Not giving up: Testosterone promotes persistence against a stronger opponent

Recent research suggests that when we lack a sense of control, we are prone to motivational failures and early quitting in competitions. Testosterone, on the other hand, is thought to boost competitiveness. Here we investigate the interaction between these factors, testing the testosterone's potential to enhance persistence in a competition against a stronger opponent, depending on experimentally manipulated perceived control. Healthy participants were administered a single dose of testosterone or placebo. They first underwent a task designed to either induce low or high perceived control and then entered a costly competition against a progressively stronger opponent that they could quit at any time. In the placebo group, men with low perceived control quitted twice as early as those with high perceived control. Testosterone countered this effect, making individuals with low control persist in the competition for as long as those with high perceived control, and did so also despite raising participants' explicit awareness of the opponents' advantage. This psychoendocrinological effect was not modulated by basal cortisol levels, CAG repeat polymorphism of the androgen receptor gene, or trait dominance. Our results provide the first causal evidence that testosterone promotes competitive persistence in humans and demonstrate that this effect depends on the psychological state elicited prior to the competition, broadening our understanding of the complex relationships between testosterone and social behaviors.


Introduction
Competition is an important feature of society and beating a competitor is a powerful motivator (e.g., Le Bouc and Pessiglione, 2013;Studer et al., 2016;Vansteenkiste and Deci, 2003). But what makes us persist when opponents outperform us? Theoretical and empirical research identifies perceived personal control as one deciding factor of motivation in challenging situations . Perceived personal control is defined as the belief in the ability to influence one's environment (Rotter, 1966;Tobias-Webb, et al., 2017), and is thought to enhance motivation by increasing our perceived competence , expectations of performing well (Wulf et al., 2014) and of achieving a wanted outcome (Bandura and Locke, 2003;Eccles and Wigfield, 2002;Lawler and Porter, 1967;Thompson et al., 2007). Consistent with this, high control-and competence-related beliefs have been linked to enhanced competitive behavior, such as participation in sports, math tournaments (Niederle and Vesterlund, 2007), or gambling (Lim et al., 2014). Importantly, perceived control is not a mere reflection of objective control. Previous empirical research has shown that it is possible to induce a high level of perceived control-even when objective control is null-by manipulating factors such as choice, frequency of reinforcement, outcome sequences, the need to avoid aversive outcomes, and involvement (Langer, 1975; see meta-analysis by Stefan and David (2013)). In the context of gambling, where odds are against the player, such induced "illusory control" enhances wish to continue gambling (Clark et al., 2014) as well as actual playing (Côté, et al., 2003). Moreover, recent laboratory research revealed that experimentally induced illusory control influences subsequent neural responses to self-generated stimuli (Seidel et al., 2021), and boosts persistence under diminishing returns (Studer et al., 2020). These findings indicate that perceptions of high control could make us persist in competitions, even against stronger opponents.
A separate line of research suggests a critical role of the hormone testosterone in driving competition behavior. In nonhuman animals, testosterone injections increase persistence with food searching and social investigation (Thor, 1980). In men, basal testosterone levels were linked to a preference for entering a competition (Eisenegger et al., 2013, but see Apicella et al. (2011); Carré and McCormick, 2008). Furthermore, competition-induced changes in testosterone concentrations have been found to correlate with physical competitive performance (Casto et al., 2020), as well as one-time willingness to compete again, particularly when the first competition had resulted in a loss (Mehta and Josephs, 2006) or an ambiguous outcome (Carré and McCormick, 2008). Together, these correlational studies suggest that basal levels and competition-induced release of testosterone may promote efforts to regain or solidify social status (Geniole and Carré, 2018; see also Losecaat Vermeer et al. (2020)). No studies to date, however, have examined the hormone's causal effects on persistence in an ongoing competition over more than one round and-most relevant-whether and how such effects interact with those of perceived control.
We investigated the effect of testosterone administration (single dose, 150 mg) on persistence in a rigged social competition in which the opponent became progressively stronger than the participant. To test whether testosterone's impact on competition persistence is dependent on an individual's perceived personal control, we experimentally manipulated participants' perceived control prior to them entering the competition. In each round of the competition, both the participant and their opponent tried to illuminate a light bulb presented on their screen by pressing one of two response buttons. Participants had to pay a nonrecoverable entry fee for each competition round and, critically, could quit the competition whenever they wanted (and keep any remaining funds). Unbeknownst to participants, neither light bulb illumination nor competition outcomes were contingent on their selected responses; instead, the light bulb illuminations were rigged in such a way that the opponent became progressively stronger. We hypothesized that, compared to placebo, testosterone administration would enhance persistence in this rigged, disadvantageous competition.

Participants
The sample consisted of 88 healthy men aged between 18 and 40 years (M = 25.2, SD = 3.7). Participants were recruited via flyers placed around university campuses and online advertisements and screened by an online questionnaire and a telephone interview. The exclusion criteria comprised a history of neurological or psychiatric disorders, endocrine, cardiovascular, or other internal diseases, obesity, substance dependence, and the use of steroids. Only male participants were included because testosterone metabolism is subject to sex differences and because the pharmacokinetics of topical administration of testosterone are unknown in women (Eisenegger et al., 2013).
The sample size was determined based on previous testosterone administration studies available at the time of designing the experiment Mehta et al., 2015b;van Honk et al., 2016) and our own prior work on persistence-enhancing effects of illusory control (Studer et al., 2020). We inferred that for relevance in clinical and nonclinical applications, between-condition differences in persistence would have to be of moderate to large size. Our sample size and design allow detecting effects of size f 2 ≥ 0.14.

Procedure and double-blind testosterone administration
Testing took place in groups of four to six participants who were seated individually in small cubicles within the same testing room. Experimental sessions started at 14:00 h or 14:30 h. First, a buccal smear sample for the analysis of AR CAG polymorphism was taken, followed by a baseline saliva sample collected 20 min after arrival. Participants were asked to drool 2 mL of saliva directly into a polyethylene collection tube. All samples were frozen on-site and stored at -30 • C until analysis. Participants were then administered topical testosterone or placebo gel in a double-blind between-subjects design with random group allocation. Those allocated to the testosterone group received a single dose of testosterone gel, containing 150 mg testosterone [Androgel®]; participants in the placebo group received an equivalent amount of placebo gel. The only difference between the testosterone and placebo gel was that the placebo gel did not contain testosterone, and both the investigator and participants were fully blinded to whether the placebo or testosterone was administered at any given testing session and to any given individual. Participants rubbed the gel onto their upper arms and shoulders in small increments using disposable latex gloves until the full sample was rubbed into their skin. Gel administration was followed by a 2-h waiting period, during which participants remained in the laboratory premises, completed the Dominance-Prestige Scale (Cheng et al., 2010) and demographic questionnaires, and were offered leisure-time reading materials. One hour and 50 min after the gel application, participants provided a second saliva sample and subsequently began the experimental task (see Fig. 1A). The experimental task consisted of two parts: (1) illusion of control (IoC) induction and (2) competition (main task phase). In the IoC induction phase, participants were randomly assigned to one of two between-subject conditions aimed to induce either high or low levels of perceived personal control (see Section 2.3. for details). Participants were thus divided into four experimental groups: testosterone high IoC group (N = 22), testosterone low IoC group (N = 22), placebo high IoC group (N = 20), placebo low IoC group (N = 24). The IoC induction phase comprised 160 trials and lasted on average 8 min.
Immediately following this first task phase, the competition phase began. The length of this task was determined by each individual's persistence and therefore varied across participants. On average, it lasted 7.5 min [Min = 1.35 min, Max = 27.5 min]. Twenty minutes after the individual end of the competition, participants provided a third saliva sample. Participants were debriefed and received a flat participation fee plus a bonus payment based on their real performance in competition.
All participants provided written consent. All procedures were approved by the local research ethics board and conducted following the latest revision of the Declaration of Helsinki (World Medical Association, 2013).

Experimental task
Participants completed a competitive persistence task, programmed in PsychoPy2 (Peirce et al., 2019), inspired by our prior research on the effects of illusory control upon persistence (Studer et al., 2020). The task started with an IoC induction based on the manipulation of the (non-contingent) density of the positive outcome (see Alloy and Abramson (1979), Gillan et al. (2014) and Studer et al. (2020)), during which participants played the task alone (Fig. 1B). Participants were instructed that their goal was to illuminate a lightbulb on their screen as often as possible, by pressing one of two response keys (self-paced). They were informed that the relationship between the keys and the light bulb illumination can be different in each block, therefore it was recommended to try both keys. Following a keypress, the lightbulb either illuminated (positive outcome) or remained off (negative outcome). In truth, light bulb illumination was non-contingent on the selected key; instead, the probability of a positive outcome varied based on a predefined schedule involving three within-subject conditions: a low-density condition, in which the light bulb illuminated in 25% of trials, a medium-density condition, in which the light bulb illuminated in 50% of trials, and a high-density condition, in which the light bulb illuminated in 75% of trials. To ascertain that this outcome density manipulation After every 20 trials of the IoC induction, participants were asked to rate their perceived personal control. In the competition phase, participants were asked to rate both their and their opponent's perceived control. D: Competition (main task phase). On each trial, participants decided whether to play on or leave the competition. If they decided to remain in the competition, they next chose a bet (0-5 cents) and afterward attempted to illuminate their light bulb. Once they observed their own outcome (normal light bulb on or off), the opponent's outcome (square light bulb on or off) was displayed and the competition score was updated. Original texts were in German.
successfully modulated participants' perceived personal control, they were askedafter every 20 trialsto rate their own control over the light bulb illumination on a visual analog scale (Fig. 1C) ranging from 0% (= "NO CONTROL, the lighting of the bulb had nothing to do with my button choices and was thus entirely random") to 100% (= "COM-PLETE control, the lighting of the bulb was completely determined by my button choices"). In order to evoke different levels of perceived personal control immediately before the start of the competition, two different sequences of the outcome density conditions were used across participants. Participants assigned to the 'high IoC induction group' underwent the density conditions in ascending order, finishing with the high-density condition before starting the competition. Participants assigned to the 'low IoC induction group' underwent the density conditions in descending order, finishing with the low-density condition before starting the competition. This mixed design allowed us to test the effects of the pre-competition level of illusory control on subsequent competition persistence (comparison between induction groups) while also checking for potentially confounding effects of testosterone administration on the IoC induction itself (i.e., comparison of the personal control ratings in the high-vs low-density condition). Afterward, the main task phase (competition) started (Fig. 1D). Participants were told that they would compete against an opponent present either in the same or neighboring testing room, in truth, opponents were computer-controlled. In each round of the competition, both the participant and their opponent tried to illuminate a light bulb presented on their screen, by pressing one of two response buttons (self-paced). Next, they saw their own outcomethat is, their lightbulb either illuminated or not. This was followed by a presentation of the opponent's outcome, i.e., participants saw whether the opponent's lightbulb was illuminated or not. Participants won the round if their lightbulb illuminated but the opponent's did not, tied if both light bulbs illuminated or did not, and lost the trial if their bulb remained off but the opponent's light bulb illuminated. Each participant was endowed four euros at the beginning of the competition and had to pay a non-recoverable two-cent entry fee for each competition round that they decided to enter. In addition, participants could bet up to 5 cents on each competition round. If they won, they received double the wager back, if there was a draw, the original wager was returned, if they lost, the wager was lost. Unbeknownst to participants, the illumination of their light bulb was again independent of which key they selected. Instead, the light bulb illumination probability of the participant was fixed to 50% (non-contingent on their selected response), whereas that of the opponent steadily increase from 50% to 80% over the first 30 trials and then stayed at 80% for the remaining competition. The opponent thus became progressively stronger and persistence in the competition became increasingly disadvantageous and costly. Crucially, participants were instructed that they could quit the competition at any time, receive their current monetary reward, and instead play a non-competitive version of the task (in which no money could be won or lost) until the end of the session. The number of completed competition trials served as the main outcome measure. Bets placed (trial-by-trial) and overall monetary loss (determined when the participant quit the competition) served as secondary outcome measures.
At the beginning of the competition, every 20 competition trials, and at the time of quitting the competition, participants were again asked to rate their own control over the light bulb illumination and that of the opponent on the same 0-100% visual analog scale as in the first task phase.

Data processing and statistical analyses
The statistical analyses were performed in the R statistical software (version, 4.0.3, R Core Team, 2020). We analyzed normally distributed, homoscedastic outcome data using general linear models or, in the case of nested observations, general linear mixed models (GLMM) (nlme package, Pinheiro et al., 2020). Outcome data with non-gaussian distribution were analyzed with generalized linear models (GzLM) using gamma distribution with log link function or with generalized linear mixed models (GzLMM) in case of nested observations (lme4 package, Bates et al., 2015). The respective models are specified below. All coefficients and 95% confidence intervals (CIs) are reported on the log scale, reported mean values are exponentiated. For interactions, we calculated the Type 3 sum of squares and used orthogonal contrasts. Follow-up post-hoc comparisons were computed with the emmeans (Lenth, 2020) and the sjPlot (Lüdecke, 2020) packages. All reported p-values are based on Wald tests from the car package (Fox and Weisberg, 2019). Plots were created using the ggplot2 (Wickham, 2016) and ggpubr (Kassambara, 2020) package.

Verification of the testosterone manipulation
After data collection was complete, saliva samples were shipped on dry ice to Dresden LabService GmbH lead by Clemens Kirschbaum's, Germany. Liquid chromatography-tandem mass spectrometry was used to measure the levels of testosterone and cortisol. Due to high kurtosis, testosterone data were winsorized to a score of 3 SD above or below the mean for each time point. To verify the effectiveness of the gel administration, testosterone levels at baseline, 1 h 50 min after administration, and 20 min after the end of the competition phase were compared across the between-subject factors drug treatment (testosterone/placebo) and IoC induction group (high/low) using a GzLMM with a random intercept. Cortisol levels were analyzed in the same manner.

Verification of pre-competition induction of illusory control
To verify the successful manipulation of perceived personal control before the start of the competition, we conducted an ANOVA with the factors drug treatment (testosterone/placebo) and IoC induction group (high/low), and the dependent variable pre-competition control rating.

Statistical analyses of competition data
Our primary analyses aimed to investigate the effects of testosterone and perceived personal control on our primary outcome measure, competition persistence. First, we examined whether the potential influence of personal control on competition persistence is fully captured by the individual pre-competition control ratings (continuous), or whether the fixed dichotomous factor of the IoC induction group (high/ low) makes a significant contribution to the predictive accuracy of the persistence model. We, therefore, compared a series of increasingly complex, hierarchically related GzLMs with the predictors drug treatment (testosterone/placebo), individual's pre-competition ratings of personal control (mean-centered), IoC induction group (high/low), and their interactions, using Bayesian information criterion (see Supplementary material A for details). The strongest model (which included the predictors drug treatment, pre-competition ratings of personal control, and their interaction) was then used also for the analysis of our secondary outcomemonetary loss (in euro cents). Our other secondary outcome measure, bets placed trial-by-trial during the competition, was analyzed with a GLMM with the same predictors as used in the strongest model from the primary analyses, plus the additional predictor outcome of the previous trial (win/loss/draw) and all resulting interactions. Outcome of the previous trial was entered as a random slope, and an autoregressive first-order model of covariance structure AR(1) was used.
In addition, control ratings during the competition phase were analyzed, to examine the potential changes in the perception of own and opponent's control. The ratings of participants who completed at least one competition block of 20 trials (N = 58; N Placebo = 28), were entered into a GLMM with a between-subject factor drug treatment (testosterone/ placebo), continuous predictor individual pre-competition rating of personal control, and within-subject predictors agent (self/opponent) and time (beginning/end of the competition). The within-subject factors time and agent were included as random slopes in the model.
Seven participants (N placebo = 3, N testosterone = 4), who quit the task before playing a single competitive round, were not included in the analyses. 2

Control analyses
In addition to the aforementioned main analyses, we explored two alternative pathways through which drug treatment could in theory influence competition persistence. First, we tested whether testosterone administration had a systematic effect upon the effectiveness of the IoC induction, by conducting an ANOVA on pre-competition control ratings with the between-subject factors drug treatment and IoC group. Such an effect would allow us to test whether testosterone boosted illusory control before the competition, which could potentially account for any differences in persistence during the subsequent competition phase. Second, we assessed if testosterone administration systematically influenced participants' sensitivity to positive and negative outcomes during the IoC induction phase, by fitting a reinforcement learning model to their choice data (Jocham et al., 2011;Sutton and Barto, 1998). Again, such an effect could also covertly affect behavior in the competition phase. The reinforcement learning model estimated the expected value of each action (top or bottom button press) in every trial. At the beginning of each condition, the expected values were set to zero, and then the value of the chosen option was updated after each trial according to the following rule: where V(a) t is the value of action a (top or bottom) selected on trial t, r t is the reward (0 or 1) obtained on trial t, and α O is the outcome-specific learning rate that scales how strongly each outcome is used to update value estimates. We used separate learning rates, α positive and α negative for positive (light bulb on) and negative (lightbulb off) outcome trials.
The probability of choosing a particular action (here, top) on a given trial was computed using a softmax rule: where ΔV is the value difference (here: top minus bottom) and τ is the softmax temperature. The free parameters α positive , α negative , and τ were estimated by maximum likelihood (Burnham and Anderson, 2002) and then separately compared between the drug treatment and IoC induction groups by means of a GzLM.

Supplementary analyses on modulating biological mechanisms
A series of supplementary analyses explored potential biological mechanisms that might elucidate the pathways through which testosterone exerts its effect. One such potential pathway is via androgen receptors expressed in multiple brain regions (Rubinow and Schmidt, 1996). The efficiency of the androgen receptors substantially varies between individuals and was reported to be negatively related to the CAG repeat length (Zitzmann and Nieschlag, 2003). Testosterone's effects have previously been shown to be enhanced among individuals with fewer CAG repeats (Geniole et al., 2019a). Interactive effects between exogenous testosterone and endogenous cortisol levels have also been found, with testosterone influencing status-seeking behaviors more strongly when cortisol levels are low (Knight et al., 2020;Mehta and Prasad, 2015). Finally, one recent study found that testosterone administration increased competitive decisions only among high-dominant individuals (Mehta et al., 2015b). We, therefore, explored whether persistence-enhancing effects of testosterone also varied as a function of CAG repeat polymorphism, baseline cortisol, and trait dominance by adding these factors as covariates/moderators to the GzLM of competition persistence (see Supplementary material A for more details).

Verification of testosterone manipulation
Baseline testosterone and cortisol levels did not significantly differ across experimental groups (all ps > .140, see Table S2).
Two hours after gel administration, we observed higher testosterone levels in the testosterone group (

Verification of pre-competition induction of illusory control
Ratings of perceived personal control at the end of the IoC induction phase were significantly higher in the high IoC induction group compared to the low IoC induction group (M high = 71.88, SE high = 2.94; M low = 11.22, SE low = 2.81; IoC group main effect: F(1,84) = 220.06, p < .001, η2 = .722, Fig. 2A), confirming an effective manipulation of perceived personal control immediately prior to the start of the competition.

Competition behavior
Competition persistence was best explained by a model including predictors drug treatment, pre-competition ratings of perceived personal control (i.e., the individual's perceived control as induced by our manipulation), and their interaction; the IoC induction group per se did not improve model fit over and above the ratings of perceived control, which is why it was removed from the final model (see Table S1). The results from this best fitting model showed that the effect of testosterone Simple slope analysis (Aiken and West, 1991) of this interaction revealed that pre-competition levels of personal control positively predicted competition persistence in the placebo group (B = 0.013, CI = [0.005, 0.021], t(79) = 3.15, p = .003), such that higher levels of control were associated with higher persistence. However, this was not the case in the testosterone group (B = − 0.005, CI = [− 0.014, 0.003], t (79) = − 1.266, p = .213. That is to say, testosterone administration disrupted the relationship between perceived personal control and persistence (see Fig. 2B). Follow-up pairwise comparisons conducted separately in participants with high perceived personal control (control rating > group median of 28) and with low perceived personal control (control rating ≤ 28) showed that testosterone administration significantly and selectively increased persistence in participants with low pre-competition levels of perceived personal control, such that these participants on testosterone persisted twice as long as those on placebo (M placebo = 28.65, SE = 2.69; M testosterone = 56.19, SE = 4.36, z(77) = 2.305, p = .021). In contrast, testosterone (compared to placebo) did not 2 A complimentary analysis where these participants were included with a persistence value of 0 provided qualitatively equivalent results.  Induction of illusory control (IoC) and competition. A Perceived personal control at the end of the IoC induction phase (i.e., immediately before the competition) was rated significantly higher by participants in the high IoC induction compared to those in the low IoC induction group. B The interaction effect of drug treatment and perceived personal control on competition persistence. Testosterone administration disrupts the positive relationship between the pre-competition ratings of perceived personal control and subsequent persistence in the disadvantageous competition. C Testosterone administration increases competition persistence uniquely among participants with low levels of perceived personal control (groups plotted based on a median split of individual pre-competition control ratings). D Testosterone administration increased the amount of lost money among participants with low levels of perceived personal control (groups plotted based on a median split of individual pre-competition control ratings). E, F The interaction effect of the drug treatment, agent, and time on the ratings of perceived control during the competition (plots divided based on a median split of individual pre-competition control ratings). Participants in the testosterone group rated the control of the opponent as higher at the end of the competition than at the start of the competition. Participants in the testosterone group after competition also rated the opponent's control as higher in comparison to their own control. Shaded area and error bars: Mean ± SE. testosterone group during the competition reflected the objective advantage of the opponent. Meanwhile, in the placebo group, no significant differences were found in either of these contrasts (B = 0.96, CI = [− 9.10, 11.01], p = 0.851; B = 9.67, CI = [0.00, 19.34], p = .050, respectively). We also observed a main effect of the pre-competition rating (B = 0.25, CI = [0.12, 0.38], p < .001) indicating that higher (vs lower) pre-competition ratings predicted higher ratings at the end of the competition. No significant interaction effects between precompetition ratings and drug treatment (B = 0.01, CI = [− 0.12, 0.14], p = .891), time (B = − 0.07, CI = [− 0.15, 0.08], p =0.701) or agent (B = 0.01, CI = [− 0.05, 0.08], p = .701), or any higher-order interactions (all ps > .379), were found.

Control analyses
Testosterone treatment did not affect pre-competition control ratings

Discussion
The present study investigated testosterone's effects on competition persistence and the psychological and biological mechanisms that may underlie such effects. Our results show that the causal effect of testosterone on men's persistence in a disadvantageous social competition depends on their subjective control beliefs. A single dose of exogenous testosterone boosted persistence against an increasingly stronger opponent uniquely among participants who entered the competition with low perceived personal control over task outcomes. To the best of our knowledge, this work provides the first causal evidence that testosterone modulates competitive persistence and that it does so dependent on one's psychological state prior to the competition. This result critically extends previous research reporting that testosterone's effect on the willingness to compete again is dependent on the outcome of the previous contests (Losecaat Vermeer et al., 2020;Mehta et al., 2015a) and indicates that testosterone's impact upon competitive drive is moderated by a broader situational context exceeding the competition setting.
In the placebo group, perceptions of low (vs high) personal controlinduced immediately before the competitionpromoted earlier quitting in the disadvantageous competition. This finding aligns with previous experimental and theoretical work (Bandura and Locke, 2003;Eccles and Wigfield, 2002;Studer et al., 2020). In contrast, in the testosterone group, such reductions in control did not translate into earlier quitting. Rather, testosterone made such individuals with low perceived control act as if they entered the competition with high perceived control, boosting persistence despite the opponent becoming increasingly stronger.
One explanation for these findings could be that testosterone rendered participants insensitive to the opponent's superior performance. However, ratings collected during the competition suggested that participants who had received testosterone appeared even more aware of the opponent's advantage than those who had received a placebo. Thus, after testosterone administration, participants maintained, and even slightly gained, sensitivity to the superior performance of the opponent, yet still engaged in monetarily disadvantageous competitive behavior. These effects are consistent with a recent testosterone administration study (Geniole et al., 2019b) in which the hormone reduced submissive resource-ceding to high-(but not low-) threat competitors, but did not diminish participants' sensitivity to this threat information. Together, these findings suggest that rather than modulating explicit assessment of social threat/competitiveness, testosterone appears to act by modifying behavioral responses to such information. Not all studies demonstrate such effects though: for example, Panagiotidis et al. (2017) found that testosterone administration increased self-reported but not behavioral aggressive responses to non-social provocation. These differences across studies further highlight the idea that testosterone effects are crucially dependent on the social context (Kutlikova et al., 2020).
When we have the opportunity to pursue a relevant goal, but goal attainment is costly, our decision to persist or discontinue is thought to be contingent on the outcomes experienced during previous, similar attempts (Sturgeon and Zautra, 2016). Given that testosterone has been observed to shift the motivational balance by lowering sensitivity to punishment (van Honk et al., 2004), it could also be speculated that testosterone decreased sensitivity to negative outcomes more generally (e.g., failed bulb illuminations), regardless of other features related to the competition. However, the results of our reinforcement learning model argue against such an outcome-insensitivity effect. Neither learning from negative nor from positive outcomes was systematically altered by exogenous testosterone (i.e., testosterone did not alter button-press choices in response to successful or unsuccessful bulb illuminations in the induction phase, preceding the competition).
Another potential explanation could be that testosterone increased the rewarding effect of competition per se (Hermans et al., 2010, Purves-Tyson et al., 2012. However, such an effect would arguably be expected to manifest independently of perceived control, rather than selectively in participants entering the competition with low perceived control. Instead, we posit that a likely mechanism driving the observed persistence-enhancing effect of testosterone in those with low (induced) perceived control is that these participants appraised persistence in the competition as a means for social-status enhancement (Losecaat Vermeer et al., 2020;Mazur and Booth, 1998) and were consequently motivated to persist regardless of the outcome and monetary value. Convergent with this proposition, previous research has shown that testosterone can affect the appraisal of competitive environments (Salvador, 2005) and that higher testosterone levels prior, during, and after a competition are associated with increased satisfaction with personal performance even in the case of a loss (Casto et al., 2017).
Contrary to persistence, we did not find an effect of testosterone or induced levels of control on the bets placed during the competition. Instead, betting was modulated only by the outcome of the preceding competition round, with betting decreasing after a loss compared to a draw or win. This aligns with previous studies reporting that betting behavior is insensitive to perceived control (Studer et al., 2020) and does not always follow decision confidence (Studer et al., 2015).
Our supplementary analyses found no significant modulation of testosterone's persistence enhancing effects by CAG repeat length (a genetic determinant of androgen receptor sensitivity to testosterone), basal cortisol levels, or trait dominance. In contrast, prior studies observed an influence of CAG repeated length on testosterone's effects upon status-seeking behaviors (Geniole et al., 2019a;Losecaat Vermeer et al., 2020), and increased testosterone effects on status-seeking behaviors among individuals with low basal cortisol (Knight et al., 2020;Mehta and Prasad, 2015) and high dominance (Mehta et al., 2015b). One speculative reason could be that the current psychological state (in our case induced perceived personal control) overrides the effects of such trait(-like) predictors. In any case, one limitation of our study lies in the relatively small sample size, which led to reduced statistical power, especially when analyzing some of these three-way interactions. The null findings (e.g., of CAG repeat length and trait dominance) should therefore be interpreted with caution. Another limitation, shared by most other psychoneuroendocrinological research using testosterone, was that due to the sex differences in testosterone metabolism and unknown pharmacokinetics following the topical administration of testosterone in women (Eisenegger et al., 2013), the study included only male participants. Hence, the validity of these findings and generalizability to biological females and those identifying as women will require further investigation.
Our results also raise questions for future research. For instance, neuroimaging studies might elucidate the mechanisms through which testosterone disrupts the link between perceived control and behavioral persistence. Even in the absence of an identified mechanism, however, evidence that testosterone boosts persistence especially in individuals who do not feel in control might provide helpful information for settings that require extensive repetitive training, such as neurorehabilitation (Studer et al., 2016). To expand this application potential, it would also be useful to test the transferability of these effects to different tasks and environments, for instance, disadvantageous persistence versus persistence that leads to success (McFarlin et al., 1984).
In conclusion, the present study demonstrates that testosterone's effects on competitive behavior depend on one's psychological state, with the hormone specifically making individuals with low perceived control persist longer against a stronger opponent. This experimental evidence of context-dependent testosterone effects highlights the importance of studying the intersection of biological and psychosocial factors that shape testosterone functioning.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.