# Gender of the opponent and reaction to competition outcomes

C Mollier, A García-Gallego, T Jaber-Lopez, S Zaccagni

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C Mollier, A García-Gallego, T Jaber-Lopez, S Zaccagni. Gender of the opponent and reaction to competition outcomes. Journal of Behavioral and Experimental Economics, 2025, 119, pp.102475. 10.1016/j.socec.2025.102475. hal-05358737

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# Gender of the opponent and reaction to competition outcomes

C. Mollier<sup>a, ID</sup>, A. García-Gallego<sup>b, ID</sup>, T. Jaber-Lopez<sup>c, ID</sup>, S. Zaccagni<sup>d, ID, *</sup>

## ARTICLE INFO

JEL classification:

C91
D910
J16

Keywords:

Competitiveness
Gender
Feedback
Career decisions
Lab experiment

## ABSTRACT

We investigate how competition outcomes and the opponent's gender affect the decision to compete again, using a lab experiment. Our experimental design adopts the strategy method to measure individuals' reactions to winning or losing. Subjects indicate their willingness to compete again based on performance gaps with their opponents. Furthermore, gender is inferred from participant-selected-names, allowing us to explore the role of the opponent's gender. Against our main hypothesis, after winning against a female opponent men exhibit a decrease in their willingness to compete again. The primary mechanism underlying men's behavior appears to be the presence of inaccurate beliefs—specifically, expecting to win but ultimately losing. Our main finding is that men with inaccurate beliefs, when competing against women, are significantly more likely to re-enter the competition and to outperform their female opponents in subsequent rounds.

> "I'm out to prove that a guy 55 years old, with one foot in the grave, can play with the best woman in the world and maybe beat her." "My biggest problem is overconfidence."<fnref n="1" />

> [- Bobby Riggs (1973)]

## 1. Introduction

According to the latest report of UN Women (2023), only 28.30% of women held managerial positions worldwide in 2020. Robust evidence from developed countries indicates that this persistent occupational segregation significantly contributes to wage disparities between men and women (Blau & Kahn, 2017; Cortes & Pan, 2018; Groshen, 1991; Sorensen, 1990). Women's access to top executive positions remains limited, as evidenced by the number of women leading a CAC40 company (i.e. only four in 2024).<fnref n="2" /> It is well established that occupations are disproportionately distributed by gender, with female-dominated professions tending to offer lower wages than male-dominated ones (Goldin, 2014). Beyond horizontal occupational segregation, vertical segregation – marked by the concentration of women and men in distinct grades, levels of responsibility, or positions

– warrants considerable attention. Among OECD countries, a 19.10% salary gap favors men in the 9th decile of earnings, compared to a 10.60% difference among lower-income groups (OECD, 2023). These figures provide evidence of the “glass ceiling” effect (Arulampalam, Booth, & Bryan, 2007). Several factors explain why women do not advance in their careers at the same pace as men. Perceived or experienced discrimination (e.g., Azmat & Petrongolo, 2014; Hersch, 2007) and the trade-off between professional careers and personal lives (DiBenedetto & Tittle, 1990) are key contributors to this gender gap. Women's aspirations may be constrained by self-perception biases (Beaman, Duflo, Pande, & Topalova, 2012) as well as external barriers; one example is their promotion opportunities diminish in contexts where male leaders dominate (De Paola & Scoppa, 2015). The under-representation of women in senior and high-paying positions perpetuates a vicious circle, discouraging younger women from aspiring to similar roles (Ellingrud, Madgavkar, & Manyika, 2016; Morais Maceira, 2017).

Career advancement often requires navigating competitive environments and situations, including admission processes, job applications, promotion tournaments, and entrepreneurial competition. Therefore,

<footnote><sup>a</sup> Economix, Paris Nanterre University, France</footnote>

<footnote><sup>b</sup> LEE and Department of Economics, Universitat Jaume I, Castellón, Spain</footnote>

<footnote><sup>c</sup> Institute of Public Goods and Policies (IPP), Spanish National Research Council (CSIC), Madrid, Spain</footnote>

<footnote><sup>d</sup> Department of Economics and Business Economics, Aarhus University, Denmark</footnote>

<footnote>* Correspondence to: Department of Economics and Business Economics, Fuglesangs Allé 4 building 2632, 229 8210 Aarhus V, Denmark.
E-mail address: sarah.zaccagni@econ.au.dk (S. Zaccagni).</footnote>

<footnote n="1">¹ See https://www.nytimes.com/1973/08/25/archives/that-happy-hustler-brings-his-talkathon-to-town-porky-pig-is-no-2.html.</footnote>

<footnote n="2">² CAC40 is the French stock market index that tracks the 40 largest French companies.</footnote>

<footnote n="3">³ A recent strand of literature has put the role of competitiveness under scrutiny. In particular, Gillen, Snowberg, and Yariv (2019) show that measurement errors in assessing risk attitudes and overconfidence may lead to an overestimation of the importance of competitiveness in lab experiments. Van Veldhuizen (2022) re-examine this result using a novel experiment and claims that the entire gender gap is driven by gender differences in risk attitudes and self-confidence.</footnote>
an individual's attitude toward competition plays, at least partially, a
significant role in shaping career trajectories (Buser & Yuan, 2019). An
extensive experimental literature provides evidence of gender differ-
ences in competitiveness, which has become a widely cited explanation
for gender disparities in labor market outcomes (e.g Balafoutas & Sut-
ter, 2012; Gneezy & Rustichini, 2004; Niederle & Vesterlund, 2007).³
Building on this evidence, several studies have examined how various
aspects of competition – such as high vs. low stakes, opponent identity,
repeated vs. one-shot, and feedback provision – or individual char-
acteristics (e.g. family background, age, culture, and race) influence
competitive behavior (Almäs, Cappelen, Salvanes, Sørensen, & Tungod-
den, 2016; Dreber, Von Essen, & Ranehill, 2014; Hauge, Kotsadam, &
Riege, 2023; Nicholls, 2022; Sutter & Glätzle-Rützler, 2015).

In this paper, we examine key features of competition, focusing on
the combined effects of past competition outcomes (winning or losing)
and opponent gender on individuals' willingness to compete again.
These factors are particularly relevant, as they reflect crucial aspects of
real-world competitive environments. Career decisions are inherently
sequential – employees repeatedly apply for promotions – and at each
stage, they are typically informed of both the outcome (i.e. whether
they obtained the promotion) and the gender of their competitors.
Hence, achieving top positions depends not only on individuals' ini-
tial willingness to compete but also on their willingness to re-enter
competition after a loss. Empirical evidence indicates that women are
more likely than men to drop out after setbacks, especially in male-
dominated fields (Buser & Yuan, 2019; Ellis, Fosdick, & Rasmussen,
2016; Price, 2010). Therefore, understanding how men and women
react to winning or losing, and whether these reactions depend on the
opponent's gender, provides valuable insights into labor market dynam-
ics. Additionally, our study explores how prior competitive outcomes,
particularly unexpected losses, influence subsequent decisions to re-
enter competition. The controlled setting of a lab experiment allows
us to isolate and examine these behavioral responses.

The seminal experimental study on gender differences in willingness
to compete is Niederle and Vesterlund (2007). It documents, in a
lab experiment, a significant gender gap in tournament entry, driven
by men being more overconfident and more willing to perform in
a competition. Subsequent research has consistently confirmed that
men tend to be more confident and competitive than women (Alan,
Ertac, Kubilay, & Loranth, 2020; Dreber et al., 2014; Kamas & Preston,
2012; Ludwig, Fellner-Röhling, & Thoma, 2017). This leads to an over-
representation of low-performing men and an under-representation of
high-performing women in competitive settings. While in a lab envi-
ronment, these suboptimal choices directly affect individuals' earnings,
at a broader level, a loss of efficiency is incurred if qualified women
are not assigned to high positions in favor of less competent men. The
analysis of public interventions, aimed at reducing the gender gap in
competitiveness and in the labor market, shows that these differences
are not irreversible (Balafoutas & Sutter, 2012; Beaman et al., 2012).

Moving from individual characteristics to competition features,
Buser, van den Assem, and van Dolder (2023) test and confirm the
validity of gender differences in competitive preferences in a quasi-
experimental real-world setting with exceptionally high stakes.<fnref n="4" /> In
this study, the authors also analyze how the gender of the opponent
influences the decision to enter competition, finding that women tend
to avoid competing against men. On the other hand, men seem to
anticipate female behavior and show a greater willingness to compete
against women. In contrast, when considering hormonal influences,
women appear more responsive than men to the characteristics of their
opponent. Brañas-Garza, Chowdhury, Espín, and Nieboer (2023) show
that females exhibit greater competitiveness against individuals with

low prenatal testosterone exposure. Specifically, females exhibit greater
aggressiveness toward those with a higher second-to-fourth digit ratio
(H-type), associated with lower fetal exposure to testosterone. Accord-
ing to the meta-analysis from Markowsky and Beblo (2022), same-sex
competition tends to serve as a moderator of the gender gap. This effect
is mainly driven by women who appear as competitive as men when
competing against female (Paryavi, Campos, & Santos, 2025). In recent
experiments in the US and China, He and Noussair (2024) investigate
whether men experience a psychological cost when outperformed by
a female competitor. They find that in China, men are willing to pay
more to hide that they lost regardless of the gender of the competitor,
while there is no gender difference in the US. In China, women feel
more ashamed to lose to another woman than to a man, whereas
in the US, the opposite occurs. The identity of the opponent is also
the focus of Apicella, Demiral, and Mollerstrom (2017), who compare
competition against oneself versus against others and find no evidence
of a gender difference in the willingness to self-compete. Both papers
highlight the importance of the identity of the subject against whom
an individual competes.

Another important feature of competition is whether the decision
to compete is one-shot. To better mimic the labor market setting,
it is crucial to study not only the willingness to compete in a sin-
gle competition, but also how this willingness evolves in response to
winning and losing in repeated competitions. Empirical evidence has
shown that in male-dominated fields, women are more likely than men
to drop out after experiencing setbacks (Fischer, 2017; Goldin, 2015;
Katz, Allbritton, Aronis, Wilson, & Soffa, 2006). Some experimental
studies test whether competition results affect subjects' behavior in a
subsequent competition, and whether men and women react differently
in ways that may enhance the gender gap. In a lab experiment, Buser
(2016) studies the effect of a competition's outcome on the willingness
to seek further challenges and find notable gender differences: men
react to losing by picking a more challenging target, while women
lower their performance. Gill and Prowse (2014) investigate the effect
of winning or losing on later performance and find that women's
performance decreases after losing, while for men, this effect occurs
only in high-stakes environments.

Testing how competition outcomes influence behavior in a second
competition raises the question of whether feedback induces belief
updates. The evidence remains inconclusive. Some studies (Ertac &
Szentes, 2011; Wozniak, Harbaugh, & Mayr, 2014) suggest that pre-
cise performance feedback reduces the gender gap in competitiveness.
Others (Cason, Masters, & Sheremeta, 2010; Möbius, Niederle, Niehaus,
& Rosenblat, 2022) find that the gap persists, with men updating their
beliefs less conservatively and being less feedback-averse. In Vitaku,
Palma, and Toney (2025), providing feedback alongside information
about the opportunity costs of alternative payment schemes reduces
men's tendency to over-enter competitions. Research (Albrecht, Von Es-
sen, Parys, & Szech, 2013; Berlin & Dargnies, 2016; Buser, Gerhards, &
Van Der Weele, 2018; Coutts, 2019) consistently shows that women
update their beliefs more cautiously and respond more strongly to per-
sonal performance feedback. Baier, Davis, and Jaber-Lopez (2024) find
that rank feedback encourages more women to compete, while Buser
and Yuan (2019) reveal that women are less likely than men to compete
again after losing. Fang, Zhang, and Zhang (2021) link this gender dif-
ference to labor market disparities, noting that girls are more likely to
drop out after failing in previous competitions, especially in countries
with larger labor market gender gaps.

Compared to previous studies, we are the first to examine the com-
bined effects of two key features of the competitive environment: the
outcome of a prior competition (winning or losing) and the gender of
the opponent. Our primary focus is on the willingness to compete again.
We implement a novel design using a strategy-elicitation method, in
which subjects indicate if they are willing to compete a second time,
based on a sequence of different point gaps between their performance
and their opponent's performance. This strategic method allows us

<footnote n="4">⁴ Cai, Lu, Pan, and Zhong (2019) also report that, compared to male students, females underperform on China's most competitive and high-stakes entrance exam.</footnote>
to identify the switching point in subjects' decisions to re-compete, providing a continuous and hence more nuanced measure of participants' (dis)taste for competition. Recent literature on preferences for competition has typically adopted continuous rather than binary measures. For instance, Lozano and Reuben (2022) use a multiple price list (MPL) to classify individuals as competition-averse, neutral, or seeking, offering a more nuanced understanding of competitive preferences. Vittaku et al. (2025) introduce granularity by implementing a multi-tiered competitive structure across repeated interactions. In their setting, women tend to avoid the most competitive tier, while men avoid the non-competitive option. Saccardo, Pietrasz, and Gneezy (2018) allow participants to allocate a chosen share of their earnings between piece-rate and tournament schemes, uncovering a wider gender gap than binary metrics suggest. Similarly, Ifcher and Zarghamee (2016) show that women require a higher incentive premium to compete at levels comparable to men. In this paper, we use a strategy-elicitation method that provides a continuous measure of willingness to compete, allowing us to examine how individuals respond to competition outcomes and whether the size of the performance gap influences this reaction. Crucially, our design captures reactions after individuals have self-selected into the tournament, enabling a closer look at within-competition dynamics. Contrary to Buser (2016), we focus on a subsample of competitive participants. We believe this feature better reflects real-world environments – such as labor markets – where individuals who have already opted into a competitive process (e.g., applying for a promotion) compete against one another.

At a secondary level, we examine how subjects perform after winning or losing to investigate potential gender differences in the inclination to outperform an opponent of the opposite (same) gender. Additionally, we elicit individuals' beliefs to track how they evolve throughout the competition. If gender stereotypes are shared by men and women, beliefs about the opponent could play a role in their decision to re-compete.<fnref n="5" />

In line with previous studies, our findings reveal a gender gap in the taste for competition, with men exhibiting a higher willingness to compete than women. After winning against a woman, men are less willing to re-compete against her compared to after winning against a man. After losing against a woman, men are more inclined to compete again than after losing against a man. This pattern is significant only among overconfident men, i.e., those who expect to win but end up losing. This result suggests that, for men, the reaction to winning or losing does not necessarily operate through belief updating. On the other hand, women compete more after winning and compete less when they are overconfident, regardless of their opponent's gender. Regarding the evolution of performance, we observe that men after losing and re-entering competition against women substantially improve their performance. This effect is shown to be mainly driven by overconfident males, suggesting that holding inaccurate beliefs strengthens their motivation to outperform female opponents. Women, by contrast, exhibit consistent performance across both stages, regardless of the outcome or the opponent's gender.

The rest of the paper is structured as follows. In Section 2, the experimental design is presented. Sections 3 and 4 report the testable hypotheses and the main results, respectively. Finally, Section 5 concludes.

## 2. Experimental design

### 2.1. Task

We conduct an experiment in which participants perform a real task: adding up sets of five two-digit numbers and filling in the sum in a blank box (Niederle & Vesterlund, 2007). Each subject repeats this task for 3 min across four stages (detailed in Section 2.2 for a detailed description of the stages). Participants can use paper and pens provided, but are not allowed to use their phones or calculators.<fnref n="6" />

At the beginning of the experiment, subjects fill in a questionnaire with socio-demographic questions (gender, age, and education). Next, they select a name from a list of the most given babies' names in 2020 in France (INSEE). Participants choose from a list of female and male names based on the gender they declared in the survey. A pre-experiment survey ensures that the names were unanimously recognized as either male or female (see Appendix A.1).<fnref n="7" /> At this point, subjects are randomly paired with an opponent. The matching is made in order to have a sufficient number of participants in each condition: Male vs. Male, Female vs. Female, Male vs. Female and Female vs. Male (henceforth respectively MM, FF, MF and FM, where the first letter refers to the gender of the subject and the second letter to the gender of the opponent). Subjects keep the same opponent throughout the experiment. In Stage 2, participants are implicitly informed of the gender of their opponent through the disclosure of the name previously chosen by our subjects. They are then reminded of their opponent's name at each tournament stages.

The experiment consists of two parts. Sections 2.2 and 2.3 present the game description (Part I) and the elicitation task for risk preferences and gender stereotypes (Part II), respectively.

### 2.2. Game description—Part I

We describe all the stages of the game that participants play in the first part of the experiment (Part I). Fig. 1 shows the timeline of the game.

#### Stage 1: Piece rate

In Stage 1, participants perform the task for 3 min, under a piece rate payment scheme. They receive 0.50 Euro for each correct sum. Subjects are informed on their performance in this stage at the end of Part I of the experiment.

#### Stage 2: Tournament

In Stage 2, subjects perform the task for 3 min, under a tournament scheme. At the beginning of the stage, we disclose the names chosen by the subjects. They are randomly paired and compete against each other. In this winner-takes-all tournament, the best performer receives 1.50 Euros for each correctly solved problem, while the other receives zero.<fnref n="8" /> Ties are broken randomly. Subjects are informed on their performance in this stage at the end of Part I of the experiment. At the end of this stage, we elicit subjects' beliefs about their status: subjects guess whether they won or lost. Correct beliefs are rewarded with 1.00 Euro (henceforth *Beliefs 2*).

#### Stage 3: Choice of payment-scheme

In Stage 3, subjects decide on their payment scheme, i.e. whether they want to be paid based on a tournament or based on a piece rate, before performing the task. If they opt for the piece rate (henceforth

<footnote n="5">⁵ In Mago and Razzolini (2019) and Geraldes (2020), women are discouraged from performing against males. In Datta Gupta, Poulsen, and Villeval (2013), when men are informed that they compete against a woman, they compete more, but this trend is reversed when they perceive the woman as more capable than them.</footnote>

<footnote n="6">⁶ Refer to Section 2.4 for a description of the procedure and to Appendix A.5 for the complete experimental instructions.</footnote>

<footnote n="7">⁷ In selecting “Others”, participants are offered both male and female name options. At the end of the experiment, 75.17% of participants correctly guessed the gender of their opponent.</footnote>

<footnote n="8">⁸ Our tournament incentive differs from Niederle and Vesterlund (2007), as we opted for a higher expected payoff aiming to increase tournament participation in Stage 3, an aspect that is central to our analysis. Since this may interact with risk preferences, we control for risk aversion (see Section 2.3).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Timeline of Part I of the experiment.</figcaption></figure>

referred to as Stage 3PR), compensation is determined by the number of correct answers, as in Stage 1. Alternatively, if participants choose the tournament option (henceforth referred to as Stage 3T), their performance is compared to their opponent's performance in Stage 2. If they solve more problems in Stage 3T than their opponent solved in Stage 2, they receive 1.50 Euros per correct answer; otherwise they receive 0.00 Euro. Subjects perform the task for 3 min and their remuneration is based on the chosen payment scheme. At the end of this stage, we elicit subjects' beliefs about their status: subjects guess whether they won or lost. Correct beliefs are rewarded with 1.00 Euro (henceforth *Beliefs 3*). Subjects are informed on their status at the end of this stage (i.e., whether they won or lost). Subjects who choose piece rate are informed about their performance at the end of Part I of the experiment.

After Stage 3, we split our sample based on the chosen payment scheme, allowing us to distinguish between subjects who show a taste versus distaste for competition. Only participants who chose the tournament payment in Stage 3 are assigned to Stage 4.

**Stage 4: Second entry into competition**

After receiving feedback on their status (winner/loser) at the end of Stage 3, participants enter Stage 4. In this stage, they are given the option to decide whether they want to re-compete against the same opponent. Using a strategy elicitation method, we present a sequence of hypothetical point gaps between their performance and their opponent's. Subjects observe a scale displaying the gaps and are given the option to accept the competition (or not) for each gap (see Fig. 2). Once a decision is made, we disclose the actual point gap between the participant's performance and that of their opponent in Stage 3. If the participant's choice was to decline the competition for the actual point gap, they receive payment according to the piece rate (Stage 4PR). Alternatively, if the participant's choice was to accept to compete, payment is determined by the tournament payment scheme (Stage 4T). Subsequently, their performance in Stage 4 is compared to the performance of their opponent in Stage 2. At the end of this stage, we elicit subjects' beliefs about their status: subjects guess whether they won or lost (henceforth *Beliefs 4*). Correct beliefs are rewarded with 1.00 Euro.

## 2.3. Risk preferences and gender stereotypes—Part II

In the second part of the experiment (Part II), we elicit participants' Risk Preferences and Gender Stereotypes, with the primary

intention to incorporate them as control variables in subsequent analyses. Risk Preferences are measured using the Bomb Risk Elicitation Task (BRET), by Crosetto and Filippin (2013) and available in the oTree version (Holzmeister & Pfurtscheller, 2016). In this game, there are 100 boxes with one containing a bomb. Subjects know that the bomb can be anywhere with the same probability and they simply have to choose how many boxes they want to collect. If they fall on the bomb they win a total of 0.00 Euro; otherwise, they win 0.05 Euros per box collected.<fnref n="9" /> Gender Stereotypes are assessed through the Gender Role Attitudes Scale (GRAS) (García-Cueto, Rodríguez-Díaz, Bringas-Molleda, López-Cepero, Paíno-Quesada et al., 2015). This survey includes questions that elicit Transcendence and questions that elicit Sexism. Sexism refers to discriminatory attitudes or beliefs about gender. Transcendence is characterized by the rejection of traditional gender norms, or what García-Cueto et al. (2015) describe as “defenders of equality”.

In order to rule out potential experimenter demand effects, we also ask our subjects about the presumed topic of our study. Finally, to ensure that the gender of the opponent is sufficiently salient, we ask participants to report the name chosen by their opponent during the experiment and the gender of their opponent. To prevent these questions from drawing attention to the study's focus, we include two additional random questions: “Why did you choose the tournament in Stage 3?” and “What was your final payment?”.<fnref n="10" />

## 2.4. Procedure

The experiment was pre-registered at AEA RCT Registry,<fnref n="11" /> and approved by the Ethics Committee of the University of Paris Nanterre. We conducted the experimental sessions at the “Laboratoire d’Economie Expérimentale de la Défense” (Courbevoie, France) between December

<footnote n="9">⁹ The BRET task offers several advantages: “minimizes the number of observations that cannot be assigned to any category due to inconsistent or dominated choices” (Crosetto & Filippin, 2013). Also, it minimizes the risk of wealth effects (especially when being conducted after the main task) since it minimizes the predictability of the payoff (Crosetto & Filippin, 2016).</footnote>

<footnote n="10">¹⁰ In Appendix A.3, we present a textual analysis of the participants' answer to the presumed topic of our study and their motives to choose (or not) the tournament at Stage 3.</footnote>

<footnote n="11">¹¹ Registry number AEARCTR-0010102 (link: https://www.socialscienceregistry.org/trials/10102).</footnote>
(a) Winners

Would you "accept or "not accept" to compete again against Louis,
according to the following different scenarios from the previous stage?

<table><thead><tr><th></th><th>I accept</th><th>I do not accept</th></tr></thead><tbody><tr><td>You have solved correctly the same number of sums, so you are tied</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 1 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 2 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 3 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 4 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 5 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 6 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 7 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 8 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 9 more sum</td><td>0</td><td>0</td></tr><tr><td>You have solved correctly 10 more sum</td><td>0</td><td>0</td></tr></tbody></table>

(b) Losers

Would you "accept or "not accept" to compete again against Louis,
according to the following different scenarios from the previous stage?

<table><caption>**Fig. 2.** Example of the performance gap's scale.</caption><thead><tr><th></th><th>I accept</th><th>I do not accept</th></tr></thead><tbody><tr><td>You have solved correctly the same number of sums, so you are tied</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 1 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 2 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 3 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 4 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 5 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 6 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 7 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 8 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 9 more sum</td><td>0</td><td>0</td></tr><tr><td>Your opponent solved correctly 10 more sum</td><td>0</td><td>0</td></tr></tbody></table>

2022 and January 2023. The experiment was computerized using the oTree software (Chen, Schonger, & Wickens, 2016).

The average duration and payment of each experimental session were 45' and 13.70 Euros, respectively. For the final payment, we used the Random Incentive System: subjects were aware that only one out of the four stages of the game was taken into account for the final payment. The final amount received by each subject was the sum of the following: the payoff from the randomly chosen stage in Part I, the payoff from the BRET task (Part II), and a show-up fee of 9.00 Euros.

3. Testable hypotheses

This study examines individual behavior in a competitive environment, with a particular focus on how individuals respond to the outcome of a previous competition (winning or losing), and whether the gender of the opponent influences it. We assess these reactions by identifying each subject's switching point for re-entering into the competition, which is determined by the point difference between the subject and their opponent in the previous stage (see Fig. 2). A higher switching point indicates a higher inclination to repeat the competition. We propose hypotheses, separately for men and women, regarding how the outcome of the previous tournament and the opponent's gender affect the switching point.

Buser et al. (2023) reveal that willingness to compete is influenced by the gender of the opponent: women tend to avoid competing against men, while men, anticipating this behavior, show a greater willingness to compete against women. Buser (2016) finds that men respond to losing by selecting more challenging targets. Similarly, Buser and Yuan (2019) report that men are more likely than women to re-enter competition after a loss. Moreover, men tend to be more overconfident than women, especially in stereotypically masculine tasks such as mathematical tasks (Bordalo, Coffman, Gennaioli, & Shleifer, 2019; Guiso, Monte, Sapienza, & Zingales, 2008; Nosek, Banaji, & Greenwald, 2002). According to Bordalo et al. (2019), beliefs about others often align with beliefs about one's own performance. Given that men generally perform better in mathematical tasks (Guiso et al., 2008; Nosek et al., 2002), we expect male subjects in our sample to be confident in both their own performance and that of other men. Based on the aforementioned stereotypes, men are also likely to expect women to perform worse in mathematics, leading them to anticipate winning against female opponents. Therefore, we predict men's willingness to re-compete after winning to be higher against a woman than against a man (Price, 2008).

On the other hand, losing to a female opponent alters expectations, leading to a lower willingness to re-compete. This may reflect that men experience an "additional disutility" after losing to a high-performing

woman (Datta Gupta et al., 2013). We interpret this disutility as stemming from gender-based performance stereotypes—specifically, the belief that women perform less well in mathematical tasks. As a result, men are generally more confident when facing female opponents in this type of task. When they receive negative feedback (i.e., learning that they have lost), this feedback challenges their prior expectations and reduces their willingness to re-enter competition. We hypothesize that men are less willing to re-enter competition when they have lost to a woman than when they have lost to a man. This is consistent with Datta Gupta et al. (2013), who find that men avoid competition to prevent the reputational cost of losing to a woman. The key difference in our setting is that this decision comes after the defeat has already occurred. We derive then our first hypothesis:

**Hypothesis 1.** Men's willingness to re-compete is higher (lower) after winning (losing) against a woman than against a man.

Empirical studies have shown that women are more likely than men to withdraw after setbacks in male-dominated fields (Fischer, 2017; Goldin, 2015; Katz et al., 2006). Buser (2016) finds that women tend to reduce their performance after losing. Similarly, Gill and Prowse (2014) examine the effects of winning and losing on subsequent performance and find that women's performance declines after a loss. Additionally, Buser and Yuan (2019) show that women are less inclined than men to re-enter competition after losing. Fang et al. (2021) further demonstrate that girls are more prone to withdrawing after failures in previous competitions, particularly in countries with wider gender gaps in the labor market. Regardless of losing or winning, female players tend to be more reluctant to compete against men (Geraldes, 2020). Therefore, we hypothesize that women's willingness to re-compete depends not only on the outcome of their previous performance but also on the gender of their opponent. Furthermore, since women are generally more risk-averse and less confident than men, we expect them to shy away from competition after losing. Winning in Stage 3T may encourage women to compete by boosting their confidence and reducing uncertainty. However, we believe that this pattern is only observed when competing against female counterparts. Against male opponents, women may refuse to compete even if they won previously. When facing larger point gaps in their favor, women choose the piece rate scheme instead of competing against men, potentially due to self-restraint or the female modesty effect (Heatherington et al., 1993).

**Hypothesis 2.** Women's willingness to re-enter competition is lower when competing with a man compared to when competing with a woman. Additionally, women's willingness to re-enter competition is
<table><caption>**Table 1**
Summary of descriptive statistics.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Gender</th><th colspan="3">Condition</th></tr><tr><th>Female</th><th>Male</th><th>p</th><th>All</th><th>MM</th><th>FF</th><th>MF-FM</th></tr></thead><tbody><tr><td>Competitiveness (%)</td><td>49.70</td><td>67.75</td><td>0.00</td><td>57.24</td><td>60.71</td><td>53.85</td><td>58.14</td></tr><tr><td>Average performance (s.d.)</td><td>4.30<br>(2.10)</td><td>4.85<br>(2.56)</td><td>0.07</td><td>4.55<br>(2.35)</td><td>4.73<br>(2.63)</td><td>4.29<br>(2.20)</td><td>4.64<br>(2.26)</td></tr><tr><td>Stage 1</td><td>3.60</td><td>4.12</td><td>0.11</td><td>3.84</td><td>4.07</td><td>3.65</td><td>3.84</td></tr><tr><td>Stage 2</td><td>4.34</td><td>4.77</td><td>0.28</td><td>4.53</td><td>4.66</td><td>4.30</td><td>4.64</td></tr><tr><td>Stage 3PR</td><td>4.34</td><td>3.82</td><td>0.14</td><td>4.18</td><td>4.14</td><td>3.96</td><td>4.39</td></tr><tr><td>Stage 3T</td><td>5.21</td><td>5.83</td><td>0.06</td><td>5.56</td><td>5.65</td><td>5.23</td><td>5.67</td></tr><tr><td>Stage 4T</td><td>5.20</td><td>6.48</td><td>0.02</td><td>5.91</td><td>6.33</td><td>5.24</td><td>5.98</td></tr><tr><td>Stage 4PR</td><td>4.75</td><td>5.56</td><td>0.26</td><td>5.15</td><td>5.46</td><td>5.30</td><td>4.74</td></tr><tr><td>Distribution of victory belief (%)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Beliefs 1</td><td>55.03</td><td>75.00</td><td>0.00</td><td>63.45</td><td>69.64</td><td>58.65</td><td>64.34</td></tr><tr><td>Beliefs 2</td><td>84.52</td><td>76.54</td><td>0.19</td><td>80.72</td><td>85.29</td><td>87.50</td><td>73.33</td></tr><tr><td>Beliefs 3</td><td>76.79</td><td>74.07</td><td>0.74</td><td>75.68</td><td>80.95</td><td>75.76</td><td>73.21</td></tr><tr><td>Distribution of winners (%)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Stage 2</td><td>56.94</td><td>43.05</td><td>0.60</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Stage 3T</td><td>49.04</td><td>50.96</td><td>0.53</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Stage 4T</td><td>48.78</td><td>51.22</td><td>0.44</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Risk preferences</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Number of boxes (BRET)</td><td>38.70</td><td>49.85</td><td>0.00</td><td>43.20</td><td>51.61</td><td>39.03</td><td>43.20</td></tr><tr><td>Gender stereotypes</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Sexism</td><td>26.75</td><td>32.63</td><td>0.00</td><td>29.15</td><td>32.77</td><td>27.32</td><td>29.15</td></tr><tr><td>Transcendence</td><td>26.35</td><td>25.12</td><td>0.04</td><td>25.85</td><td>25.62</td><td>26.10</td><td>25.73</td></tr><tr><td>Age</td><td>37.82</td><td>31.83</td><td>0.02</td><td>35.34</td><td>30.84</td><td>39.32</td><td>34.08</td></tr><tr><td>Education (%)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>- Arts, Letters and Languages</td><td>10.65</td><td>6.67</td><td>0.24</td><td>8.97</td><td>8.93</td><td>15.38</td><td>3.88</td></tr><tr><td>- Law, Politics, Economics</td><td>37.28</td><td>41.67</td><td>0.45</td><td>38.97</td><td>35.71</td><td>28.85</td><td>48.84</td></tr><tr><td>- Social and Human Sciences</td><td>13.02</td><td>13.33</td><td>0.94</td><td>13.45</td><td>16.07</td><td>14.42</td><td>10.85</td></tr><tr><td>- Techno, Health and Engineering</td><td>10.65</td><td>23.33</td><td>0.00</td><td>15.86</td><td>28.57</td><td>11.54</td><td>13.95</td></tr><tr><td>- Other</td><td>28.40</td><td>15.00</td><td>0.01</td><td>22.76</td><td>10.71</td><td>29.81</td><td>22.48</td></tr><tr><td>N</td><td>169<br>(58.28%)</td><td>120<br>(41.38%)</td><td></td><td>290</td><td>56<br>(19.38%)</td><td>104<br>(35.99%)</td><td>129<br>(44.64%)</td></tr></tbody></table>

Notes: The table reports the means or the share of each variable across each gender and condition. P-values derived from $\chi^2$ for the binary variables and from MWU for continuous ones.

lower after losing than after winning, regardless of the gender of the opponent.

## 4. Results

Our sample is composed of 290 participants, with 58.28% identifying as female, 41.38% as male, and 0.34% of the participants not reporting their gender.<fnref n="12" /> Subjects are, on average, 35.34 years old. Table 1 presents a summary of descriptive statistics, including competitiveness, performance across different game stages, distribution of victory beliefs (i.e., percentage of subjects believing they won in the previous stage), percentage of winners, risk preferences, gender stereotypes, age, and education. We show the statistics for the full sample, splitting by gender (male/female), and by condition (MM, FF, MF-FM). Competitiveness corresponds to the choice of payment scheme in Stage 3 (0 = piece rate and 1 = tournament). The variables Sexism and Transcendence correspond to the sum of the Likert scale scores. A lower Sexism score indicates weaker sexist beliefs, while a higher Transcendence score reflects lower compliance with sexist norms.<fnref n="13" />

Subjects collect an average of 43.20 boxes out of 100 in the BRET. Women are significantly more risk-averse than men (Mann-Whitney, henceforth MWU, $p = 0.00$). Men show a significantly higher level of sexism than women (MWU, $p = 0.00$) and a lower level of transcendence (MWU, $p = 0.04$).

Overall, we find no significant gender differences in task performance (4.85 vs. 4.30) (MWU, $p = 0.07$).<fnref n="14" /> Nevertheless, there is an equal distribution of male and female winners in each tournament. Indeed, we find no significant differences between men and women in the proportion of winning, in any tournament (Stage 2, Stage 3T, Stage 4T, $\chi^2$, $p = 0.60$; $p = 0.53$; $p = 0.44$). We do not find significant differences in performance in Stage 1 (4.12 vs. 3.60, MWU, $p = 0.11$) and in Stage 2 (4.77 vs. 4.34, MWU, $p = 0.28$).

As shown in Table 1, in Stage 3, 49.70% of women and 67.75% of men choose the tournament payment scheme ($\chi^2$, $p = 0.00$). This finding is consistent with previous studies on gender differences in competitiveness (Balafoutas & Sutter, 2012; Niederle & Vesterlund, 2007; Van Veldhuizen, 2022). Fig. 3 illustrates the percentage of subjects opting for competition in Stage 3, across conditions. On the left, we present the bars representing males (MM and MF conditions), while on the right, we depict the bars for females (FM and FF conditions). We observe non-significant differences, as both men and women appear indifferent to the gender of their opponent ($\chi^2$, respectively $p = 0.14$ and $p = 0.17$). This result aligns with findings from previous studies (Burow, Beblo, Beninger, & Schröder, 2017; Datta Gupta et al., 2013). Belief elicitation after the task reveals that men are significantly more confident than women: 75.00% of men expect to win versus 55.03% of women ($\chi^2$, $p = 0.00$) according to Table 1.

For both men and women, confidence is not affected by the gender of the opponent ($\chi^2$, respectively $p = 0.20$ and $p = 0.23$).

In Table 2, we conduct four specifications using a Probit model to identify the factors influencing the choice of payment scheme in Stage 3. The dependent variable takes the value 1 if the subject chooses the tournament, and 0 otherwise. Columns 1–2 refer to male observations,

<footnote n="12">¹² Only one participant selected “Others”. We excluded this observation from analyses that differentiate by gender, but retained it when pooling all participants. Importantly, we preserved the gender information that was communicated to their opponent via the chosen name.</footnote>

<footnote n="13">¹³ The two notions are significantly negatively correlated (Pearson's $r = -0.50$, $p = 0.00$).</footnote>

<footnote n="14">¹⁴ See Figure A.2 (Appendix A.2) for the performance evolution across the stages, based on the chosen payment scheme.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Percentage of subjects choosing the competition in Stage 3, by gender and condition.</figcaption></figure>

and columns 3–4 to female observations. In all specifications, the explanatory variables are: Female opponent (takes the value 1 if the opponent is a female, and 0 otherwise), Risk aversion (takes the value 1 if the subject collects less than 50 boxes at the BRET task, and 0 otherwise),<fnref n="15" /> Age, Sexism, Transcendence, and *Beliefs 2* (takes the value 1 when the participant expects to win in Stage 2, and 0 otherwise). In columns 2 and 4, we add the interaction between the gender of the opponent and the beliefs on Stage 2 (Female opponent × *Beliefs 2*).

Entry into the competition is mainly influenced by *Beliefs 2*: men and women who expect to win in Stage 2 are significantly more likely to choose the tournament payment scheme over the piece rate in Stage 3. We observe a significant and positive effect of Transcendence for males (columns 1–2), suggesting that lower gender stereotypes (i.e., being more transcendent) significantly increase the probability of choosing the tournament in Stage 3.<fnref n="16" /> We do not report any significant coefficient for Female opponent,<fnref n="17" /> Risk aversion,<fnref n="18" /> Age, or Sexism on the decision to compete. Our interaction term is non-significant for males and females, indicating that confident participants are indifferent to the gender of their opponent when deciding whether to compete in Stage 3. In fact, the main driver behind the decision to compete is beliefs: participants who expect to win in Stage 2 are more likely to enter the competition in Stage 3, irrespective of their own gender or that of their opponents.

## 4.1. Willingness to compete again

In this section, the analysis focuses on the second choice of payment scheme, specifically the decision to choose the tournament at Stage 4. By allowing subjects to decide whether to opt into the tournament before this stage, we ensure that the analysis focuses exclusively on

competitive individuals. We therefore combine the standard binary analysis (conducted in the previous section) with a more granular and continuous measure of competitiveness. In this stage, we measure competitiveness based on the switching point. The switching point is defined as the performance gap at which individuals switch from choosing to compete to opting out, or vice versa. The advantage of the switching point is that it provides a continuous measure of subjects' level of competitiveness.<fnref n="19" /> To facilitate the interpretation of the results, we standardize the switching point to ensure that it points always in the same direction. Therefore, the higher the value of the switching point, the more willing is a participant to compete again.

It appears essential to mention that, as for other strategy methods such as the multiple price list mechanisms, we report some inconsistencies in participants' responses. In our coding of the “switching point” variable, we choose to exclude participants who switch more than once, although our results are robust when including them.<fnref n="20" /> However, we consistently exclude from the analysis those (N = 2) who only accept to compete for a single point gap (other than the “tie”) and those (N = 15) who switch in the opposite direction for the switching point after winning. Moreover, no participant behaves inconsistently after a defeat by preferring to compete for large gaps rather than small ones. This suggests good comprehension of the task and limited inconsistency in responses.

Fig. 4 illustrates the distribution of the switching points based on the outcome of Stage 3T (winning, in panel (a), and losing, in panel (b)) and the gender of the participant (green bars for males and orange bars for females). Overall, we observe similar patterns in the distribution of switching points for men and women (two-sample Kolmogorov-Smirnov, *p* = 0.81). After winning (Fig. 4(a)), the distribution is right-skewed with a peak at the upper limit (a switching point of 11), while after losing (Fig. 4(b)), the distribution is left-skewed with a mild peak around a switching point of 2 for men and 3 for women. After losing, men and women are equally willing to compete for any point gap, indicated by a switching point of 11 (13.04% vs. 10.34%, χ², *p* = 0.51). Nevertheless, after winning, women are more likely than men to accept competition for any point gap (65.00% vs. 43.18%, χ², *p* = 0.04). The findings suggest that both men and women exhibit increased levels of competitiveness after winning, but this effect is more pronounced among women.

### 4.1.1. Gender of the opponent and willingness to compete again

We further investigate whether the gender of the opponent affects the decision to compete again. Fig. 5 shows the average switching point for men and women, conditional on the outcome of Stage 3T (winning or losing) and the condition they were assigned to (MM, FF, MF and FM). Overall, we find no significant differences in the average switching point between men and women (respectively, 7.36 vs. 7.10, MWU, *p* = 0.83),<fnref n="21" /> when we elicit their beliefs, men and women equally expect to win in Stage 4T (χ², *p* = 0.19). This suggests that competitive women (who self-selected in Stage 3) exhibit similar levels of competitiveness compared to competitive men.

<footnote n="15">¹⁵ The results are robust when conducting the regressions with a continuous measure labeled “Number of boxes collected (BRET)” as presented in Table A4 (Appendix A.4). Table A5 presents the results with standard errors clustered at the session level.</footnote>

<footnote n="16">¹⁶ Competitive males display significantly higher levels of transcendence compared to non-competitive males (*p* = 0.01, MWU).</footnote>

<footnote n="17">¹⁷ Even if the gender of the opponent does not seem to have, on average, an impact on the decision to compete, two subjects reported that they took this variable into account when choosing the tournament. Indeed, to the question “why did you choose the tournament?”, the participants’ answers were: “my opponent’s name was female” and “because I thought I had a good chance of winning against a girl, girls are generally less good at maths than boys”.</footnote>

<footnote n="18">¹⁸ On average, competitive participants collect 44.22 boxes, and non-competitive collect 41.84 boxes (MWU, *p* = 0.25).</footnote>

<footnote n="19">¹⁹ The main challenge lies in the dichotomous direction of the switching point depending on the outcome. After losing, participants switch from accepting to compete for smaller points gaps to refusing to compete for larger points gaps. For example, after losing, a switching point of 8 means that the participant is willing to compete when the point gap is lower than 8, but if the opponent solves 8 or more problems more than the participant, the subject refuses to compete. Reversely, after winning, the switching point goes in the opposite direction: participants switch from refusing to accepting. For example, after winning, a switching point of 5 means that the participant does not want to compete for point gaps lower (or equal) than 5.</footnote>

<footnote n="20">²⁰ Table A6 in Appendix A.4 presents robustness checks using a Tobit model with switching points ranging from 0 to 11, including those who switch more than once (7 men and 7 women).</footnote>

<footnote n="21">²¹ The decline of gender differences in competition could be explained by the absence of gender differences in confidence after Stage 3T. As shown in Table 1.</footnote>
<table><caption>**Table 2**
Determinants of entry into competition in Stage 3.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Entry competition<br>Males</th><th colspan="2">Females</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>Female opponent</td><td>0.40<br>(1.50)</td><td>0.71<br>(1.36)</td><td>0.24<br>(1.14)</td><td>0.27<br>(0.88)</td></tr><tr><td>Risk aversion</td><td>0.22<br>(0.84)</td><td>0.22<br>(0.82)</td><td>0.01<br>(0.04)</td><td>0.01<br>(0.04)</td></tr><tr><td>Age</td><td>0.00<br>(0.21)</td><td>0.00<br>(0.18)</td><td>-0.00<br>(-0.69)</td><td>-0.00<br>(-0.67)</td></tr><tr><td>Sexism</td><td>0.00<br>(0.00)</td><td>0.00<br>(0.08)</td><td>-0.01<br>(-0.57)</td><td>-0.01<br>(-0.57)</td></tr><tr><td>Transcendence</td><td>0.10<sup>**</sup><br>(2.66)</td><td>0.10<sup>**</sup><br>(2.69)</td><td>-0.01<br>(-0.27)</td><td>-0.01<br>(-0.27)</td></tr><tr><td>Beliefs 2</td><td>1.04<sup>***</sup><br>(3.48)</td><td>1.25<sup>**</sup><br>(2.95)</td><td>0.78<sup>***</sup><br>(3.79)</td><td>0.82<sup>*</sup><br>(2.47)</td></tr><tr><td>Female opponent × Beliefs 2</td><td></td><td>-0.44<br>(-0.73)</td><td></td><td>-0.06<br>(-0.15)</td></tr><tr><td>Constant</td><td>-3.05<sup>*</sup><br>(-2.31)</td><td>-3.23<sup>*</sup><br>(-2.37)</td><td>0.01<br>(0.01)</td><td>-0.02<br>(-0.01)</td></tr><tr><td>Observations</td><td>120</td><td>120</td><td>169</td><td>169</td></tr></tbody></table>

Notes: Probit model regressions. *t* statistics in parentheses and standard errors are robust. Dependent variable in 1-4: Entry competition. Specifications 1-2: Only males. Specifications 3-4: Only females. Independent variables are described in the text. *, **, *** indicate significance at the 5%, 1%, 0.1% level, respectively.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Distribution of the switching point, by outcome in Stage 3T and gender of the subject.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Average switching point, by outcome in Stage 3T and condition.</figcaption></figure>
<table><caption>**Table 3**
Determinants of switching point.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Switching point<br>Males</th><th colspan="4">Females</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Female opponent</td><td>0.31<br>(0.43)</td><td>2.42<br>(1.93)</td><td>0.14<br>(0.18)</td><td>-0.66<br>(-0.76)</td><td>-0.13<br>(-0.19)</td><td>0.92<br>(0.83)</td><td>0.13<br>(0.16)</td><td>-0.10<br>(-0.11)</td></tr><tr><td>Risk aversion</td><td>-0.92<br>(-1.23)</td><td>-0.98<br>(-1.35)</td><td>-1.06<br>(-1.33)</td><td>-0.96<br>(-1.23)</td><td>-0.42<br>(-0.58)</td><td>-0.53<br>(-0.74)</td><td>-0.16<br>(-0.20)</td><td>-0.19<br>(-0.24)</td></tr><tr><td>Age</td><td>-0.04<br>(-1.61)</td><td>-0.04<br>(-1.64)</td><td>-0.06*<br>(-2.05)</td><td>-0.06*<br>(-2.15)</td><td>0.03<br>(1.50)</td><td>0.04<br>(1.77)</td><td>0.02<br>(0.79)</td><td>0.02<br>(0.87)</td></tr><tr><td>Sexism</td><td>0.03<br>(0.78)</td><td>0.06<br>(1.40)</td><td>0.07<br>(1.48)</td><td>0.09<br>(1.99)</td><td>0.05<br>(1.06)</td><td>0.04<br>(0.85)</td><td>0.06<br>(1.02)</td><td>0.06<br>(0.99)</td></tr><tr><td>Transcendence</td><td>0.01<br>(0.08)</td><td>0.06<br>(0.56)</td><td>0.10<br>(0.82)</td><td>0.16<br>(1.28)</td><td>0.16<br>(1.12)</td><td>0.17<br>(1.26)</td><td>0.15<br>(0.95)</td><td>0.16<br>(1.00)</td></tr><tr><td>Winner Stage 3T</td><td>5.31***<br>(6.79)</td><td>7.02***<br>(6.21)</td><td></td><td></td><td>6.30***<br>(9.10)</td><td>7.37***<br>(6.64)</td><td></td><td></td></tr><tr><td>Female opponent × Winner Stage 3T</td><td></td><td>-3.25*<br>(-2.06)</td><td></td><td></td><td></td><td>-1.79<br>(-1.22)</td><td></td><td></td></tr><tr><td>Overconfidence Stage 3T</td><td></td><td></td><td>-6.10***<br>(-5.74)</td><td>-7.98***<br>(-5.83)</td><td></td><td></td><td>-6.06***<br>(-7.23)</td><td>-6.51***<br>(-4.84)</td></tr><tr><td>Female opponent × Overconfidence Stage 3T</td><td></td><td></td><td></td><td>4.53*<br>(2.14)</td><td></td><td></td><td></td><td>0.73<br>(0.42)</td></tr><tr><td>Constant</td><td>4.05<br>(0.95)</td><td>0.78<br>(0.17)</td><td>5.67<br>(1.24)</td><td>3.89<br>(0.86)</td><td>-2.87<br>(-0.65)</td><td>-3.89<br>(-0.87)</td><td>2.92<br>(0.57)</td><td>2.81<br>(0.55)</td></tr><tr><td>Observations</td><td>66</td><td>66</td><td>66</td><td>66</td><td>69</td><td>69</td><td>69</td><td>69</td></tr></tbody></table>

Notes: Tobit model regressions. *t* statistics in parentheses and standard errors are robust. Dependent variable in 1-8: Switching point. Specifications 1-4: Only males. Specifications 5-8: Only females. Independent variables are described in the text. *, **, *** indicate significance at the 5%, 1%, 0.1% level, respectively.

In Table 3, we explore the determinants of the switching point by conducting Tobit estimations with the switching point as the dependent variable ranging from 0 to 11. Our explanatory variables are: Female opponent, Risk aversion<fnref n="22" />,<fnref n="23" /> Age, Sexism, and Transcendence. In specifications 1–2 and 5–6, we include the variable Winner Stage 3T which takes the value 1 if the subject wins in Stage 3, and 0 otherwise. Additionally, in specifications 3–4 and 7–8, we incorporate the variable Overconfidence Stage 3T that takes the value 1 when the participant expects to win in Stage 3T but actually loses. It takes the value 0 in any of the following three cases: 1-expects to win and actually wins, 2-expects to lose and actually loses, or 3-expects to lose but actually wins. In columns 2 and 6, we add the interaction term: Female opponent × Winner Stage 3T. In columns 4 and 8, we include the interaction between the gender of the opponent and overconfidence in Stage 3T (Female opponent × Overconfidence Stage 3T).<fnref n="24" />

Consistent with our descriptive results, we observe a significant and positive coefficient for Winner Stage 3T in specifications 1–2 and 5–6, suggesting that winning in the previous competition (Stage 3) significantly increases the switching point for both males and females. In the second specification, the interaction term Female opponent × Winner Stage 3T has a negative and significant effect, indicating that male winners lower significantly their switching point when winning against a female compared to when winning against a male. In other words, after winning, men have a lower willingness to compete again against a woman than against a man. The interaction term is not significant for females in column 6, indicating that, after winning, women are not influenced by the gender of their opponent when deciding whether to repeat the competition.

To summarize our first finding, we observe a deviation from Hypothesis 1 in men's reactions after winning, since winning against a female opponent decreases their switching point. Contrary to our hypothesis, men exhibit a behavioral shift after winning.

**Result 1a.** After winning against a female opponent, men exhibit a decrease in their willingness to re-compete.

In contrast to our second hypothesis, the gender of the opponent does not significantly influence women's switching point. Remarkably, women do not demonstrate increased reluctance to re-enter competition when facing men as opposed to women. One plausible explanation is that non-competitive women, who opt for the piece rate in Stage 3 and are subsequently excluded from our sample, may be the ones avoiding competition against men. This nuanced perspective aligns with

<footnote n="22">²² Even if competitive and non-competitive participants do not significantly differ in risk aversion, we control for it in our regressions given its possible interaction with the switching point. Indeed, risk-averse individuals may choose to re-compete after a defeat (victory) for a smaller (larger) performance gap, compared to risk-seeker individuals.</footnote>

<footnote n="23">²³ Again, the results are robust when conducting the regressions with a continuous measure labeled “Number of boxes collected (BRET)” as presented in Table A7 (Appendix A.4).</footnote>

<footnote n="24">²⁴ We test the robustness of our results by using an alternative specification where we include a variable for confidence instead of overconfidence. This new variable takes the value 1 if the subject is overconfident, 0 if the beliefs are accurate, and -1 if the subject is underconfident. The results of our Tobit estimations on the switching point, incorporating this new measure as an explanatory variable, are presented in Table A8 (Appendix A.4). Furthermore, we perform an additional robustness check by excluding subjects who did not correctly report the gender of their opponent at the end of the experiment. Table A9 in Appendix A.4 presents results of Tobit estimations on the switching point of those who correctly guessed the gender of their opponent. This ensures</footnote>

<footnote>the validity of our results for participants who accurately perceive the gender they are competing against. We test the robustness of our results by replicating Table 3 in Table A10 (Appendix A.4) using OLS estimations and we find qualitatively the same results. Finally, we cluster at the session level in Table A11.</footnote>
the insights from Geraldes (2020), suggesting that women's reluctance to compete might be more directed towards competing against men specifically, rather than a general aversion to competition. We partially confirm the second part of our hypothesis, since women's (and men's) switching point is lower after losing than after winning, regardless of the gender of their opponent. However, we do not observe a significant reluctance to compete against men after a victory. This leads us to formulate our second key result:

**Result 2a.** After winning, women are more willing to re-compete. On average, women exhibit indifference to the gender of the opponent when deciding whether to compete again.

### 4.1.2. The role of overconfidence

When we look at beliefs, we find a significant and negative coefficient for Overconfidence Stage 3T in the four specifications where this variable is included (columns 3-4 and 7-8 of Table 3), suggesting that when participants hold inaccurate beliefs (i.e., they expect to win but end up losing) they tend to lower their switching point. This result aligns with Gill and Prowse (2012)'s findings on aversion to outcomes that do not meet expectations. In other words, participants are discouraged from re-entering the competition when they learn that their outcome is not the one expected. In column 4, a positive and statistically significant effect emerges for the interaction term Female opponent × Overconfidence Stage 3T for males, indicating that their switching point is significantly higher when they hold inaccurate beliefs after losing against a woman, compared to against a man. In other words, the effect of inaccurate beliefs is less pronounced when a male engages in competition with a female as opposed to a male counterpart. This observation implies that men who hold inaccurate beliefs are more eager to repeat the competition against a woman than against a man. Again, the interaction term Female opponent × Overconfidence Stage 3T is not significant for women, indicating that women do not make a distinction between having a male or female opponent when deciding whether to compete again.<fnref n="25" />

This additional finding shows that the primary mechanism underlying men's behavior appears to be the presence of inaccurate beliefs. Indeed, when focusing only on overconfident men, we observe that holding inaccurate beliefs (i.e., expecting to win but losing) reduces their inclination to compete again against a male opponent. On the other hand, overconfident men who hold inaccurate beliefs after being outperformed by a female appear more inclined to re-enter the competition.

**Result 1b.** After winning against a female opponent, men exhibit a decrease in their willingness to re-compete, whereas holding inaccurate beliefs when losing to a female opponent (i.e., expecting to win but losing) leads to an increase in their willingness to re-compete.

**Result 2b.** Women who hold inaccurate beliefs (i.e., expecting to win but losing) are less likely to re-enter the competition regardless of the gender of the opponent.

Although overconfidence plays a significant role in determining the decision to compete again, we do not find any significant effect of transcendence and sexism. While we observe that transcendence significantly predicts men's entry into competition in Stage 3, neither transcendence nor sexism explain men's or women's willingness to re-enter competition in Stage 4. At first sight, this might appear inconsistent with the evidence that men's inaccurate beliefs (expecting to win but losing) affect their decision to compete again. Yet, the difference reflects the nature of the two decisions. Initial entry into competition may be shaped by more stable attitudes and values, such as weaker endorsement of gender stereotypes, which encourage transcendent men to opt into tournaments. In contrast, the re-entry decision occurs after participants receive direct performance feedback, and is therefore less influenced by stable attitudinal measures and more driven by situational psychological factors. In line with our findings discussed above, men's reactions after losing – particularly to women – point to mechanisms such as shame, pride, or the desire for revenge, which help explain why overconfidence rather than gender stereotypes drives re-entry. In other words, once competition has been experienced, short-term emotional responses to outcomes appear to dominate more general beliefs about gender roles in shaping the willingness to compete again.

### 4.1.3. Additional outcome: performance in second competition

Although our analysis primarily focuses on the decision of re-entering competition, we are further interested in analyzing the performance in the tournament and its evolution across stages. Men perform significantly better in Stage 4T after losing in Stage 3T against a woman (MF) than against a man (MM). As shown in Fig. 6 panel (b), men significantly improve their performance between Stage 3T and Stage 4T against a female opponent (Wilcoxon signed-rank, *p* = 0.02): they solve on average 2.00 more problems in Stage 4T, compared to Stage 3T. After winning, differences in performance are not significant (panel (a)). We do not find any significant results for women's performance.

In Table 4, we run an OLS estimation with performance in Stage 4T as the dependent variable. We break down our sample, including only males in columns 1-4 and only females in columns 5-8. The explanatory variables in the models include: Female opponent, Loser Stage 3T (takes the value 1 if the participant lost in Stage 3T, 0 otherwise), the interaction term Female opponent × Loser Stage 3T, and Performance in Stage 3T in columns 1 and 5. In columns 2 and 6, we add the following control variables: Age, Sexism, and Transcendence. In columns 3-4, and 7-8, we focus on the effect of overconfidence in Stage 3T (takes the value 1 if the participant expects to win but loses and 0 otherwise) and its interaction with Female opponent.

We observe a positive and significant coefficient for Performance in Stage 3T, indicating that higher performers in Stage 3T also perform better in Stage 4T. The interaction term in columns 1-2 also exhibits a positive and significant coefficient, confirming that after losing, men enhance their performance against a female opponent compared to a male opponent. Moreover, the significant and positive coefficient of Female opponent × Overconfidence Stage 3T in columns 3-4 suggests that the increase in performance is driven by overconfident males. Men who expect to win the tournament but lose in Stage 3 are more likely to improve their performance in Stage 4T when playing against a female opponent, compared to a male counterpart. However, no similar effect is observed for women. These results remain robust after including control variables.

Consistent with Result 1b, we observe that after losing, men exhibit an increased determination to succeed against female opponents. This is evident in two dimensions: an increase in their willingness to re-compete and an improvement in performance after losing against women. Since these results are driven by overconfidence, it suggests that holding inaccurate beliefs when losing to a female opponent may trigger a stronger motivation to outperform in subsequent rounds.

<footnote n="25">²⁵ While our initial pre-registered target was to recruit 400 participants, logistical and institutional constraints limited our final sample to 290 participants. This reduction in sample size has important implications for the interpretation of our findings, particularly when analyzing subgroup effects. For our main analyses, such as differences in the willingness to re-enter competition after winning versus losing, the sample size remains sufficient to detect meaningful differences with high statistical power (>0.94 at $α = 0.05$), including within gender subsamples. However, when we further disaggregate the data, for example, by considering the gender of the opponent—the resulting cell sizes are substantially smaller, and the statistical power declines sharply. In these cases, the lack of significant findings should be interpreted with caution, as it may reflect insufficient power rather than the absence of a true effect.</footnote>
<figure><img src="image_8.png" /><figcaption>(b) Losers in Stage 3T</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Performance in Stage 3T and Stage 4T, by outcome in Stage 3T and condition.</figcaption></figure>

<table><caption>**Table 4**
Determinants of performance in stage 4T.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Performance in stage 4T</th><th colspan="4">Females</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Female opponent</td><td>-0.12<br>(-0.19)</td><td>-0.35<br>(-0.52)</td><td>0.27<br>(0.45)</td><td>0.19<br>(0.29)</td><td>0.31<br>(0.58)</td><td>0.57<br>(1.00)</td><td>0.34<br>(0.64)</td><td>0.56<br>(1.08)</td></tr><tr><td>Age</td><td></td><td>-0.01<br>(-0.30)</td><td></td><td>-0.00<br>(-0.10)</td><td></td><td>-0.02<br>(-1.48)</td><td></td><td>-0.02<br>(-1.75)</td></tr><tr><td>Sexism</td><td></td><td>0.06<br>(1.76)</td><td></td><td>0.04<br>(1.07)</td><td></td><td>0.03<br>(0.93)</td><td></td><td>0.03<br>(0.90)</td></tr><tr><td>Transcendence</td><td></td><td>0.12<br>(1.14)</td><td></td><td>0.08<br>(0.80)</td><td></td><td>0.11<br>(1.12)</td><td></td><td>0.10<br>(1.05)</td></tr><tr><td>Loser Stage 3T</td><td>-1.48<br>(-1.89)</td><td>-2.57*<br>(-2.58)</td><td></td><td></td><td>-0.50<br>(-0.78)</td><td>-0.33<br>(-0.50)</td><td></td><td></td></tr><tr><td>Female opponent × Loser Stage 3T</td><td>3.12**<br>(3.40)</td><td>4.61***<br>(3.82)</td><td></td><td></td><td>-0.11<br>(-0.12)</td><td>-0.39<br>(-0.42)</td><td></td><td></td></tr><tr><td>Overconfidence Stage 3T</td><td></td><td></td><td>-1.16<br>(-1.49)</td><td>-2.09<br>(-1.75)</td><td></td><td></td><td>-0.33<br>(-0.50)</td><td>-0.35<br>(-0.54)</td></tr><tr><td>Female opponent × Overconfidence Stage 3T</td><td></td><td></td><td>3.21**<br>(2.93)</td><td>4.35**<br>(2.80)</td><td></td><td></td><td>-0.23<br>(-0.26)</td><td>-0.40<br>(-0.44)</td></tr><tr><td>Performance in Stage 3T</td><td>0.91***<br>(7.52)</td><td>0.92***<br>(7.89)</td><td>0.89***<br>(8.47)</td><td>0.90***<br>(8.11)</td><td>0.81***<br>(7.43)</td><td>0.80***<br>(6.31)</td><td>0.83***<br>(7.51)</td><td>0.81***<br>(6.57)</td></tr><tr><td>Constant</td><td>0.93<br>(0.96)</td><td>-3.67<br>(-1.00)</td><td>0.85<br>(1.06)</td><td>-2.23<br>(-0.65)</td><td>0.75<br>(0.97)</td><td>-2.46<br>(-0.74)</td><td>0.60<br>(0.79)</td><td>-2.22<br>(-0.68)</td></tr><tr><td>Observations</td><td colspan="4">54</td><td colspan="4">56</td></tr></tbody></table>

Notes: OLS model regressions. t statistics in parentheses and standard errors are robust. Dependent variable in 1-4: Performance in Stage 4T. Specifications 1-2: Only males. Specifications 3-4: Only females. Independent variables are described in the text. *, **, *** indicate significance at the 5%, 1%, 0.1% level, respectively.

## 5. Conclusions

We conduct an experiment in which participants perform a simple task of adding two digits. They face two main decisions: first, choosing between being paid for the task based on a piece rate or a tournament; and second, deciding on their payment scheme for the subsequent round after observing the outcome (win or loss). We examine whether individuals are more likely to repeat the competition or refrain from it, focusing on how the preference for competition is influenced by the prior competition's outcome, and if the gender of the opponent plays a role in this decision-making process. Additionally, we introduce a novel design that obtains a continuous measure of subjects' willingness to compete, deviating from the standard binary decision framework.

Our data reveals that in the first choice, men are more willing to compete than women, consistent with previous studies. Participants, however, show indifference to the gender of their opponent, and their decision to compete is mainly influenced by their expectation to win in previous stages where the task is performed. In the second choice to (not) compete, regardless of their opponent's gender, both men and women exhibit increased levels of competitiveness after winning, with this trend being particularly pronounced among women. Nevertheless,

we observe that men decrease their willingness to repeat the competition after winning against women. One plausible explanation for these findings could be that men may previously have built a reputation for prevailing over women. Consequently, they may be inclined to avoid the potential risk of losing a competition against a woman, as doing so could jeopardize their established reputation. In essence, men might be motivated to uphold their perceived dominance, thereby preventing women from outperforming them and hence avoiding potential disutility (He & Noussair, 2021). We further observe that overconfidence plays a critical role in participants' decision to avoid competition for a second time. Overall, participants compete less when they hold inaccurate beliefs, that is, when they expect to win and end up losing. Males are less affected by this mismatch between expectations and outcomes when they lose against women, showing a greater willingness to compete again. In line with this, we find significant results regarding the reaction after losing, particularly in terms of performance. Men's performance significantly improves after losing against females, revealing that males have a significantly higher drive to win over their female opponents compared to male opponents. This result suggests that the losers are indeed stimulated by the challenger option, i.e., winning over a woman who has previously outperformed them (Buser,
2016). Men's willingness to outperform their female opponents in the next round might be driven by various psychological factors, such as shame, revenge, or pride. As suggested by the positive impact of overconfidence on performance, we argue that men may attempt to surpass their female opponents in two ways: 1- by re-entering the competition more frequently and 2- by enhancing their performance.<fnref n="26" /> On the other hand, women are not affected in any case by the gender of their opponent: they are more likely to compete after winning and less likely to compete when they hold inaccurate beliefs, regardless of their opponent's gender. Overall, men seem to be reluctant to be outperformed by women which can explain the underrepresentation of women in senior and high-paying positions (De Paola & Scoppa, 2015).

This work contributes substantially to the existing literature by offering valuable insights into gender differences in competitive behavior. We confirm previous findings showing that men are generally more sensitive to feedback and the gender of the opponent, compared to women. For example, Dilmaghani (2022) find that in super-elite chess games, males are quicker to quit when facing a female opponent compared to a male, while female players exhibit consistent behavior regardless of the opponent's gender. Furthermore, Berlin and Dargnies (2016) indicate that women are more focused on their performance level, while men are more influenced by the skill level of their competitors. Additionally, Wozniak, Harbaugh, and Mayr (2009) show that feedback diminishes gender differences by reducing men's reluctance to participate. Finally, Baier, Davis, Jaber-Lopez, and Seidl (2018) conclude that men are more responsive to feedback in task choice, whereas women display greater stability in task selection across different information.

Our findings contribute to a better understanding of the mechanisms that may underlie persistent gender disparities in leadership and high-level positions. The experimental evidence presented here is especially relevant in contexts characterized by repeated interactions and cumulative career evaluations, such as job promotions or performance-based tournaments, where initial disadvantages may compound over time. These dynamics are consistent with the “glass ceiling” phenomenon, where women’s progression into top roles remains disproportionately limited. Importantly, participants in our experiment first decide whether to enter the tournament in Stage 3, and we then compare in Stage 4 women and men with similar levels of competitiveness. In real-life settings, they are likely to be the ones pursuing highly competitive educational or professional trajectories. Within this competitive subsample, we find no evidence that women are more discouraged from re-entering competition. This suggests that once women self-select into competitive environments, their persistence and willingness to compete are comparable to those of men. By identifying the behavioral roots of competitive engagement across gender lines, our results shed light on the micro-foundations of vertical occupational segregation and offer insights for policies aimed at fostering more equitable career trajectories.

Our experiment concludes the game at Stage 4 without disclosing information about opponents' decisions or performances in Stage 4. This feature presents an opportunity for future research to explore potential renunciation effects when such information is revealed. Additionally, it could provide further evidence regarding whether high-performing women exert less effort when facing a persistent male opponent.

### CRediT authorship contribution statement

C. Mollier: Writing – review & editing, Writing – original draft, Software, Project administration, Methodology, Formal analysis, Data curation, Conceptualization. A. García-Gallego: Writing – review & editing, Writing – original draft, Supervision, Resources, Methodology, Funding

acquisition, Formal analysis, Conceptualization. T. Jaber-Lopez: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. S. Zaccagni: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

### Acknowledgments

We are grateful to Olivier Renault and Maria J. Montoya-Villalobos for their useful comments and suggestions during Nanterre's Doctoral seminar. We are also thankful to Fabien Cerrotti and Chouaib Jouf for their precious help with the coding of the experiment. We thank the participants at the Workshop of the PSE Summer School, Workshop "Social behavior and discrimination" at Nanterre, SEET 2023 in Valencia, Webinar "Gender, Behavior and Decision-Making" at Paris Dauphine, AFSE 2023 at Sciences Po and ESA World Meeting 2023 in Lyon. García-Gallego is grateful to the Spanish Ministerio de Ciencia, Innovación y Universidades (grants RTI2018-096927-B-100 and PID2021-1230530B-100), and the Generalitat Valenciana, Spain (grant CIAICO/2023/102) for the funding of the experimental sessions.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.socec.2025.102475.

### Data availability

Data will be made available on request.

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