Testosterone promotes either dominance or submissiveness in the Ultimatum Game depending on players’ social rank

Endogenous testosterone promotes behaviours intended to enhance social dominance. However, recent research suggests that testosterone enhances strategic social behaviour rather than dominance seeking behaviour. This possibility has not been tested in a population whose members are known to vary in social status. Here, we explored the relationship between pre-existing social status and salivary testosterone level among members of a rugby team at a Japanese university, where a strong seniority norm maintains hierarchical relationships. Participants played a series of one-shot Ultimatum Games (UG) both as proposer and responder. Opponents were anonymised but of known seniority. We analysed participants’ acquiescence (how much more they offered beyond the lowest offer they would accept). The results showed that, among the most senior participants, higher testosterone was associated with lower acquiescence. Conversely, higher testosterone among the lower-status participants was associated with higher acquiescence. Our results suggest that testosterone may enhance socially dominant behaviour among high-status persons, but strategic submission to seniority among lower-status persons.

First, we provide tables to report more detailed information about the general linear model analysis reported in the main text. Although the data analyses we report in both the main text and SI were generated using SAS 9.4., we calculated the effect size of generalized omega squared using the free statistical software HAD (Shimizu, 2016). Table S1. Details of the general linear model analysis with Mean Acceptable Offer (MAO) as the dependent variable, game type as a repeated factor, and seniority as a between-participants factor.  Table S3. Details of the general linear model analysis with offer as the dependent variable, game type as a repeated factor, and seniority as a between-participants factor.

Other variables investigated in this study
From here we report the results of our tests involving other independent variables and testosterone indices: post-measured testosterone (post-T), change levels of testosterone (change-T = post-T minus pre-T), right hand digit ratio (R2D:4D), left hand digit ratio (L2D:4D) and facial width-to-height-ratio (fWHR). 2D:4D is a marker for prenatal testosterone levels (Manning, 2002) Table S7 shows the average of six testosterone indices and the standard deviation for participants at each seniority level. There were no significant differences between seniority levels within each index. Change levels of testosterone are depicted in the Figure   S1 in each grade. As shown in Figure S1, change levels decreased overall from before to after the experiment. Except for the first years, the average levels of change-T significantly differed from zero. Table S7. Salivary testosterone levels after log-transformation (pmol/L) in pre-T, post-T, and change-T and both hands' 2D:4D and fWHR for players at each seniority level. A one-way between-participants ANOVA was conducted to compare the effect of seniority on each testosterone index shown in the lower row.
(note) We failed to collect one participant's hand scans (2 nd year student) and three of the participants' facial photos (two 2 nd year students and one 3 rd year student).  Figure S1. The Y axis shows the change levels of testosterone from before to after the experiment for players at each seniority level (X axis). Positive values indicate increase and negative values indicate decrement. Asterisks indicate the statistical significance of t tests for difference from zero (* p < .05, *** p < .001).  Table S8 shows values of the Spearman correlation coefficient for the relationship between each testosterone index. Across salivary testosterone indices, preand post-measured testosterone showed strong positive and significant correlations.
Conversely, change levels showed smaller or moderate correlations with pre-and postmeasures. These three salivary testosterone indices did not show statistically significant correlations with the other indices. Right hand 2D:4D correlated strongly with left hand 2D:4D and both also showed moderate correlations with fWHR in the predicted direction.

Association between other indices of testosterone and rejection in the UG
In the main text, we report the association between pre-T and MAO. Here we report the association between post measured testosterone/changes in levels of testosterone and mean MAOs across the four game types. Participants who did not show a linear rejection threshold were excluded from the relevant analyses. We investigated how rejection thresholds across the four games affected testosterone levels by conducting two-way ANOVAs to test for differences in post-T and change-T based on means of MAO, seniority level, and their interaction (Table S9). We found no statistically significant main or interaction effects of post-T. Similarly, we tested if MAO and seniority affected change in level of testosterone, and found a significant main effect of MAO, F(1, 59) = 4.75, p = .033. No other effect was significant. As shown in Figure S2, change in level of testosterone was positively correlated with mean MAO. This suggests that participants who tended to reject smaller offers across all four partner conditions (i.e., participants who tended to indicate large minimum acceptable offers) maintain or increase their testosterone levels by the end of the experiment.  We also examined the effect of other previously measured indices of testosterone in a general linear model analysis of MAO by seniority, game type, testosterone index (right hand 2D:4D, left hand 2D:4D, and fWHR), and their interactions. Since there were no effects of game type, we examined mean MAO, as reported in the Table S10. Right hand 2D:4D interacted significantly with seniority on mean MAO. fWHR had a marginally significant main effect on mean MAO. Figure S3 illustrates the association between right 2D:4D and mean MAO over each seniority level. Figure S4 shows the association between fWHR and mean MAO. As shown in Figure S3, mean MAO and right 2D:4D were positively correlated among fourth years, which means that senior participants who are likely to have been exposed to high levels of testosterone prenatally tended to accept smaller offers on average than participants whose exposure was low. However, junior participants showed null or negative correlations between mean MAO and right 2D:4D. Figure S4 illustrates the positive correlation between mean MAO and fWHR, indicating that those with a physical cue to high testosterone tended to reject smaller offers than those without a cue to high testosterone. To summarize, pre-T and post-T have no effect on rejection thresholds, but change-T is positively correlated with MAO, indicating that those who rejected smaller offers tended to maintain or increase their salivary testosterone levels between playing the UGs. R2D:4D shows inconsistent patterns across seniority levels. fWHR shows patterns consistent with expectations, though the effects were marginal when we considered the effect of seniority in a general linear model analysis.

Association with testosterone and amount of offer in the UG
We conducted two-way ANOVAs to test for post-T and change-T effects on mean offer and seniority (Table S11). Mean offer had a significant main effect on levels of post-T. As shown in Figure S5, those who offered more across the four games showed higher levels of post-T than those who offered less. The pattern was similar to that for pre-T, as reported in the main text. The interaction between seniority and mean offer on change-T was marginally significant. However, post hoc Tukey-Kramer least square tests showed no significant effect in either combination.
Table S11. Post-T or change-T were the dependent variables and participant seniority and mean offer over four games were the independent variables. Figure S5. Scatter plot illustrating the relationship between mean offer and post-T.  We also separately examined the effect of other indices of testosterone in a general linear model analysis of offers by seniority, game type, testosterone index (i.e., right hand 2D:4D or left hand 2D:4D or fWHR), and their interactions. No significant main effect or interaction effect was found for right 2D:4D. There was also no significant main effect of left 2D:4D, but a three-way interaction effect between game type, seniority, and left 2D:4D was significant, though difficult to explain. No significant main effect or interaction effect was found for fWHR. When we combined four games into one (i.e., mean offer), none of the significant main effects or interaction effects remained (Table   S12).

Association between acquiescence and post-T or change-T
To test whether mean acquiescence affected the levels of post-T or change-T, we conducted two-way ANOVAs.  Figure S6. Scatter plot of the Post-T levels (X-axis) and mean acquiescence (Y-axis) for participants in each seniority level.
As shown in Table S13, there was a significant interaction effect of seniority and mean acquiescence on levels of post-T but not change-T. Scatter plots of post-T and mean acquiescence at each seniority level ( Figure S6) indicate that post-T and mean acquiescence positively correlate in junior players. Only the fourth years showed the opposite pattern. These patterns were the same as that observed between pre-T and acquiescence, as reported in the main text. The change levels of testosterone were not predicted significantly by mean acquiescence or the interaction with seniority.
As shown in Table S14, none of the remaining testosterone indices had any significant effect on mean acquiescence, nor did they interact with seniority.

Instructions For The Experiment
On Social Interaction ・ During the experiment please follow the experimenters' directions.
・ Talking with others is strictly prohibited.
・ Please enter your ID number in the box provided.
・ Once everyone is ready the experimenter will explain the experiment. Please follow along carefully as the experimenter reads through the explanation starting on the next page.
・ If during the explanation there is anything you do not understand or if you have other questions, please do not hesitate to raise your hand and let the experimenter know.

#1 Instructions for all participants
General Outline of the Experiment ➢ This is an experiment involving a type of monetary transaction.
➢ The amount of your earnings in the experiment will ultimately vary according to decisions made by each person in the monetary transaction.
➢ The money you earn in this experiment will be paid to you today in cash at the end of your rugby practice.
➢ For each monetary transaction you will be paired with one of the other players.
➢ One person in each pair will be proposer and the other will be recipient of the proposal. (A more detailed explanation will follow.) ➢ In all, the transaction will be repeated four times.
➢ You will be paired with a different person for each transaction.
� The total reward money you earn today will be calculated from the results of 2 of the 4 transactions.
� Which transactions are used for the calculation will be determined by lottery at the end of the experiment. � However, it is possible that, depending on the results of the transactions, the reward will be ¥0. Therefore, we promise that we will pay everyone today's minimum guaranteed amount of ¥500 as show up fee, without exception.
� Whether you can earn extra money above and beyond the ¥500 will depend on the results of your monetary transactions.
� None of you will find out whom you are paired with, or who made what decisions during or after the experiment.
� Everyone's anonymity will be completely maintained, so please relax and freely make whatever decisions you like.
Next, let us explain about the "monetary transaction" in this experiment in more detail.

[ About The "Monetary Transaction" ]
1. The "monetary transaction" takes place between two people, a proposer and a recipient.
2. The experimenters give the proposer ¥1000 to fund the monetary transaction.
3. The proposer considers how to split the ¥1000 with the recipient and makes a proposal.
Of this ¥1000 I'll give you ¥ because I want to keep ¥.

[ About your transaction partners ]
That concludes our explanation of the "monetary transactions" in this experiment. If there is anything that you do not understand, please raise your hand and address your question to the experimenter.
1. We will run the monetary transactions four times.
2. For every transaction you will be paired with a different person and never with the same person twice.
3. Which player will be the proposer and which player the recipient in each transaction has not been decided yet.
4. At the end of the experiment lotteries will be held to determine which role each person will play and which 2 transactions will be used to calculate the rewards.
5. Therefore, in every monetary transaction... 1) First, everyone acts as a proposer and proposes how to split the ¥1000 with the other player.
2) The proposal is made in increments of ¥100 from ¥0 to ¥1000.
3) Next, everyone acts as a recipient and decides whether to accept or reject the other player's (the proposer's) proposal for that transaction. 4) However, at that point, the actual split proposed by the other player will not be known. Therefore, you will look at a list of possible ¥1000 splits and decide whether you will accept or reject each of them.
6. This procedure will be performed 4 times, with different pairs of players.
We now begin the experiment.
・ You will be given instructions by the experimenter.
・ Complete the task as instructed.
・ Read this cover page. Do not move on to the next page until you are instructed to do so.

An Experiment on Monetary Transaction Decision Sheets: First transaction
・ Your paired partners in these transactions will be different in each transaction.
・ You will not know who your transaction partners are either during or after the experiment.
・ Your transaction partner will be determined by lottery at the end of the experiment.
・ Further, which 2 of the 4 transactions will be used for actual reward calculation will be determined by lottery. Your earnings for the day will be the total of a minimum guaranteed ¥500 plus a reward calculated from the results of the 2 transactions selected by lottery.
・ We ask that you write your decisions about each transaction on the decision sheets. After all participants have made their decisions, these will be input into a computer to tabulate the results.
・ Please wait until the experimenter says to proceed to the next step.
・ After completing each transaction, do not turn to the next page. Wait quietly until instructed to continue on to the next page by the experimenter.
・ It is strictly forbidden to try to look at the work of those around you! Enter your ID number here.
If you have understood the explanation thus far, please wait until instructed to proceed by the experimenter.

#2
No information game decision sheet for all participants.
to divide it with the other player? Please write your proposal in the following box.
Of ¥1000: Yourself ¥ Other player ¥ Total ¥ 1000 You will be paired with one of the other participants.
Please decide what you would do if you were the proposer.
Please wait until everyone has finished.
However, please take care others cannot see your proposal.
Possible proposals the other player may make are listed below. Please decide whether you would accept or reject each and circle the appropriate response. You will be paired with one of the other participants.