# Explanations for the Changes in Tournament Entry Between the Individual Tournament and the Team Tournament

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In the next stage, the subjects who had participated in the training period were asked to answer a set of ten questions (five questions on general knowledge followed by five questions on economic knowledge) by giving their best estimation of the answer and then by providing 10%, 50% and 90% confidence intervals. Subjects in the control group had to complete the same task. After the pilot experiment was run, we removed and replaced the most diﬃcult questions for which subjects seemed to have no clue about the answer.
Before the beginning, subjects were explained in detail what were 10%, 50% and 90% confidence intervals. They were also told that they would receive remunera-tion regarding this task but that they would only know how the remuneration was established later. There was no feedback between the questions and subjects could proceed at their own pace.

Evaluation of miscalibration

As in Cesarini et al. (2006), the remuneration for the calibration tasks depended on the evaluation the subjects were asked to make afterwards of their and the average subject’s performance during the calibration task. For instance, they were asked how many correct answers they thought fell inside the 10%, 50% and 90% confidence intervals they provided and how many correct answers fell inside the intervals given by the average subject.
After that, they were asked to make two choices between two bets. The first choice was between betting that at least one correct answer out of ten fell outside the subject’s 90% intervals and betting that at least one correct answer fell inside the subject’s 10% intervals. Each one of these bets would have a probability of 1-0.910, close to 0.65 to be true for a perfectly calibrated subject. The second choice was between betting that, out of three questions randomly drawn from the ten questions, at least one correct answer belonged to the subject 50% intervals (1-0.53=0.875) and betting that the correct answer to a randomly chosen question belonged to the 90% interval provided by the subject (0.9). Each successful bet was rewarded by 300 extra ECUs. These bets were bound to inform us on how people are aware of their miscalibration.

A diﬀerent impact between genders

This general picture masks some heterogeneity across subjects. We can control for several sources of heterogeneity. However, the gender variable captures almost all of it. We observe indeed that there is virtually no improvement in women’s calibration especially when we compare the median hit rates between the treatments while men increase their median hit rate by 0.5 point at the 50% level and by 1 point at the 10% and 90% levels (see Figure 3).
The diﬀerence in interval width between the control and the training treatments seems to be larger for men than for women, indicating that men learned more than women to reduce their overconfidence. Using a Wilcoxon-Mann-Whitney test, we find that 10% confidence intervals are significantly wider for the trained group respec-tively for five questions out of ten and zero question out of ten for men and women.

What Needs to be Controlled for

The experimental design needs to allow one to disentangle the role played by sev-eral factors in explaining the change in the gender gap in entry when the tournament becomes team-based. In order to avoid making the design even more complicated than it already needs to be, the notion of team I selected is the most simple one: two teammates who would not be aware of the identity of their teammate or of that of their opponents. This way, the eﬀect of the gender of one’s teammate or opponents on the decision to enter the tournament does not have to be taken into account. Every potential eﬀect of the team tournament had then to be listed before an appropriate way to control for it was found.
First of all, the tournament being team-based rather than individual changes one’s expected payoﬀ from entering the tournament for each level of performance. Nev-ertheless, as the probability changes in the exact same way for men or women, it is unlikely that this change of probability might cause a reduction in the gender gap in tournament entry.
Secondly, NV and NSV found a significant gender gap in overconfidence. It could be the case that overconfidence about one’s team chances of winning the tournament diﬀers from overconfidence about one’s chances to win the individual tournament. Tajfel (1970) discovered that groups formed on the basis of almost any distinction are prone to ingroup bias. Within minutes of being divided into groups, people tend to see their own group as superior to other groups. It could be the case that men and women diﬀer in how they are aﬀected by this ingroup bias. Women could for example be more optimistic than men about their teammate’s performance.
Thirdly, being part of a team could have a diﬀerent eﬀect on men’s and women’s am-biguity, risk or feedback aversion. Teams and individuals do not have the same risk preferences. Shupp & Williams (2007) found that the variance of risk preferences is generally smaller for groups than individuals and the average group is more risk averse than the average individual in high-risk situations, but groups tend to be less risk averse in low-risk situations. Rockenbach et al. (2007) showed that compared to individuals, teams accumulate significantly more expected value at a significantly lower total risk. Being part of a team may have a diﬀerent impact on men’s and women’s risk preferences. Women could, for example, be less risk averse as part of a team than alone.
Fourthly, in a team competition one’s performance influences one’s teammate’s pay-oﬀs and one’s payoﬀs are influenced by one’s teammate’s performance. For instance, if my teammate is worse than I am, it will lower both my probability of winning the tournament and my payoﬀ if we do win. Charness & Jackson (2009) explore play between groups where one member of each 2-person group dictates the play of that group and is therefore responsible for the payoﬀ of the other group member. They find that a substantial part of the population plays a less risky strategy when choosing for a group than when playing only for themselves. Again, men and women may react diﬀerently to this responsibility issue.

### Belief-assessment Questions

A diﬀerence in confidence between men and women may explain a significant part of the gender gap in tournament entry. NV and NSV found that both men and women are overconfident but men are more so. In order to control for diﬀerences in confidence both in one’s chances of winning the individual tournament and in one’s team chances of winning the team tournament, participants had to answer belief-assessment questions at the end of the experiment. Participants had to guess the mean Task 1 and Task 2 performances of the participants in their session.

#### Gender Diﬀerences in Performance and in Entry in the Individual Tourna-ment

In this subsection, I check whether there are some gender diﬀerences in perfor-mance, which was the case in NSV but not in NV. I also look at the gender gap in the individual tournament entry. In the present chapter, a participant in the individual tournament is the winner if she beats one opponent. This one-to-one competition could have an eﬀect on the participants’ decision to enter. In NV, one has to beat the performances of three other participants to be considered the winner of the tournament. Here, I chose to consider a one-to-one competition as a matter of simplicity since I subsequently needed to introduce teams.
As in NV, there is a gender gap in the individual tournament entry: 51.35% of women and 84.62% of men chose to enter the individual tournament. This diﬀerence is sig-nificant with a two-sided exact Fisher’s test (p=0.00). While men enter significantly more often than expected (p=0.00), it is not the case for women (p=0.65). However the gender gap in tournament entry is greater for participants with above median Task 2 performances. 50% of low performing women and 62% of low performing men chose to enter the individual tournament (a two-sided Fisher test yields p=0.70). Among high performing participants, 52% of women and 96% of men entered the tournament (p=0.00). The first logit regression of Table 3.1 shows tournament entry as a function of the participant’s gender and Task 2 performance.

Résumé
0.1 Avantages et inconvénients de l’économie expérimentale
0.2 Différences hommes-femmes de confiance en soi, goût pour la compétition et besoin de relevé des défis: une revue de littérature des résultats expérimentaux existants
0.3 Les origines des préférences: inné ou acquis?
0.4 Implications en terme de politique économique
0.5 Plan de thèse
General Introduction
0.6 Advantages and drawbacks of experimental economics
0.7 Gender differences in self-confidence, competitiveness and need for challenges: A review of experimental results
0.8 Nature or nurture: On the origins of preferences
0.9 Policy implications
0.10 Outline of the dissertation
1 Incentives to Learn Calibration
1.1 Introduction
1.2 Experimental design
1.2.1 The training period
1.2.3 Evaluation of miscalibration
1.3 Results
1.3.1 General results on calibration
1.3.2 The effect of training on miscalibration and confidence in calibration
1.3.3 What happened during the training session ?
1.4 Discussion
1.5 Conclusion
2 Men too sometimes shy away from competition: The case of team competition
2.1 Introduction
2.2 Experimental Design
2.2.1 What Needs to be Controlled for
2.3 Results
2.3.1 Gender Differences in Performance and in Entry in the Individual Tournament
2.3.2 Gender Differences in Entry in the Team Tournament
2.3.3 Explanations for the Changes in Tournament Entry Between the Individual Tournament and the Team Tournament
2.4 Consequences on Efficiency of the Type of Competition.
2.5 Conclusion
3 Group Identity and Competitiveness
3.1 Introduction
3.2 Experimental Design
3.2.1 Identity sessions
3.2.2 Benchmark sessions
3.3 Results
3.3.1 Group identity building activities
3.3.2 The effect of social identity on performance, confidence and entry in the individual tournament
3.3.3 The effect of social identity on entry in the team tournament
3.3.4 Explanations for the changes in decision to enter the team tournament
3.3.5 How male vs female competition affects men and women’s competitive behavior
3.4 Discussion
3.5 Conclusion
General Conclusion
Bibliography

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