic world could have both benefits as costs. The negative consequences of overconfidence are that individuals start to have more extreme daring behavior, resulting in risky decisions within many economic situations. On the other hand, positive effects do occur, because it is proven that overconfidence does result in an increased motivation and therefore higher levels of effort. Economic situations where overconfidence has significant consequences are for example the stock market, where overconfidence results in an increase in the trading volume, an increase in volatility and a bigger bubble.
Overconfident individuals are the ones to undertake ventures that might not be undertaken by the more rational individuals. Therefore, the high failure rate for new firms could also be (partly) explained. Due to the excessive risk taking of overconfident individuals, it is proved that these individuals will take the higher positions in the top level of management.
Besides the different consequences of overconfidence, also different factors
influencing team performance are discussed. Team output could be influenced by factors such as the free-rider problem, peer pressure, altruistic feelings, team competition and cooperation and group size. To investigate the effects of overconfidence on team performance, this study discussed several articles. They all concluded that the levels of effort of overconfident agents were higher; therefore also the levels of effort of the unbiased agents (due to complement levels of effort) as well as the payoffs for all agents resulting in a higher team output.
To answer the research question, mentioned in the introduction, this research will test several hypotheses. These hypotheses, based on the main results of the literature review, are described below. For the experiment of this study, ‘confidence’ is the most important
independent variable. The term confidence is used in the experiment, because it is interesting to investigate what the effects are on the other agent if he/she observed the first agent to be confident or not. As mentioned in the existing literature, the reason why agents who work together with a confident agent exert more effort is because these confident agents are certain of their abilities. By knowing this, it is optimal to also exert effort to increase marginal utility. This ‘certainty of abilities’ is therefore not an overestimation of the individuals’ skills, but is more in line with ‘confidence’. Overconfidence would also result in other hypotheses, because overconfidence is an overestimation. This would imply that this overconfident agent has lower abilities than he predicts he has. If agents know they work together with someone who overestimates their abilities, this could also result in lower levels of effort, because an overestimation does not automatically result in a high performance. Due to the experimental
design, the importance of the confidence answers of the agents is emphasized. In the following sections of this study, the term ‘confidence’ is therefore used.
Hypothesis 1: Confident agents will have more good solutions than non-confident agents in the complements treatment
Hypothesis 2: Confident agents will have more good solutions than non-confident agents in the substitutes treatment
Agents who are confident about their own skills are extra motivated to exert effort, measured with the number of good solutions in this experiment, because they predict their extra
contribution to be higher than their costs of effort. Therefore, confident agents will have more good solutions than the agents who are not confident. This prediction holds for both
treatments. It is optimal in both treatments for the confident agents (who made the exercises first) to exert as much effort as they can, because they do not know the confidence level of the other player. Exerting no effort will result in a lower utility.
Hypothesis 3: The first players in the complements treatment will let their team mate know they are confident
Hypothesis 4: The first players in the substitutes treatment will let their team mate know they are not confident
All first players had to make a strategic decision about their confidence sign. In this study, two treatments existed. Due to the differences in the relation of number of good solutions within the teams, different results are expected. In one treatment, the effort decisions of both agents are complements, whereas in the other treatment the effort decisions are substitutes. In the complements treatment, the extra remuneration was only earned when both players earned a point. As a result, it is optimal for the first player to sign they are confident, because
otherwise the second player would not exert effort. If the second player knows his/her team mate is confident, he/she knows they still have a chance for the extra remuneration. Therefore, the first player should sign that he/she is confident to the second player in the complements treatment. However, in the substitutes treatment, only one of the two players had to earn a point. Therefore, the first player had to make sure that the second player was going to exert
effort. To achieve this goal, the second player should not signal that he/she is confident. Because if the second player observed a confident team member, the second player had less incentives to also exert effort, because this would not increase his/her benefits. As a result, first players in the substitutes treatment should signal they are not confident, to make sure the second player is going to have a high number of good solutions.
Hypothesis 5: Agents will have more good solutions if they observe they work together with a confident team member in the complements treatment
Hypothesis 6: Agents will have more good solutions if they observe they work together with a confident team member in the substitutes treatment
The optimal effort choices for second players in the complement treatment are in line with the existing literature, mentioned in this study. In the complement treatment, it is optimal for the second player to make many exercises if the first player is confident, because this will increase the team output. If both players have a high score in the complement treatment, this will result in extra benefits for both players. On the other hand, the existing literature expects the strategic decisions to be unrelated to the others’ effort decision when levels of effort are substitutes. In the substitute treatment, it is optimal for the second player to make no exercises if he/she observes the other, first player to be confident, since exerting extra effort will only result in extra costs, but no extra benefits. On the other hand, the fear to be behind and underperform compared to the other player could also result in agents to complete many exercises. Although this extra effort does not result in a higher team output, it could result in a higher utility for the agent. This is because the utility could also depend on status and the urgency to outperform the other player. Therefore it is hypothesized that, also in the substitute treatment, that the second agent will exert effort if he/she observes the first player to be confident.
Hypothesis 7: Teams where the first agent is confident, outperforms the teams where the first agent is not confident in the complements treatment
Hypothesis 8: Teams where the first agent is confident, outperforms the teams where the first agent is not confident in the substitutes treatment
The discussed articles in this study have shown that confident agents will increase the team performance. Besides their own payoffs, also the payoffs of the other team members will increase, therefore resulting in a higher team output. This hypothesis should anyhow hold in the complement treatment, since the confident agent is expected to motivate the other agent to also choose a high level of effort, therefore resulting in a high team output. In the substitute treatment, the same hypothesis should hold, due to the fact that in hypothesis 6 it is predicted that the second agent will also choose a high level of effort if he/she observes the other (first) agent to be confident.
3. Method and data
The methodology of this research will be discussed in this paragraph. This contains the design of the experiment, the tested model and the statistics which were provided by answering the research question.
3.1 Introduction
The research question will be answered by doing a quantitative empirical research. Ideally some date from firms should be gathered about the exerted efforts of team members and their confidence level. However, it is hard to identify if individuals/workers know how confident or non-confident the other team member is. Therefore it could not be investigated if individuals choose different levels of effort if they observe a overconfident team member. Furthermore, controlled experiments at firms are hard to implement and prohibitively expensive. Therefore, this study will run class experiments at two primary schools, resulting in an more controlled experiment and a situation where the experimenter can gather the desired data and have random assignment. Before the start of the experiment, the director and a teacher of the two primary schools in Abcoude are asked for permission (see Appendix 1). Also, the parents are informed about this experiment by way of receiving a letter with information about the experiment.
3.2 Subjects
The subjects were 54 children from two primary schools in Abcoude. The first primary school was the ‘Paulusschool’, having 26 children in the sixth grade, 7 boys and 19 girls. The second primary school was the ‘CNS’, having 28 children in their sixth grade, 14 boys and 14 girls.
The children ranged in age from 10 to 13 years, with a median age of 12 years. In Table 1, the descriptive data about the subjects is described. According to the teachers, all the children in the sixth grade who participated in this experiment were capable of reading the digits 0 through 9.
Table 1. Gender and age of subjects
School Gender % Minimum Age Maximum Age
CNS Boy 50% 11 12
Girl 50% 10 12
Paulusschool Boy 27% 11 12
Girl 73% 11 13
Total 10 13
3.3 The experimental design
During the experiment, the class was divided in two groups. Before the experiment started, every subject received a personal number on their table. At the blackboard, it was mentioned which numbers belonged in which group. In Table 2, the disposition of table numbers at the two different schools is described.
Table 2. Disposition of table numbers
Group 1 Group 2
CNS 1 t/m 14 15 t/m 28
Paulusschool 1 t/m 13 14 t/m 26
The experiment had in total four parts. In each part, subjects had to complete a task during 2 minutes. The task consisted of 25 exercises, each exercise consisted of three two-digits numbers which subjects had to count up (for an example, see Appendix 2). During all parts, the procedure of the experiment was quite the same, but still differs at some points:
Part 1
• The subjects had a chance of a extra remuneration at the end of the experiment when both team members earned a point during the exercises
• Subjects from group 1 were the first to start with the exercises Part 2
• The subjects had a chance of a extra remuneration at the end of the experiment when both team members earned a point during the exercises
Part 3
• The subjects had a chance of a extra remuneration at the end of the experiment when at least one team members earned a point during the exercises
• Subjects from group 1 were the first to start with the exercises Part 4
• The subjects had a chance of a extra remuneration at the end of the experiment when at least one team members earned a point during the exercises
• Subjects from group 2 were the first to start with the exercises
An important note to make is that in each part, the first group had to answer a confidence question before they started with the task (for an example, see Appendix 3). This confidence question was very important for this study, because it measured the confidence level of subjects. Therefore, the first group had to answer the question:
Do you think you will have ≥13 good solutions, resulting in gathering 1 point? Yes / No Subjects could earn a point when they successfully completed at least 13 of the 25 exercises. Before the second group of subjects started with making the exercises, the experimenter told them if their team mate was confident or not. The experimenter encircled yes or no as answer on the question if their team mate thought to be able enough to earn of point or not. This answer was above the sheet with exercises of the second group (for an example, see Appendix 4).
The differences between Part 1&2 and Part 3&4 were crucial for this study. In the first two parts, the levels of effort for both subjects were complementary. On the other hand, in the second two parts, the levels of effort for both subjects were substitutes. The levels of effort in the first two parts were complements, because it was optimal for the second team member to exert the same level of effort as the first team member. If the first team member did not earn the point, the extra remuneration cannot be obtained any more. But, if the first team member did earn the point, it was optimal for the second team member to exert also effort, because this would have increased his/her utility from no extra remuneration to an extra remuneration. On the other hand, the levels of effort in the second two parts were substitutes, because it was optimal for the second team member to exert the opposite level of effort as the first team member. If the first team member did not earn the point, the extra remuneration could still be
obtained, therefore it was optimal for the second team member to exert effort. But, if the first team member did earn the point, it was optimal for the second team member to exert no effort, because the extra remuneration was already obtained, so exerting effort would not have
increased the utility.
There also existed a difference between Parts 1&3 and Part 2&4. In Part 1&3, the subjects of group 1 were the first ones to complete the exercises. In the other two parts, the subjects of group 2 were the first group to start. This has resulted in more observations for this study.
During the class experiment at the Paulusschool, the order of parts mentioned above was used. So, first the two complement treatments and at last the two substitute treatments. Actually, during the class experiment at the CNS, the order was the order way around. Part 1 & 2 had substitute levels of effort and Part 3 & 4 had complement levels of effort. This was done to ensure that the order would not affect the results.
At the end of the experiment, subjects all earned a little remuneration (some sweets) and two subjects have earned an extra remuneration if they really earned the extra bonus. The latter is randomly selected. First, it was randomly chosen which part is going to be
remunerated. Second, the experimenter has chosen one number out of a bucket with 26 or 28 numbers. This number related to the number of one of the team members. The second subject who was extra remunerated was the one who was matched with the randomly chosen number during the randomly chosen part. Finally, the answers of these two subjects were checked and therefore it was decided if these subjects earned an extra remuneration or not.
3.4 The procedure
Before each subject entered the class room, they had to pick out randomly a number out of a collection cards. This to ensure there existed randomization. Beforehand, they could not see which numbers were on the cards. The numbers on the cards were ranged from 1 till 26 or 28, depending on the total class size. Each number was linked with a table in the classroom, this to have random assignment. After all subjects picked out a card and were seated at the table with the same number on it, the experiment could start. The experimenter read out loud the instructions, these were the same for all subjects (see Appendix 5). Now, the four parts of the experiment started. In Part 1, first group 1 had to answer the confidence question and when they had completed this, they had time to complete the exercises. They had to complete as much as possible exercises within 2 minutes, by giving the right solutions. Thereafter, group 2
had time to read the message if their team mate thought to have earned the point or not and then they also had some time to complete the exercises. Now Part 2 started, having the same procedure as Part 1, only differentiating in the order of groups making the exercises. In Part 2, group 2 started with the confidence question and exercises. After Parts 1 & 2 ended, the subjects received new instructions (see Appendix 6). Thereafter the procedure was the same as in Part 1 & 2 (see Figure 1 & 2). After the subjects completed all parts, they earned their remuneration. The experimental design of the class experiment at the Paulusschool is described in Figure 1.
3.5 Description of variables
Due to the experimental design, some variables have been created which are used to test the hypotheses. For each hypothesis, other variables are used. A summarizing table of all variables is shown in Table 3.
Table 3. Description of the variables
Variables Description
school = 0 for the Paulusschool, 1 for the CNS
treatment = 1 in the complements treatment, 2 in the substitutes treatment
part = C1 when group 1 played first in complements treatment, C2 when group 2 played first in complements treatment, S1 when group 1 played first in substitutes treatment, S2 when group 2 played first in substitutes treatment nr = number of formed team, possible values: 1-108
gender1 = 1 when first player* is a girl, 0 when first player is a boy gender2 = 1 when second player** is a girl, 0 when second player is a boy age1 = age of first player, possible values: 10-13
age2 = age of second player, possible values: 10-13
confidence = 1 whenf first player is confident, 0 when first player is non-confident performance1 = number of good solutions of the first player, possible values: 2-20 points1 = 1 when first player earned 1 point, 0 when first player earned 0 points performance2 = number of good solutions of the second player, possible values: 3-22 performance2diff = number of good solutions after confidence sign of team mate minus the
number of good solutions when this same agent was the first team member to answer the questions, possible values: -6 till 5
points2 = 1 when second player earned 1 point, 0 when second player earned 0 points
teamperformance = performance1 + performance2, possible values: 11-36 teampoints = points1 + points2, possible values: 0-2
extra-bonus = 1 when teampoints equals 2 & treatment equals 1 and when teampoints equals 1 or 2 & treatment equals 2, 0 when teampoints equals 0 or 1 & treatment equals 1 and when teampoints equals 0 & treatment equals 2
* first player is defined as the first agent who had to make the exercises **second player is defined as the second agent who had to make the exercises
For all hypotheses, it is evident that the confidence level of all first players are measured. Therefore, ‘confidence’ is the most independent variable. It is predicted for Hypothesis 1 & 2, that it has a significant positive effect on the number of good solutions of the first players. The latter is the variable ‘performance1’, the total of good solutions of the agent who had to make the exercises first, having values of 2-20 good solutions and therefore a continuous variable. For Hypothesis 3 & 4, the strategic decisions of the first players are compared. The
different outcomes of the variable ‘confidence’ are compared. For Hypothesis 5 & 6. ‘confidence’ is expected to have a positive effect on the extra good solutions that second players will have. The differences in good solutions of a second player after observing a confident player and when this same player played first is the variable ‘performance2diff’. In other words, the number of good solutions after receiving the message about confidence level team mate (variable ‘performance2’) minus the number of good solutions when this same agent played first (variable ‘performance1’ in the part where this same agent had to make the exercises first). If this variable had a positive value, this indicated that this agent reacted positive on the confidence message. The opposite holds when this variable had a negative value. For Hypothesis 7 & 8, ‘confidence’ is expected to have a positive effect on the total team output. The latter is measured with the variable ‘teamperformance’, a continuous variable which is the sum of ‘performance1’ and ‘performance2’. For all hypotheses, the variable ‘treatment’ is used. Each hypothesis made a prediction for just one of the two
treatment, the complements treatment or substitute treatment. Treatment is equal to 1 when it was the complements treatment and equal to 2 when it was the substitutes treatment. Some control variables are ‘school’, ‘gender1’, ‘gender2’, ‘age1’ and ‘age2’.
In Table 4, descriptive data about the variables is shown. For all important
independent and dependent variables, the observations, mean, standard deviation, minimum and maximum values are shown in the table below.
Table 4. Descriptive data
Variable Observations Mean Std.
Dev. Minimum Maximum
Independent variables Confidence 108 0.713 0.454 0 1 School 108 0.519 0.502 0 1 Gender1 108 0.611 0.490 0 1 Gender2 108 0.611 0.490 0 1 Age1 108 11.537 0.571 10 13 Age2 108 11.537 0.571 10 13 Dependent variables Performance1 108 11.389 3.825 2 20 Performance2diff 108 0.593 2.484 -6 5 Teamperformance 108 23.370 5.368 11 36
3.6 Analyzing the results
To analyse the results, several one-sample t-tests, two-sample t-tests and OLS regressions are done. One-sample t-tests are used to test if subjects made the optimal strategic decisions or not. Here, an one-sample t-test is used, because it compares the mean score of the strategic decisions to a halve, to test if a significant part of the subjects made the strategic decision or not. Also two-sample t-tests are used, because it indicates whether there exists a statistically significant difference between the two group means. The two groups are differentiated between a group where the first player is confident and a group where the first player is not confident. Therefore, the factor variable is for all hypotheses the variable ‘confidence’. The responding variable is dependent on the hypotheses which are tested. These are mentioned in paragraph 3.5: performance1, performance2diff & teamperformance. Actually, after
observing the results of several two-sample t-tests, it is not sure if the results are totally reliable. Aided by the two-sample t-tests, it can be concluded if there exists a statistically significant difference between the means of the two confident groups. Actually, it is hard to conclude if these results significantly differ due to only the differences in confidence. There could be some coincidence, where other factors could have affected the results and did result in the differences in group means. To test if other variables did affect the results, OLS-regressions are used. An OLS-regression uses the observed data and approaches to fitting a model. The most important independent variable for all regressions is the variable
‘confidence’. The dependent variables are the same as mentioned above. In every model, some control variables are added to investigate if the effect of the variable ‘confidence’ changed when adding these control variables. In other words, some robustness checks are done to examine how certain the coefficient of ‘confidence’ is when regressors are added.
4. Results and analysis
4.1 Results
4.1.1 Testing hypothesis 1 & 2
To answer the research question, eight hypotheses should be tested. First, the results are analysed by some simple calculations and tables. Second, the results are analysed by doing some statistical tests.
Hypothesis 1:
H0: there is no difference between the number of good solutions of confident and
non-confident agents in the complements treatment
H1: confident agents will have more good solutions than non-confident agents in the
complements treatment
Hypothesis 2:
H0: there is no difference between the number of good solutions of confident and
non-confident agents in the substitutes treatment
H1: confident agents will have more good solutions than non-confident agents in the
substitutes treatment
To test both hypotheses, the number of good solutions of all first players will be compared for confident agents and non-confident agents, for both treatments separated. Two-sample t-tests showed that in the complements treatment, the number of good solutions for the two groups differed significantly (p ≈ .005). For the substitutes treatment, the number of good solutions between the two confident groups differed also significantly (p ≈ .057). In the OLS-regressions, after there have been added some control variables, the positive effect of
confidence on ‘performance1’ in both treatments was still significant. Therefore, it could be concluded that both the H0 of Hypothesis 1 as the H0 of Hypothesis 2 could be rejected, for
Hypothesis 1 with a 1% significance level and for Hypothesis 2 with a 10% significance level.
Graph 1. Average number of good solutions of player 1
In Graph 1, the number of good solutions of confident agents and non-confident agents are shown. For both treatments, the confident agents seemed to perform better than the non-confident agents.
For both treatments, it is shown in Table 5 that confident subjects performed better than non-confident subjects. Performanceis measured with the number of good solutions. In the complements treatment, the difference between confident agents and non-confident agents is 3.21 good solutions and in the substitutes treatment, the difference is 2.19 good solutions. It is also shown that in both treatments, the confident subjects had performance levels above the average performance level of both the experiments.
Table 5. Performance of confident and non-confident agents
Treatment Confidence Average performance of Player 1
Complements No 26% 9.14
Yes 74% 12.35
Substitutes No 31% 9.76
Yes 69% 11.95
Total 11.39
Two-sample t-tests were conducted to test for differences in the number of good solutions between the group with confident agents and group with non-confident agents. In the complements treatment, there was a significant difference between both the confident groups, t(52) = -2.94, p ≈ .005, with confident agents having a higher number of good solutions than non-confident agents. In the substitutes treatment, there was also a significant difference between the confident groups, t(52) = -1.95, p ≈ .057, with again confident agents having a higher number of good solutions than non-confident agents. But, the significance for the complements treatment was lower than the significance for the substitutes treatment. Besides the two-sample t-test, also two OLS-regressions were conducted. When adding some control variables, it is investigated if the effect of confidence on ‘performance1’ did change. In other words, some robustness checks are done.
In Table 6, the OLS-regression shows the relationship between one or more
independent variables and ‘performance1’, in the complements treatment is shown. The most important independent variable is ‘confidence’. There are added some control variables in Column (2), (3) and (4) to check if the results are robust. Column (1) showed that being confident resulted in an increase of 3.2 good solutions for player 1 in the complements treatment, compared to the situation where this dummy variable is equal to zero. In other
words, being confident resulted in an increase of 3.2 good solutions compared to a situation where an agent is non-confident. This result is significant at the 1% significance level.
Table 6. Complements treatment: Confidence and individual
performance
Dependent variable: performance1
(1) (2) (3) (4) Confidence 3.207*** 3.228*** 3.193*** 3.224*** (1.090) (1.093) (1.112) (1.133) School -0.842 -1.060 -1.086 (0.958) (1.034) (1.054) Gender1 -0.473 -0.509 (1.034) (1.059) Gender2 -0.473 -0.539 (1.034) (1.058) Age1 -0.427 (0.883) Age2 -0.270 (0.885) Constant 9.143 9.564 10.281 18.370 (0.938) (1.055) (1.569) (15.222) R-squared 0.1427 0.1555 0.1622 0.1675 Observations 54 54 54 54
Note: OLS Regression
* significant at 10% level ** significant at 5% level *** significant at 1% level
After the control variable ‘school’ has been added in Column (2), there is no difference in the significance of the coefficient of ‘confidence’. The coefficient actually increased with 0.02 good solutions, still significant at the 1% significance level. In column (3), the control variables for gender are added. Adding gender variables did again not change the significance of ‘confidence’. Adding gender and school control variables decreased the effect of confidence on the number of good solutions of player 1 with 0.01 good solutions, compared with the situation in Column (1), but the effect is still significant at the 1%
significance level. In the last column of Table 6, controls for age are also added. Adding age, gender and school variables actually increased the effect of confidence on the number of good
solutions of player 1 with 0.02 good solutions, compared to column (1), and the effect is still significant at the 1% significance level. As a results, adding control variables did not change the results. Also, the R-squared, the ratio of the regression variance to total variance, stayed quite constant in the three columns. The ratio is not very high, which means that the variances of the regression did not declare much of the total variance. This result could have a lot of causes, but does not have to be a negative effect. In fields where experimenters try to predict human behaviour, the R-squared has values lower than 50%. This is because human
behaviour is hard to predict. Although the R-squared is low, this OLS-regression had significant results. Therefore, it can be concluded that confidence had a positive significant effect on the number of good solutions in the complements treatment. As a result, the H0 of
Hypothesis 1 can be rejected.
Table 7. Substitutes treatment: confidence and individual performance
Dependent variable: performance1
(1) (2) (3) (4) Confidence 2.181* 2.039* 1.958* 2.147* (1.121) (1.117) (1.132) (1.156) School -1.398 -1.730 -1.757 (1.038) (1.122) (1.131) Gender1 -1.099 -1.293 (1.118) (1.140) Gender2 -0.310 -0.303 (1.115) (1.132) Age1 -0.963 (0.959) Age2 0.681 (0.965) Constant 9.765 10.587 11.676 14.934 (0.928) (1.105) (1.700) (14.172) R-squared 0.0679 0.0999 0.1175 0.1406 Observations 54 54 54 54
Note: OLS Regression
* significant at 10% level ** significant at 5% level *** significant at 1% level
In Table 7, the results of the OLS regression for the substitutes treatment are shown. Here, also the effect of confidence, the most important independent variable, on the number of good solutions for player 1 is measured. In column (1), it is shown that ‘confidence’ had a significant effect on ‘performancel’, being confident (confidence = 1) increased the number of good solutions with 2.18 good solutions. This result is significant at the 10% significance level. Again, in column (2), column (3) and column (4) control variables are added to check for robust results. After the control variable ‘school’ is added, the effect of ‘confidence’ decreased a little, but the effect remained still significant at the 10% significance level. In column (3), adding gender and school control variables did not change the significance of ‘confidence’. The effect of being confident is still significant at the 10% significance level and did increase the number of good solutions of player 1 with 1.96 good solutions, which is a lower number than the positive amount of good solutions in column (1). In column (4), also the control variables for age are added. Adding the gender, age and school variables did again not change the significance of ‘confidence’. Being confident is still significant at the 10% significance level and did result in an increase in good solutions of 2.15 good solutions. Therefore, the inclusion of control variables do not affect the central message of this paper with regard to confidence. The R-squared is again low, but due to the significant coefficient of ‘confidence’, the H0 of Hypothesis 2 can be rejected. Confident agents do exert more effort
than non-confident agents, in both the treatments.
4.1.2 Testing hypothesis 3 & 4
Another important aspect of this research are the strategic decisions on the confidence questions. Because each subject had to answer the confidence question two times, the total confidence observations count up to 108 observations.
Hypothesis 3:
H0: in the complements treatment, the rate of subjects who answered ‘yes’ on the confidence
question ≤ 0.5
H1: in the complements treatment, the rate of subjects who answered ‘yes’ on the confidence
