Master’s Thesis:
Confidence Level as a Strategic Tool
Theodoros Rodopoulos
Student ID: 11829737
University of Amsterdam
MSc Business Economics - Specialisation Managerial Economics and Strategy
July 15, 2018
Supervisor:
This document is written by Student Theodoros Rodopoulos who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are 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.
Abstract
In this paper we test experimentally whether people use their overconfidence and
underconfidence in a strategic way, and we find compelling evidence that they actually do. At first subjects perform a neutral task of adding three two-digit numbers and then they have to make an evaluation of their performance relative to the others. Then subjects are assigned to groups of two without knowing the identity of their groupmate and they perform the same task. There are two treatments in this experiment. In treatment 1 efforts are complements, as each needs one another to solve a specific amount of additions, while in treatment 2 efforts are substitutes, as they need to solve correctly a specific amount of additions as a team. Before the task is done, one party sends a message to the other party whether they feel overconfident/ underconfident about their skills in that task. We focus on the signaling value of overconfidence, where appearing overconfident about ones skills, can rightly or wrongly persuade the others. The hypothesis is that when efforts are complements subjects appear more overconfident, than when efforts are substitutes. Results are in line with the hypothesis and they are significant.
1. Introduction
Every day we make many decisions possessed by our overconfidence. Overconfidence is the most frequent, dominant and consistent psychological bias (Johnson & Fowler, 2011). In real life some tasks demand an exertion of effort from all parties, while in others this does not affect the outcome. In many economic models there is the basic assumption that agents are rational and biases in beliefs do not exist. Based on this assumption, the idea is that agents who keep accurate beliefs are rewarded, and in turn wrong beliefs are are eventually discarded. However, one being or appearing rational is not always the best strategy for maximizing benefits over costs when competition, increasing effort cost and uncertainty exist. In groups, it may be in one’s interest to appear confident in order to boost your partner’s motivation, so they will exert the efficient effort level. For instance, when efforts are complements, both parties need to exert their efficient effort levels so to achieve the shared goal. In this paper we use the term “complement efforts” for an effort that is used in conjunction with another effort. Specifically the complementary good has little to no value
when consumed alone, but when combined with another effort, it adds to the overall value of the offering. An effort can be considered complement when it shares a beneficial relationship with another effort offering. Kelsey and Spanjers (2004) showed how the ambiguity aversion of some agents leads them to use personal effort as insurance for the effort of others, thereby alleviating free-riding. But exerting effort is costly. Agent 1 has incentives to exert the efficient effort level, only if she thinks that the other parties will exert the efficient effort level. On the other hand, when we refer to “substitute efforts” we mean that the effort of one party, has the same value to the effort of the other party, and that the exerted effort of only one party is enough to completely satisfy the need for effort from the team. When efforts are substitutes and only one party’s effort is enough to obtain the payoff, optimal strategy alters. The subject has incentives to appear not so confident in order to persuade the other parties to put in more effort because they expect their teammates to exert not much effort, or effort of low quality. The more effort the one party invests, the less effort the other party has to invest to reach the goal.
Overconfidence is the excessive degree of a person’s subjective confidence in her
judgements over the actual accuracy of those judgements. It can also be stated as an example of miscalibration of subjective probabilities. Kahneman (2011) describes overconfidence as the most serious type of bias due to the fact that people’s judgement is very susceptible to it. Siwar (2011) defines overconfidence as the tendency of individuals to overestimate the precision of the available information. Overconfidence is divided in two categories; absolute and relative overconfidence. Absolute overconfidence can be identified as the overestimation of one’s actual performance, while relative overconfidence is “overplacement” (Moore & Healy, 2008) of one’s performance among others. Another study suggests that overplacement derives from one’s desire to see oneself in a positive way (Blanton et al., 2001). Other used forms of overconfidence (Herz et. al., 2014) are overoptimism (a tendency to overestimate one’s chances of success) and judgemental overconfidence (a tendency to overestimate the precision of information). Additionally, Moore and Heally (2008) find that in easy tasks subjects tend to appear underconfident but still overplace themselves among the others, while in difficult tasks people overestimate their performance and at the same time underplace themselves. Their hypothesis is that people are imperfectly informed about the performance of others. This results in inflated belief about own performance, and even more inflated belief about others’ performance. The experimental evidence they end up with support the
hypothesis. Moreover, the results of Hoelzl and Rustichini (2005) go along with this evidence.
In this paper we investigate whether people adjust their confidence levels according to the task and if they use their bias strategically. We use insights from economics and psychology to study the effect of overconfidence on effort provision and strategy followed in different group tasks. We focus more on the signaling value of overconfidence. This paper is organised as follows. Section 2 refers to the related literature. Section 3 describes our main model in which an agent performs the task of adding three two-digit numbers individually and then she has to indicate her relative performance among the other subjects. Then subjects are randomly paired and play a dictator game without knowing who their partner is. In this way, their social preferences will be revealed, protecting their social status and reputation. Then, in treatment 1 groups have to solve the same task, where their effort levels are complements. In treatment 2 the same procedure will be followed, with the only exception that now their effort levels are substitutes. Section 4 presents the hypotheses and the support of them with the aid of Nash Equilibrium and the related literature. Section 5 includes the results of the experiment. Various extensions of the model are considered in Section 6. Finally, Section 7 offers some empirical implications of our model, discusses a number of applications, and concludes.
2. Related Literature
There are number of papers which examine overconfidence. Decisions made driven by overconfidence can have a serious economic impact both for the individual, and for markets. In a famous experiment by Dellavigna and Malmendier (2005), the authors show that people, possessed by overconfidence about their future self-control and future time investment in exercising, they end up paying double or even triple prices for going to the gym compared to what they could have paid if they had signed-up subscriptions related to their actual
appearance. A miscalibration of subjective knowledge in the form of overconfidence may lead consumers to buy a high-end digital camera that they think is consistent with their knowledge. In reality the camera is too complicated to be fully exploited (Burson, 2007). Michailova, Julija, Schmidt and Ulrich (2011) test for the effect of overconfidence on
individual’s behavior and how this relates to market bubbles. They find a correlation between these two forces. Furthermore, it is widely known that most new businesses fail within the first few years (Potts, 1977). Even though starters know about it, they think that they will be an exception but the overwhelming majority of them end up being bankrupted (Cooper, Woo, and Dunkelberg ,1988; Camerer and Lovallo, 1999; Koellinger, Minniti, and Schade, 2007). There is evidence that overconfident CEOs and individual investors are likely to trade more
(Odean, 1998, 1999; Barber and Odean, 2001; Heaton, 2002; Malmendier and Tate, 2005; Grinblatt and Keloharju, 2009).
It is crucial for the success of group tasks that team members are cooperating and
coordinating effectively. However, even when synergistic factors are brought together in one firm, the attainment of their potential value is not occurring automatically. The main
problems in team tasks when the agents’ effort choices are not observable, are the moral hazard and free-riding problem (Holmstrom, 1982). Overconfidence may have a positive effect on individuals and groups as someone who overestimates her own marginal
productivity works harder, thereby increasing the marginal productivity of her teammates who then work harder as well (Gervais and Goldstein, 2004 a). Moreover, the overconfidence bias seems to be correlated with motivation. Individual effort provision is increasing in beliefs about own productivity (Bénabou and Tirole, 2002 a; Chen and Schildberg-Hörisch, 2017).
Individuals are overconfident not only about their own performance but also about the performance of their group relative to other groups. This overconfidence can have severe consequences for the economy. It is not an overstatement to say the overconfidence of some individuals caused several global disasters. Johnson and Fowler (2011) blame overconfidence to be a cause of the First World War, Climate Change, and even the 2008 Financial Crisis. There is evidence that groups are more rational (Bornstein and Yaniv, 1998), and so more accurate in their evaluations. Interestingly, competition among teams leads individuals to perceive, in-group members as more favorable personalities than members of the rival groups (Wilson and Miller, 1961), even when they have been randomly assigned in these groups. Group identity has been shown to create in-group favoritism and reduce within-group conflict. As a result, overconfidence within group-members reduced (Brookins et al., 2014).
“Believing in oneself” is one of the main drivers of personal success (James, 1890). The maintenance and development of self-esteem has always been identified as a human instinct of vital importance. High self-esteem can be used as a good measure of beneficial self-deception, which is positive for promoting mental health and adjustment of the person (Taylor and Brown, 1988a). Koszegi (2006) confirms it by using a formal economic model of overconfidence and ego utility, in which an agent increases his or her internal interests by having a positive view about his or her skills. Overconfidence is beneficial on average, even if sometimes it is costly, because it enhances ambition, morale, resolve, persistence, or the credibility of bluffing. Bénabou and Tirole (2002 b) pinpoint three main reasons why people may prefer optimistic self-views to accurate ones: the consumption value (or ego value by Koszegi, 2006), the motivation value and the signaling value. Firstly, on the one hand people may extract utility from thinking positive of themselves (Sedikedes and Gregg, 2008;
Fabricius and Büttgen, 2013), and on the other hand they perceive a poor self-image hurtful. A positive reflection of themselves makes people happier and helps to create a psychological safety for them (Roberts, Dutton, Spreitzer, Heaphy, and Quinn, 2005). Secondly, one convincing oneself about their abilities and efficacy can motivate the individual to engage in more challenging goals, reach higher performance levels and keep going on despite any obstacles, failures, or lack of willpower under bad circumstances (Taylor and Brown, 1988; Benabou and Tirole, 2002; Compte and Postlewaite, 2004; Weinberg, 2009). Confidence level works as a leverage to undertake difficult tasks and go all the way until they are fulfilled. In addition, it applies to economic motivations, as people are more willing to cooperate with confident coworkers, employees, managers and teammates, instead of underconfident ones. Finally, appearing overconfident about one’s abilities or morale in a task, one can easily persuade others rightly or wrongly of it. Statements about one’s beliefs are often made to affect the beliefs, and hence the decisions of others. In this paper, we focus more on the signaling value of confidence level.
There is another theory which supports that the benefits of overconfidence are social in nature. Robert Trivers states that overconfidence, or self-deception more widely, allows people to convince or deceive others about one’s competencies as it makes the need for conscious deception unnecessary (Trivers, 1985, 2011; Von Hippel and Trivers, 2011). It is often said that to lie most convincingly a person must believe his own lies.The idea is that those who doubtlessly believe in their own skills confront lower costs when present an advantageously image of themselves to others.
Literature is mostly focused on establishing over-confidence in different tasks, with different populations, and/ or under specific circumstances. There is a lack of search on whether people use their confidence labels strategically. Rullière et al. (2011) study how perceptions of skill influence teamwork. Authors based their research on Gervais and Goldstein (2007) theory of teams, that skill and effort are complements, and workers’ effort choices are complements. Their results suggest that having overconfident agents in teams is beneficial for firms since it increases the exerted effort and team output. Moreover, they find that overconfidence leads to a Pareto improvement in employees’ payoffs, and that underconfident agents are detrimental to firms. Ewers (2012) studies the influence of information on entry choices in a competition with a controlled laboratory experiment. Their results suggest that aggregated information on the productivity distribution significantly reduces competition failure to the half. In both experiments subjects reveal their confidence level. In the first experimental design each individual perform a single task and they elicit their confidence level. They have to make an estimation of their performance relative to others and if they think they have performed better than the others and this is not accurate, then they assumed to be overconfident. In the next part the experimenters reveal the confidence status of each individual to her, but also to her partners to check the possibility that the perception of skill of the team partner influences a subject’s effort choice. In the second experimental design again they elicit each individual’s confidence level and in
treatment group they let the competitors of each agent knows, while in the control group they do not. In both experiments people transmit their confidence state to others, but not in a strategic way. Senders reveal their confidence level without knowing that this information is shown to others.
Ewers and Zimmermann (2015) find evidence that appearing overconfident is a consequence of social approval seeking. They demonstrate that the desire to impress an audience causes experimental subjects to publicly state higher confidence when these reports are to be viewed by the audience, than when these reports remain private. Also in this case there is no strategic background that can influence the confidence level.
Schwardmann and van der Weele (2018) conducted an experiment to test the hypothesis that people become overconfident in order to more effectively persuade or deceive others. In the first part there was a cognitively challenging task. In the treatment group subject had to persuade others about their superiority in that task. They concluded that information about a persuasion opportunity increases confidence. Participants perceive a confident person as a more persuasive one. There is also evidence that confident participants are more likely to convince others in face-to-face interactions. Thoma (2015) shows that men strategically exaggerate their confidence in order to appear more attractive.
Charness, Rustichini and van de Ven (2014) try to fill the gap in literature of overconfidence and its use in a strategic way, by using a model where agent 1 sends a strategic message about her abilities in a tournament, and agent 2 (the receiver) has to decide whether he enters the competition or not. The message need not be truthful. If the receiver chooses to enter, then both players compete in their tournament, and their payoffs are determined by their abilities. The strong player has an incentive to appear underconfident, so that her opponent enters the competition, and end up with a higher payoff than her outside option. When the player is weaker than his opponent, he has an incentive to choose his outside option. In this experimental environment, the majority of individuals converge to the equilibrium. Their main conclusion is that agents use their confidence level strategically, unconsciously most of the times. In our experimental design, subjects form a group and they are asked to exert effort. Their efforts can be complements or substitutes.
3. Experimental design
The experiment was conducted over three different days. Three sessions were run with 12 participants in each session. The subject pool aged from 20 to 26 years old. They were people from different cultural and educational backgrounds (Greeks, French, Spanish, Germans, Mexican, Norwegian) (Economics and Business studies, Law, Philosophy, and people who have just finished High School). 42 percent of these subjects were female. Instructions for
every part were given to them at the end of each part. Participants were told that their decisions and their identity would remain anonymous throughout the whole experiment and also after that. The participants who were randomly paid earned on average Euro 4.67 in about 1.5 hour at the end, in private.
The session was constructed in 4 different parts. Subjects played 2 rounds in the first part, (specific instruction sheets were distributed for every part, see appendix). Participants were randomly allocated in the room, and they all received a random ID that they had to keep for the whole experiment and write down in every task they performed during the session. This ID indicates their role in the group task. Players were randomly given the role of sender or receiver (in the instructions we always used neutral labels “A” and “B” for the two roles); each sender was randomly matched with one receiver. Subjects did not yet know what each ID meant for the procedure (A players: Y2, Y4, Y6 and so on. B players Y1, Y3, Y5 and so forth). In the group task player A, Y2 is paired with player B, Y11. Player A Y4 is paired with player B, Y9 and so forth. In the following scheme we can see the disposition of th9 participants in the room:
With this allocation we ensured that partners from the same group would not be seated together, and additionally agents with the same role would not be seated together to avoid communication between each other. Agent A was never seated with a participant from the same group or with partner.
In the first part subjects had thirty (30) seconds to solve as many problems as they could, and did not get any feedback after completion on the number of questions they answered. Then they were asked to estimate their performance by comparing themselves with respect to
a pool of the other 11 subjects. All participants received the same problems. Each subject receives a page with twelve problems to solve. The reward structure was based on a performance payoff and a bonus. In every round participants could receive 1 token (0.1 €) for every correct answer and 10 tokens bonus if their performance estimation was accurate. Payments were presented in tokens. Subjects performed this task in two rounds in order to become familiar with the task and make more accurate predictions about their performance. This appraisal was needed to control the confidence level of each individual in this task. Participants knew that they would be asked to evaluate their performance later and earn some extra money if their estimation was accurate, when they were doing the task. Below you can see an example of the task:
21+86+93= 15+83+68=
The evaluation form was like this:
“Out of my pool of __ participants I think __ participants did strictly better than me. “
In order to take care of the framing effect, in one treatment group the evaluation form that was given was like this:
“Out of my pool of __ participants I think I performed strictly better than __ participants” In the second part of the experiment subjects had to play a dictator game. Agent A was paired with agent B, that would be their group partner also in the third and fourth part of the experiment. Subjects did not know their partner’s identity, nor that they would form a team together later in the experiment, in order to control for reputation motives. Social preferences are a type of preferences studied in behavioral, experimental and social psychology, and include interpersonal altruism, fairness, reciprocity and inequity aversion. Based on these preferences individuals might make a decision which does not maximize their monetary utility. One of the basic assumptions in economics is that individual want to maximize their utility. The dictator game is important in our research, in order to control for the social preferences of each individual that could explain possible deviation from appearing under-confident when effort levels are substitutes. In this game, the best strategy for the sender is to send zero (0) tokens to the other agent so to maximize their monetary utility. An amount of one hundred (100) tokens had to be distributed. Subjects played the dictator game for three (3) rounds so they had the opportunity for the learning effect and converge to the equilibrium.
In Part 3 subjects had to perform the same task in groups. Each subject was endowed with 30 tokens. Subjects played 5 rounds in order to let them reach the equilibrium. Each round
last sixty (60) seconds. In this part efforts of each subject were complements and in order for the task to be completed, each member had to correctly solve 6 problems. In Part 4 efforts were substitutes and the task was to solve correctly 12 problems as a team. For each problem solved, the subject sacrificed 1 token, which would be refunded if the solution was correct, whether the task was completed successfully by the team or not. In this way the effort becomes costly, and at the same time we control for the loss-aversion effect. Some subjects may experience greater disutility from losing their endowment, than receiving the bonus if they have reached the goal as a team. Players could still retain their endowment amount if their answers given were correct, despite their partner’s performance. If the team has reached the goal, then a bonus of 40 tokens would be distributed equally to the team members. At the beginning of the task, agent 1 had to send a strategic message to their partner whether they feel confident about their ability in the task or not. Each agent 1 had to write down the word “CONFIDENT” or “UNDERCONFIDENT” on a form. Then all forms were collected and were distributed to their partners. In this way we ensured that both parties would remain anonymous. After that subjects performed the task. The same procedure was followed for 5 rounds. In one session, subjects performed Part 4 before Part 3 in order to ensure for the order effect. Sessions ended with a questionnaire.
4. Hypotheses
Literature supports that not only can overconfidence bias make the team more effective by naturally overcoming the common free-rider and effort coordination problems, but it can also make both agents, including the overconfident one, better off (Kelsey and Spanjers, 2004). The idea is that agents who overestimate their marginal productivity work harder (Gervais and Goldstein, 2007 a). This extra effort directly reduces free-riding; however, where there are complementarities between agents it does even more because the effort of one agent increases the marginal productivity of the other, and as a result they too find that their effort is more valuable. In turn, the second agent also exerts more effort, thereby making the team even more productive (Gervais and Goldstein, 2004 b). When the production synergies between the two agents are substantial, even the biased agent ends up benefiting from her inflated investment in effort, as they share the benefits of their colleague’s extra effort (but still suffers the cost of their own overinvestment). Therefore, in our setting, an overconfident agent can increase a firm’s value by raising the equilibrium levels of effort and generate a Pareto improvement. Appearing overconfident implies no cost, and at the same time both agents are motivated to exert more effort and become better off.
At the time each agent make their effort decision, they do not know how much effort the other will exert, but anticipate the equilibrium level. When efforts are complements, both agents need to exert effort to reach the shared goal. By appearing overconfident agent 1 reaps the benefits of the consumption, motivating and signaling value of overconfidence, as they
create a psychological safety, they are more willing to undertake the task, and at the same time they convince their partner about their abilities. In turn, agent 1’s effort provision becomes clearer. Agent 2 assumes agent 1 will exert the efficient effort level, so now they have strong motives to invest effort and extract the full value from potential synergy.
Assume that α1 is the required effort level of agent 1 and α2 is the required effort level of agent 2. In order to obtain the bonus, they both need to exert their efficient effort level. Agent 2 does not know how much effort their partner will invest. By sending a strategic message showing that they believe in their abilities, agent 1 signals that they will exert the required effort level. In turn, the risk that agent 2 exerts effort α2 and does not get the bonus is reduced, as now their colleague declares that they will perform their task. Hence agent 2 anticipates that if they contributes α2 effort level, they will get the bonus, so they are more incentivized. Alongside, agent 1 has an inducement to contribute the required effort level α1 and, accordingly reach the team goal. Thus, our first hypothesis is formulated:
● Hypothesis 1: When effort levels are complements, subjects will appear confident.
On the other hand, Gervais and Goldstein (2007 b) proved that when one agent’s effort is a substitute for another agent, overconfidence can only make one worse off, as the associate then diminishes her own effort. We can see that in an equilibrium. Assume that a team consists of two members. There is a shared goal which benefits both members. The marginal benefit of the attainment of the target, is always greater than the effort cost. In a task that it can be measured, rational agents would probably split the duties equally, so they both exert the same effort level and reach the objective. The difference with the previous model is that the effort levels of the agents are substitutes, so that the bonus can be obtained even if only one agent puts effort on that. Thus, agent 1 has an incentive to send a strategic message convincing their partner that they lack the abilities for that specific task. In this way, agent 1 signals that they will not invest the required effort level, and “force” agent 2 to exert more effort for the fulfillment of the objection.
Assume that α1 is the required effort level of agent 1 and α2 is the required effort level of agent 2. In order to obtain the bonus, they both need to exert their required effort level. Agent 2 does not know how much effort their partner will invest. Exerting effort is costly for agent 1. By sending a strategic message showing that they do not believe in her abilities, agent 1 signals that they will not exert the required effort level, or that their effort will be of low quality (solve additions but with lower percentage of finding the correct result). As follows, agent 1 will maximize her utility, by minimizing the effort cost. In turn, agent 2 anticipates that in order to increase the probabilities of getting the bonus, they need to overexert their effort. Even under those circumstances, agent 2 will be better-off, as the marginal benefit of getting the bonus overwhelms the marginal cost of exerting effort. In addition, by using this strategy agent 1 ensures that their collaborative exerts at least their required effort level, and
the probabilities of obtaining the bonus are increased. Suppose that agent 1 signals that they feel overconfident about their abilities in the task. Then, agent 2 may feel reassured and exert less than the efficient effort level so that their cost is diminished. In turn, the probabilities of gaining the prize are decreased. Thus, our second hypothesis is formulated:
● Hypothesis 2: When effort levels are substitutes, subjects will appear less confident.
5. Experimental Results
5.1. Overconfidence: Summary statistics are reported in Table 1. In total we have 72 observations for the confidence level of subjects, where 42% of them are females and 58% males. Estimation error is defined as the difference between the estimation of the number of subjects that did strictly better minus the number of subjects that actually did better. We define as overconfident those agents whose estimation error is negative. In that sense, we define rational agents those with a zero estimation error, and accordingly underconfident those who have a positive estimation error. The average age of participants is 23.42 with standard error 0.27, minimum age 20 and maximum 26 years old. All participants have a western social background. In specific 72% of them are Greek, 8% Spanish, 5% French and German respectively, while 3.3% are Mexican, Norwegian and Italian. In the first round 53% of subjects are overconfident, while only 11.1% are rational and the rest are underconfident. This supports the theory that more than half of the people believe they belong to the higher 50% in various tasks. In our case the task is adding three two-digit numbers. In the next round 42% of individuals are overconfident, while 28% of them are rational and the rest underconfident. We observe a tendency of subjects to become more rational through rounds and we believe that in an infinite time of rounds people would become fully rational. We do not give feedback to subjects after the end of each round about their performance, nor about their confidence status. The increase in accuracy in round 2 can be attributed to the learning effect, as the setting of the experiment has not changed. Additionally none of the subjects expected to be the worst in any round of the experiment.
5.2. Social Preferences: Statistics are reported in Table 1. In total we have 54 observations for the dictator game in three rounds. We observe that subjects tend to have social preferences. Particularly, in the first round agents send 38.83 tokens on average with minimum value zero tokens and maximum the whole amount (100). Receivers then just look at the amount that has been distributed to them. Without any impact on their decision senders distribute less tokens in the next two rounds. They deliver 28.39 and 19 tokens respectively. The minimum value remains the same, while in round 2 and round 3 the maximum price is 70
and 50 tokens respectively. In the second round people distribute less tokens. We conclude that subjects do care for their partner even if they do not know their identity. Moreover, they do not know what the next part will be and that they will work in teams to get a bonus. We use this part of the experiment as a control variable which can explain why people might not decide rationally.
5.3 Results When Efforts Are Complements
5.3.1 Confidence Level When Efforts Are Complements: Statistics are reported in Table 2. In total we have 90 observations of the strategic message subjects send, and the effort exerted. We see that subjects appear overconfident in 71% of cases when efforts are complements.
In addition, we set Overcocfor#R variable to check how many senders remain overconfident for a number of rounds. Results are reported in Table 2. We see that 50% of the senders appear overconfident for all 5 rounds, while only 11.1% remain underconfident throughout this whole part.
5.3.2.1 Effort Level Exerted when Efforts are Complements: Results are reported in Table 4. The mean value of effort exerted by agent 1 is 5.01, while agent 2 exerts on average 5.42. The minimum exerted effort by agent 1 is 1 and the maximum 10. For agent 2 they are 1 and
9 respectively. We observe that there are people who exert even more than the optimal effort level, even though they cannot influence the outcome of their team.
5.3.2.2 Effort of Agent 2 when Agent 1 appears Overconfident: In this part we want to check the effort level exerted by agent 2 when agent 1 appears overconfident when their efforts are complements. Results are reported in Table 6. The mean effort of agent 2 when their partner feels confident about their skills in this task is 5.33 with standard error 0.21. The minimum value of exerted effort is 1 and the maximum is 9. Throughout the rounds we see that keep appearing overconfident increases the effort of agent 2. The highest mean value of effort appears in the last round of the treatment (mean = 5.85), while the lowest mean value of effort appears in the first round (mean = 4.47). The increase in effort in Part 3 can also be attributed to the learning effect, as the setting of the experiment has not changed.
5.3.2.3 Effort of Agent 2 when Agent 1 appears Underconfident: Accordingly, in this part
we check the effort level exerted by agent 2 when agent 1 appears underconfident when their efforts are complements. Results are reported in Table 6. The mean effort of agent 2 when their partner feels less confident about their skills in this task is 5.72 with standard error 0.17. The minimum value of exerted effort is 4 and the maximum is 8.We see that appearing underconfident has no statistically significant difference in the exerted effort between rounds.
Table 6
5.3.2.3 Reward When Efforts are Complements: Teams accomplish to get the bonus in 33.3% of times. We want to check whether appearing overconfident is actually the best strategy. Results are reported in Figure 1. This is done by examining after each message sent, whether teams get the bonus. In Figure 1 we observe the percentage of success of groups. We set as 1 when goal is achieved and 0 when it is not. Indeed, when agent 1 signal that they feel overconfident about their skills in that task, team units get the bonus in 36% of cases, while when agent 1 appear underconfident teams get the bonus in 27% of cases.
Figure 1
In order to take care for possible correlation between the outcome of the previous round and the message that people send at the next round we check for correlation between those two coefficients. For that reason, we can only model the correlation between the message sent and the result of the previous rounds between rounds 2 and 5 only. Results are reported in Table 7. We find that there is a negative correlation -0.047, between overconfidence level and the outcome of previous round which is not statistically significant. These coefficients are perfectly positive correlated, normally distributed and they have a linear relationship. Subjects appear overconfident despite the outcome of the previous round and this suggest that people use their confidence as a strategic tool to persuade others about their skills and motivate them to exert effort as well and get the bonus.
Table 7
5.3.4. Message: Yimessage = β0 + β1 X1ieffort + β2 X2ireward + β3 X3isignal + β4 X4i status + β5 X5isocpref +
β6 X6iage + β7 X7ieducation + β8 X8igender + β9 X9inationality + ui
In the end we want to check what drives individuals to send this message when efforts are
complements. We set the “Message” agent 1 sends in each round as the dependent variable. As independent variables we set the effort of the agent in the current round, the result of the
previous round (whether they got the bonus or not), the message sent in the previous round, the confidence status, the social preferences, the age, the educational background, the gender, and the nationality of the subject. The confidence status of the agent derives from the the last round of Part 1, while social preferences are derived as the tokens the agent distributes in the last round of Part 2. In this way, we can only model the message sent between rounds 2 and 5. We have in total 72 observations in this regression, where i=1,...,4 are the observations of the first subject in each round, i=5,...,8 the observations of the second subject in each round, and so on. We set as β 0 the intercept and as u i the error term. Our dependent variable is a dummy variable. We run a chi squared test in order to check our model against a model with only the intercept. Instead of the mean value in the model we use a logit transformation of the mean. Logit has better interpretation than probit. Logistic regression can be interpreted as modeling log odds (Paap and Franses, 2000). Results are reported in Table 8. We conclude that only the effort of this round has a statistically significant impact on the message sent. We find that for every unit change in the effort in the current round, the log odds of appearing overconfident, compared to appearing underconfident, decreases by 0.79 (Z = -2.876 , p = 0.00403). The indicator variables for the result of the previous round have a slightly different interpretation. They show that getting the bonus in the previous round, compared to not getting the bonus, will change the log odds of the message by 1.107 (Z = 1.123, p = 0.26). The indicator variables for the message sent in round 3 and 5, compared to the message sent in round 2, will decrease the log odds of the message by 0.253 (Z = -0.287, p = 0.77), and 0.438 (Z = -0.404, p = 0.686) respectively. Accordingly, the indicator variables for the message sent in round 4 compared to the message sent in round 2, will increase the log odds of the message by 0.46 (Z = 0.481, p = 0.63). The agents who are proved to be rational, compared to the overconfident ones, will change the log odds of appearing overconfident by 0.929 (Z = 0.916, p = 0.36). On the other hand, if agent is underconfident, it will diminish the log odds of appearing overconfident by 1.49 (Z = -1.353, p = 0.17). For every one unit change in the age of the sender, the log odds of appearing overconfident (versus appearing underconfident) increases by 0.32 (Z = 1.195, p = 023). Being male compared to being female increases the log odds of appearing overconfident by 1.05 (Z = 1.359, p = 0.17). Having a university educational background compared to having graduated from a high school decreases the likelihood of appearing overconfident when efforts are complements by 0.816 (Z = -0.6, p = 0.548). For a one unit increase in the social preferences of the individual, the log odds of appearing overconfident increases by 0.025 (Z = 1.047, p =0.29). Finally, Greek and Spanish agents increase the log odds of appearing overconfident by 0.55 (Z = 0.38, p = 0.7) and 1.33 (Z = 0.822, p = 0.41) respectively, compared to French agents. On the other hand, Germans decrease the log odds of appearing overconfident by 16.24 (Z = 0.009, p = 0.99).
5.4 Results When Efforts Are Substitutes
5.4.1 Confidence Level When Efforts Are Substitutes: Statistics are reported in Table 9. In total we have 90 observations of the strategic message subjects send, and the effort exerted. We see that subjects appear overconfident in 64.4% of cases when efforts are substitutes. We can see that subjects appear less overconfident when efforts are substitutes and this confirms our hypothesis.
Again We set Overcocfor#R variable to check how many senders remain overconfident for a number of rounds. Results are shown in Table 7. We detect that only 44.4% of the senders appear overconfident for all 5 rounds, while 44.6% converge to the equilibrium after appearing overconfident in the first rounds.
5.4.2.1 Effort Level Exerted when Efforts are Substitutes: Results are reported in Table 11. The mean value of effort exerted by agent 1 is 5.68, while agent 2 exerts on average 6.08. The minimum exerted effort by agent 1 and also agent 2 is 2 and the maximum 9.
5.4.2.2 Effort of Agent 2 when Agent 1 appears Overconfident: In this part we want to check the effort level exerted by agent 2 when agent 1 appears overconfident and their efforts are substitutes. In Table 12 we can see how many people appear overconfident in this treatment and the effect that this signal has to their peer. The mean effort of agent 2 when their partner feels confident about their skills in this task is 5.8 with standard error 0.23. The minimum value of exerted effort is 2 and the maximum is 9. The highest mean value of effort appears in the fourth round of the treatment (mean=6.36).
5.4.2.3 Effort of Agent 2 when Agent 1 appears Underconfident: Accordingly, in this part
we check the effort level exerted by agent 2 when agent 1 appears underconfident and their efforts are substitutes. Results are reported in Table 13. The mean effort of agent 2 when their partner feels less confident about their skills in this task is 6.31 with standard error 0.27. The minimum value of exerted effort is 4 and the maximum is 8. We can observe that the greatest value of the mean effort exerted by agent 2 is in the last round. We see that appearing underconfident in this treatment has a statistically significant influence on the exerted effort by the receiver of the message. Those who receive an pessimistic message exert more effort, than those who receive a confident statement from their partner. This result provides proof that when agent 1 appears underconfident, she convinces her partner that she lacks the abilities for that specific task and “force” agent 2 to exert more effort for the fulfillment of the goal.
Table 13
5.4.3 Reward When Efforts are Substitutes: Subjects succeed to get the bonus in 69% of cases. We want to check whether appearing overconfident is actually the best strategy. To do so, we examine after each message sent, whether teams get the bonus. In Figure 2 we observe the percentage of success of groups. Again we set as 1 when goal is achieved and 0 when it is not. Results suggest that there is not statistically significant difference between the message sent and fraction of success. In particular, when agent 1 signals that she feels underconfident about her skills in that task, team units get the bonus in 69% of cases, while when agent 1 appears overconfident groups get the bonus in 71% of cases.
Figure 2
In order to take care for possible correlation between the outcome of the previous round and the message that people send at the next round we check for correlation between those two coefficients. For that reason, we can only model the correlation between the message sent and the result of the previous rounds only between rounds 2 and 5. Results are reported in Table 10. We find that there is a negative correlation -0.363 between overconfidence level and the outcome of previous round which is not statistically significant. These coefficients are perfectly positive correlated, normally distributed and they have a linear relationship. Subjects appear either overconfident or underconfident despite the outcome of the previous round and this suggest that people use their confidence as a strategic tool to either motivate or persuade others about their skills and stimulate them to exert their maximum effort and get the bonus.
5.4.4. Message: Yimessage = β0 + β1 X1ieffort + β2 X2ireward + β 3 X3isignal + β4 X4istatus + β5 X5isocialpref
+ β6 X6iage + β7 X7ieducation + β8 X8igender + β9 X9inationality + ui
In this part we seek to analyse what drives individuals to send this message when efforts are substitutes. Again, we set the “Message” agent 1 sends in each round as the dependent variable. Identically to what we did when efforts are complements, as independent variables we set the effort of the agent in the current round, the result of the previous round (whether they got the bonus or not), the message - signal sent in the previous round, the confidence status, the social preferences, the age, the educational background, the gender, and the nationality of the subject. The confidence status of the agent derives from the last round of Part 1, while social preferences are derived as the tokens the agent distributes in the last round of Part 2. In this way, we can only model the message sent between rounds 2 and 5. We have in total 72 observations in this regression, where i=1,...,4 are the observations of the first subject in each round, i=5,...,8 the observations of the second subject in each round, and so on. We set as β 0the intercept and as u i the error term. Our dependent variable is a dummy variable. We run a chi squared test in order to check our model against a model with only the intercept. Instead of the mean value in the model we use a logit transformation of the mean. Logistic regression can be interpreted as modeling log odds (Paap and Franses, 2000). Results are reported in Table 15. We conclude that the effort of this round has a highly statistically significant impact on the message sent. Moreover, the result of the previous round, the message sent in round 3, age, being Greek or Spanish have a statistically significant impact on the message sent in this treatment. We also observe that despite the fact that being underconfident in Part 1 of the experiment does not have a statistically significant impact on the message sent, although it is close to being significant. We find that for every unit change in the effort in the current round, the log odds of appearing overconfident, compared to appearing underconfident, decreases by 1.138 (Z = -2.76 , p = 0.0323). The indicator variables for the result of the previous round have a slightly different interpretation. They show that getting the bonus in the previous round, compared to not getting the bonus, will change the log odds of the message by -2.929 (Z = 1.123, p = 0.26). The indicator variables for the message sent in round 3, 4 and 5, compared to the message sent in round 2, will increase the log odds of the message by 2.18 (Z = 1.965, p = 0.049), 1.61 (Z = 1.358, p = 0.174), and 2.44 (Z = 1.95, p = 0.05) respectively. The agents who are proven to be rational, compared to the overconfident ones, will change the log odds of appearing overconfident by -3.045 (Z = -1.385, p = 0.166). On the other hand, if an agent is underconfident, it will diminish the log odds of appearing overconfident by 2.456 (Z = -1.768, p = 0.077). For every one unit change in the age of the sender, the log odds of appearing overconfident (versus appearing underconfident) decreases by 1.287 (Z = -2.066, p = 0.038). Being male compared to being female increases the log odds of appearing overconfident by 1.488 (Z = 1.139, p = 0.25). Having a university educational background compared to having been graduated from a High School increases the likelihood of appearing overconfident when efforts are substitutes by 2.595 (Z = 1.597, p = 0.11). For a one unit increase in the social preferences of the individual, the log odds of appearing overconfident increases by 0.021 (Z = 0.674, p
=0.5). Finally, Greek and Spanish agents increase the log odds of appearing overconfident by 3.23 (Z = 2.11, p = 0.034) and 5.77 (Z = 2.21, p = 0.027) respectively, compared to French agents. On the other hand, Germans change the log odds of appearing overconfident by -9.88 (Z = -0.005, p = 0.995).
5.5 Comparison of the Results of the Two Treatments
Comparing the results of the two treatments we conclude that both our hypotheses are confirmed. Individuals use their confidence level in a strategic way. More specific, in Part 3 where efforts are complements, people have an incentive to appear more overconfident to their partner, while in Part 4 where efforts are substitutes, people have an incentive to appear less overconfident. Indeed, subjects appear overconfident in 71.1% of cases in Part 3, compare to Part 4 where agents appear overconfident in 64.4% of cases (see Tables 2 and 9). We run a chi squared test to control if there is any statistical difference between the message sent between Part 3 and Part 4. We find that the difference is statistically significantly different from zero (x2 = 6.52, p = 0.01).
Moreover, the tendency to remain overconfident in the latter part is 44.4% (see Table 10), while in Part 3 this occurs in 50% of cases (see Table 3). This is evidence that people even if they appear overconfident in the first round of Part 4, they realize that it is better for them to deviate from this strategy and appear underconfident.
We can observe that both parties exert more effort in Part 4 than in Part 3. In detail, agent 1 exerts on average 5.68 and 5.01 effort level, and agent 2 on average 6.08 and 5.42 respectively (see Tables 4 and 9). Exerting more effort in Part 4 can be attributed to the learning effect as the setting of the experiment has not changed. Besides, when efforts are substitutes individuals can depend more on their own performance to reach the goal and this is an extra motive for people to exert effort.
Appearing overconfident in Part 3 has a significant impact on the effort provision of agent 2. In order to control if appearing overconfident when efforts are complements and underconfident when efforts are substitutes is the best strategy, we check the impact that each message has in the effort provision of the receiver in each treatment. In Part 3, the mean value of the exerted effort of agent 2 when her peer appears overconfident is 5.33, while in Part 4 is 5.8 units (see Tables 5 and 12). When agent 1 appears underconfident, the average exerted effort of agent 2 is 5.72 and 6.31 respectively (see Tables 6 and 13). These results advise us that indeed appearing overconfident when efforts are complements is the best strategy. The receiver of the message then has an incentive to exert effort and increased probabilities to get the bonus. When efforts are substitutes appearing underconfident is the best strategy for agent 1, as agent 2 anticipates that in order to increase the probabilities of getting the bonus, they needs to overexert effort. Following that strategy agent 1 ensures that their collaborative exerts at least their efficient effort level, and the probabilities of obtaining the bonus are increased. Results suggest that agent 2 feels insecure about their partner’s effort provision and as long as they are always better-off by exerting more effort and get the bonus, compared to exert zero effort and not, they decide to increase their effort provision.
Additionally we further wish to check which strategy brings the desired results to the teams. For this reason we control how many times teams get the bonus in each treatment after each message. We find that when efforts are complements and agent 1 appears overconfident, teams get the bonus in 36% of cases. When agent 1 signals the opposite, teams get the bonus only in 27% of cases. We run a logistic regression with reward as the dependent variable and the message sent as the independent variable to check if there is any significant difference between the two levels of confidence. It was found that the difference in the log odds of the reward between the two confidence levels is 0.42, which is not significant ( Z = 0.82 , p = 0.41). Controlling for the same in treatment 2, we find that teams get the bonus in 71% and 69% of cases respectively (see Tables 4 and 11). Again, we run a logistic regression with reward as the dependent variable and the message sent as the independent variable to check if there is any significant difference between the two levels of confidence. We conclude that the difference in the log odds of the reward between the two confidence levels is 0.09, which is not significant ( Z = - 0.19 , p = 0.85).
We wish to ensure that the confidence statement in each part is unbiased of the outcome of the previous round (whether or not the team got the bonus). This is important to our analysis in order to ensure that the message sent in each round has not been influenced by the result of the previous round. Moreover agents show that they use their confidence level in a strategic way. It may be recalled that the message they send is whether they feel overconfident or underconfident about their skills in that task in this specific round. For that reason we check the correlation between the message sent and the result of the exact previous round. We conclude that in Part 3 this correlation is -0.047 (see Table 7), while in Part 4 this correlation is -0.363 (see Table 14). This evidence suggests that people use their confidence in a strategic way, as they appear the way they want to appear to their partner. They are not affected by the result of the previous round.
Finally we run a regression to check what influences the agent 1 to send this message. As we mentioned in the related sections 5.3.4 and 5.4.4. we set the “Message” that agent 1 sends in each round as the dependent variable. As independent variables we set the effort of the agent in the current round, the result of the previous round (whether they got the bonus or not), the message sent in the previous round, the confidence status, the social preferences, the age, the educational background, the gender, and the nationality of the subject. The confidence status of the agent derives from the the last round of Part 1, while social preferences are derived as the tokens the agent distributes in the last round of Part 2. In treatment 1 where efforts are complements, only the effort provision of agent 1 has a significant impact on the message sent by them (see Table 8). On the other hand, in treatment 2, effort provision in the current round has a highly significant impact on the message sent. Furthermore, the outcome of the previous round, the message sent in round 3, the age, and whether the sender is Greek or Spanish has a significant impact on the message sent (see Table 15). Under all these conditions, the sender is more likely to appear overconfident than underconfident. The interpretation of these results is that the exerted effort in each round is
the main driver of each message sent. Appearing overconfident in Part 3 is only affected by the exerted effort in that round and not from social preferences nor any other personal characteristics. Appearing underconfident is influenced by the result of the previous round, the age and the nationality. Subjects of an older age are more likely to adapt to this environment and appear underconfident. Finally, Greeks and Spanish people are more likely to appear overconfident in this treatment.
6. Discussion
Our results suggest that people use their confidence level in a strategic way. Our hypotheses are both confirmed. Individuals appear more overconfident to their partner when their efforts are complements. People have an incentive to appear overconfident to their colleague under that circumstance because it signals to the other party that their effort is not meaningless. We also conclude that when efforts are substitutes, people seem to appear less overconfident about their skills even if it is not true. Their exerted effort is on average 10% greater than in Part 3. In addition, the proportion of groups that reach the goal in Part 4 is double than the one in Part 3. Τhis further supports the hypothesis that subjects use their confidence level as a strategic tool. Having reach the goal more times in Part 4 can also be attributed to the learning effect as the setting of the experiment has not changed. Besides, when efforts are substitutes individuals can depend more on their own performance to reach the goal and this is an extra inducement for people to work harder.
However, we see that subjects tend to have a high level of self-esteem and appear overconfident with their skills, despite the fact that it is in their interest to appear underconfident in some cases. This evidence can account for both “can-do” optimism and “defensive” pessimism (Bénabou and Tirole, 2002). Protecting one's self-esteem is widely respected as a central and elemental goal that influences social behavior. People with a high self-esteem are more likely to be successful at this goal and reap all the benefits that result from it (Baumeister, et. al., 1993 a). Literature on task performance has found that people with greater levels of self-esteem are more able to use the information of the task and setting to decide their optimal strategy (message, effort) (Sandelands et. al., 1988). On the other hand, when people choose their goals driven by their self-esteem, they are likely to select more difficult goals, resulting in an increased probability of failure (Baumeister, et. al., 1993 b). This fact can be regarded as an additional reasonable explanation why people keep on appearing overconfident in Part 3 , even if they continuously do not reach the target.
In our data we observe a strong tendency of people, despite their sex and educational characteristics, to appear and remain overconfident despite the fact that is is costly to them.
An explanation could be that individuals derive an internal utility by appearing overconfident (Taylor and Brown, 1988b), or they strongly believe that their attitude can influence their partner’s decisions. We see people exerting a surplus of effort, even if this choice does not alter the outcome of the game. Specifically in part 3, 34% of agents solved more than 6 additions, without considering that this would not increase their chances of getting the bonus. In addition, it is costly both physically and monetarily to them. Physically because by using their mental capacity, they may appear more mentally “tired” in the next round, and monetarily, as they “invest” 1 token each time they solve a problem.
This paper contributes to the literature about overconfidence, the relation between performance level and overconfidence, as well as the performance management, and composition of teams and measurement of effort.
Some good points to note of our experimental design is that we control for the various aspects that they could have an effect on the results. At first, we have chosen a neutral task, adding three two-digit numbers, in which all participants had the same potentials to excel. Furthermore, we were able to measure the exerted effort of subjects. Although, a different task could lead to different results. Secondly, the loss-aversion effect on subjects was also taken care of, as they could exert effort and, still not decrease their utility, even if they did not get the bonus. In this way subjects were always better off by exerting effort and getting the bonus.
Another control variable is the framing effect. The evaluation form of the performance could have an influence on the overconfidence results of subjects. For that reason we used two different framings. The first evaluation form requested from subjects to indicate how many participants did strictly better than them, while the second evaluation form requested them to indicate from how many participants they thought they performed strictly better than. We see no difference between these parts.
The order effect of the treatments could also influence the results. Performance and overconfidence might follow different tendencies when changing the order of parts. A between design experiment can control this effect, by eliminating the influence of participation in previous treatments. For this reason we have chosen to use Part 3 (efforts complements) of the experiment as Part 4 and via versa. The setting of the task has not changed throughout the rounds and there is a learning effect, so it is important to also control for that.
Some aspects of the experiment are reason for discussion. Firstly, the main limitation of our research is the small sample size. We had contacted a High School in Greece to run the experiment, but because of bureaucracy this idea was postponed indefinitely. Moreover, the
majority of participants are Greek and this may influence the results. Also we would like to have had a greater number of participants from different cultural backgrounds and different ages. In future research, an experiment with a greater number of participants from more diverse cultural backgrounds and different ages should provide more robust results. Additionally, a point of discussion is that agents are paired with the same person during all rounds. A new experimental design could alter groups between parts or even between rounds. The strong point of our experimental design is that individuals have the opportunity to converge to the equilibrium as they control the impact that their message has on their partner while also reflecting on what is the best strategy. Nonetheless, controlling for the message of agents with various group mates might give a clearer view if people use their confidence level in a strategic way. Another strong point of this experimental design is that all decisions are incentivized with monetary compensation and let us have a clearer view on the decisions made. Monetary incentives outweigh other motivations like boredom or trying to help the experimenter. When monetary incentives are used subjects appear to participate more seriously, and with more consistency than when rewards are hypothetical.
7. Conclusion
Our experiment examined the determinants of overconfidence within groups when effort levels are complements and substitutes. We conclude that individuals use their confidence level in a strategic way. In this paper we focus mainly on the signaling value of overconfidence. We see that when people have an incentive to appear overconfident, they behave accordingly, by signaling to their partner that they believe in their skills for that treatment. On the other hand, when it is not in their interest to appear overconfident, people deflate their statements of confidence levels when efforts are substitutes. However, subjects have a strong tendency to appear overconfident despite the fact that they are better off by appearing underconfident in the latter case. This supports the consuming and motivation value of overconfidence. Our novel strategic environment (in which another party observes the stated confidence level of another and then chooses the exerted effort level) allows a direct test of the strategic-interest hypothesis. First, the social signal is perceived and has reactions: subjects in our experiment do respond to messages about confidence made by their incognito partners, taking that information into account when choosing how much effort to exert. When efforts are complements, individuals on average report significantly higher confidence levels than when efforts are substitutes. Appearing overconfident is the most efficient strategy. Evidence supports that agents exert more effort when their partner appears overconfident, than when they are not. Besides, teams get the bonus significantly more times when agent 1 appears overconfident. On the other hand, when efforts are substitutes agents
appear less overconfident, which is actually the best strategy. In this treatment, when people appear underconfident, partners exert a significant higher level of effort. There are several directions for future research. Some of them could be: To what degree individuals are aware of the strategic implications of their message? Do people appear in the same way when they have different partners between different rounds and treatments? To what extent is self-deception present?
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