In what follows, we analyze the experimental results using mixed-effects models, the appropriate technique when individuals are embedded within a group and are paired with each other across several interactions (and hence are not independent). This approach, combined with random selection of the individuals representing each dyad (when dyads were the proper level of analysis) and a bootstrap resampling technique, allows us to establish significance with a large degree of accuracy (see Supplemental Information).

First, we look at if (and how) the existence of a hierarchy affected success in the cooperation phase. Figure 1A shows that success (reaching or exceeding 20 units collectively) in the control condition was significantly more frequent than that of the hierarchically organized groups (95% CI for the coefficient, [0.14, 0.45]), indicating that participants were more prone to cooperation in the treatment lacking hierarchy. Interestingly, there was no difference between the random and earned hierarchy conditions, indicating that whether rank arose from personal performance or was randomly assigned did not affect cooperation success. Therefore, we pooled the two hierarchical treatments in subsequent analyses. In the control condition the average contribution to the pot was significantly greater than in the hierarchical treatments (95% CI for the coefficient, [0.23, 0.58]), cf. Fig. 1B) leading to more successful cooperation events in the absence of a hierarchy. We also found an interaction between the presence or absence of hierarchy and round of play, which emerged from the fact that the difference in cooperative success between the hierarchy and no hierarchy conditions increased as the experiment proceeded (95% CI for the coefficient, [0.007, 0.116], cf. Fig. 1C). Finally, we observed that there was a positive correlation between rank and total earnings in the experiment (see Supplemental Information), i.e., higher ranked participants received larger payments than lower ranked ones. Therefore, in this experiment we did in fact see that higher ranked individuals obtained more resources.

Figure 1 Success and contributions decrease in hierarchically organized groups, irrespective of the origin of the ranking. (A) The mean number of succesful instances of cooperation in the control condition in which there was no hierarchy was significantly higher than both hierarchical conditions. The maximum number of cooperative successes was 9. (B) The mean player contribution in the cooperative task with and without hierarchy. (C) Mean cooperation success as a function of round and hierarchy condition shows that there is a small but significant interaction among these variables, which might arise from the fact that the differences between the two treatments appear to increase as the experiment progresses. Colors correspond to the three types of hierarchical treatment as indicated in the plot. Full size image

Why does cooperation suffer in the presence of a hierarchy? While the contributions from both partners are similar in the condition with no hierarchy, they differ clearly in the two hierarchical treatments (Fig. 2A). The main reason for the decrease in successful cooperation events can be traced to diminishing contributions by lower ranked individuals (Fig. 2B). Indeed, in this respect, our analysis shows that there is a significant difference in contributions between higher and lower ranked individuals (95% CI for the coefficient, [−1.65,−0.79]) and a significant interaction of rank and round (95% CI for the coefficient, [−0.30, −0.10]). Figure 2B shows that higher ranked participants increase their contributions as the experiment procedes while lower ranked participants decrease their contributions. Thus, it is the lack of contribution from the lower ranked players that leads to more cooperation failures. Figure 3 shows that, in the hierarchy conditions, lower ranking individuals contribute little in unsuccessful attempts (when the 20 unit minimum is not reached) compared to higher ranking individuals and when cooperation is achieved, lower ranking individuals’ contributions barely surpass ten units. In view of this evidence, it appears that both individuals realized the consequences of their rankings on their potential earnings. Accordingly, lower ranked participants responded by reducing their investment, whereas higher ranked participants anticipated the reluctance of their partner and invested more in an attempt to rescue cooperation, but often not enough to be successful. In fact, when we examined whether the magnitude of the rank difference predicted cooperation investments, we found that the amount contributed by lower ranked participants increases (and the amount contributed by higher ranked participants decreases) as the rank difference became smaller, i.e., as the chances of receiving the whole pot by chance increased (95% CI for the coefficient, [−0.47, −0.25]) (cf. Fig. 2C).

Figure 2 Contributions decrease in the hierarchy condition for lower ranking partners and are predicted by the rank difference. (A) The contributions by the higher and lower ranked partners in the three experimental conditions, (B) the contributions by the higher and lower ranked partners in the hierarchy and non-hierarchy treatments across rounds, (C) the contribution as a function of the rank difference between the two partners of the dyad. Negative numbers correspond to higher ranking positions, e.g., −8 indicates the focal player (whose contribution we are evaluating), was ranked 1 and her partner was ranked 9). Full size image

Figure 3 Contributions differ markedly in the cases when cooperation is or is not achieved. (A) Mean player contribution in the cooperative task when cooperation fails (red) and when it succeeds (blue) for the higher ranked player in the three experimental conditions. (B) The same for the lower ranked player. Note that when there is no hierarchy the behavior of both types of player is the same. Full size image

Let us now move on to the behavior of players in the ultimatum game with an (hierarchy-based) outside option41, or the “splitting phase”. In the absence of hierarchy, we observed that proponents offered on average 25% less than what receivers were willing to accept. When hierarchy was introduced, this difference was again observed, but proponents offered lower amounts for higher rank differences and receivers stated a lower minimum amount they would accept (Fig. 4). On the other hand, our analysis shows that both offers and expectations are independent of the investments made in the cooperation phase. This finding is further supported by the results of two additional treatments in which the cooperation phase was omitted and players proceeded directly from the hierarchy formation stage, be it earned or random, to the splitting phase. We did not observe any significant differences in the amounts offered and expected between these treatments and those in which there was a cooperation stage (see Supplementary Information). Such a result may be explained by a similar feeling of entitlement in the splitting phase regardless of whether this phase followed successful cooperation.

Figure 4 Offers and thresholds in the splitting phase behave qualitatively as predicted by Nash equilibrium. Mean offer and threshold in the ultimatum game with (hierarchy-based) outside option41 vs k, the groups of rank differences organized as indicated in the text, with rank difference being smaller with increasing k. Plots (A) through (E) correspond to our five treatments: (A) no hierarchy, full experiment (cooperation plus splitting); (B) earned hierarchy, no cooperation task; (C) random hierarchy, no cooperation task; (D) earned hierarchy, full experiment and (E) random hierarchy, full experiment. In all plots, red circles correspond to the proposer’s offer, blue triangles correspond to the responder’s minimum acceptable offer and the green solid line is the theoretical prediction of the Nash equilibrium for both the minimum acceptable offer and the proposer’s offer. Full size image

It is interesting to observe that, in the absence of hierarchy, i.e., when the chance to receive the pot is 0.5, respondents play very closely to the Nash equilibrium of the game, accepting only 20 units or more of the pot. This is much larger than minimum acceptable offers typically found in the standard ultimatum game26. This may have arisen because of the cooperation phase as discussed above. Alternatively, it seems more likely that this arises because respondents have a large chance to keep the whole pot when they refuse the offer in this experiment, contrary to the typical ultimatum game in which they would receive nothing. When hierarchy is present, Nash equilibrium predicts that the higher ranked individual should offer 4k (see “Subgame perfect equilibrium calculation” in the Supplementary Information), k being a measure of rank difference (k = 1 corresponds to a difference in rank of 8 or 9; k = 2, to 6 or 7; k = 3, to 4 or 5; k = 4, to 2 or 3 and k = 5, to a difference of 1) and the lower ranked individual should accept it. We do not presume that the participants make these calculations, rather, they adjust their behavior based on their understanding of the experiment and their experiences in previous rounds. In the present experiment, the behavior of the two partners is only qualitatively similar to the Nash equilibrium. Remarkably, higher ranked individuals make offers closer to the prediction, while lower ranked individuals expect to receive a significantly larger amount of the pot.

Another interesting observation is that for greater rank differences (lower k), the higher ranked individuals are prone to share an amount larger than the Nash prediction. Additionally, for all rank differences, receivers state a minimum amount that they would accept that is greater than theory and dictators’ action prescribe (cf. Fig. 4). This might arise from the fact that proponents perceive the splitting phase closer to a standard ultimatum game than it actually is. When their partner is much lower in rank, even if she rejects the offer, the proponent has a large probability to keep the whole pot (while in the ultimatum game the proponent would receive nothing). Accordingly, they offer a larger amount than the Nash equilibrium would predict, probably because they fear losing their share, to which they feel entitled. This agrees with the slopes of the rank dependence of offers and acceptance levels being lower than the Nash prediction; however, they are not completely horizontal as in the control condition because participants may still partially take into account the lack of refusal power of the respondent. Such consideration would effectively make the hierarchy less important, as the individuals in the lowest positions would be treated as if they were ranked higher. It is important to note, however, that the hierarchy itself is not changed, as it is fixed from the beginning of the experiment and individuals with lower ranking were still offered less than intermediate-ranked ones.