Hierarchy is Detrimental for Human Cooperation

Studies of animal behavior consistently demonstrate that the social environment impacts cooperation, yet the effect of social dynamics has been largely excluded from studies of human cooperation. Here, we introduce a novel approach inspired by nonhuman primate research to address how social hierarchies impact human cooperation. Participants competed to earn hierarchy positions and then could cooperate with another individual in the hierarchy by investing in a common effort. Cooperation was achieved if the combined investments exceeded a threshold, and the higher ranked individual distributed the spoils unless control was contested by the partner. Compared to a condition lacking hierarchy, cooperation declined in the presence of a hierarchy due to a decrease in investment by lower ranked individuals. Furthermore, hierarchy was detrimental to cooperation regardless of whether it was earned or arbitrary. These findings mirror results from nonhuman primates and demonstrate that hierarchies are detrimental to cooperation. However, these results deviate from nonhuman primate findings by demonstrating that human behavior is responsive to changing hierarchical structures and suggests partnership dynamics that may improve cooperation. This work introduces a controlled way to investigate the social influences on human behavior, and demonstrates the evolutionary continuity of human behavior with other primate species.

In this experiment sections of 10 participants are formed randomly. You will remain in the same section throughout the entire experiment. This experiment has two phases.
In the first phase each you will carry out individual tasks for 3 minutes each.
1. In the first task, you will execute additions with three two-digit numbers. Each correct addition will give you one point.
2. In the second task, you will play the game Tetris. For each deleted row, you will obtain one point. 3. In the third task you will answer general culture questions in a quiz format.,For each question you will be provided with four possible answers. Only one of them is correct. Each correct answer will give you one point.
4. Finally, you will be able to choose one of these tasks in order to obtain additional points..
All of the points you obtain will be summed up. The more points you obtain, the better positioned you will be for the second phase of the experiment.
[In the control (no hierarchy) condition, the text starting with "In the first phase" and ending with "second phase of the experiment" was suppressed.] [In the random hierarchy condition, the text for the first phase was simply: "Each of you is assigned a random score from other sessions. The person with the highest score will be in 1 st place, the second will be the 2 nd , and so on, with the person with the lowest score achieving 10 th place."] The second phase has 9 rounds. In each round you will be paired with one of the members of your section, depending on his score and yours. Therefore, in each round, 5 pairs in each round will be formed from the section of 10 people. Your pairings will depend on the difference between your score and your partner's.

[In the control (no hierarchy) condition, the last sentence was suppressed.]
In each round, the player with the highest score will be Player A; the other player will be Player B.
At the beginning of each round, you will be provided the following information: • The score of every section member, including your own score (in green) and your partner's (in grey).
• A table of ranks for everyone in your section, yours will be marked in green.
The pair with the greatest difference between their scores (or ranks) will be called group 1. The pair with the second highest difference will be group 2, and so on. In each round you will see if your score is higher or lower than your partner's.
Each of players has 20 ECUs (experimental virtual currency) as an initial budget for each of the 9 rounds to play in the second phase. In each round, each player may make a contribution between 0 and 20 ECUs. If the sum of the two contributions is greater or equal than 20 ECU, then you will access 40 ECUs for the two members. If it is less than 20 ECUs, then nothing will be distributed.
[When the treatment did not have a cooperation phase, the above paragraph was substituted by the following sentence: "In the next phase you will have to decide on how to split 40 ECUs".] How will the ECUs be shared?
Player A in each pair can share 40 ECUs. S/He decides how many of the 40 ECUs s/he gives to player B (r A ).
Player B will indicate the least amount of ECUs s/he accepts from Player A (r B ).
If this amount is less or equal than the one given from Player A, r B ≤ r A , then the share is accepted by Player B, and each player will obtain the division share decided by Player A (r A ). The profit of Player A: 40 -r A ; the profit of Player B: r A .
In the opposite case r B > r A , the share will not be accepted by player B. Then, the computer will randomly choose a number from 1,2,…,10. If your group is x, and the number chosen by the computer is lower or equal than 10-x, then Player A will earn the total 40 ECUs. Otherwise, if the computer chooses a number greater than 10-x, Player B will earn the total 40 ECUs.

Total earnings as a function of rank
Linear regression of the effect of rank on total earnings. Earnings were pooled across all rounds for each participant, and a standard linear regression was run predicting those earnings as a function of rank, where lower values correspond to higher rank. Results show that higher ranked individuals earned more overall, with a 1 unit change in rank associated with 9.75 more ECUs.

Subgame perfect equilibrium calculation
The Subgame perfect equilibrium of the game can be calculated as follows. We start from the fact that the game has three stages, and depends on k, the difference in rank between the two participants. Therefore we proceed by backward induction to compute the Nash equilibrium at each stage starting with the last stage.
Let us describe the sequential game: In stage 1, players have to choose simultaneously their level of contribution to the common pot. Let s 1 and s 2 be the contributions of the higher-and lower-ranked player, respectively. Both quantities must be positive and less than the initial 20 units. If the players succeed in gathering 20 units among the two contributions, they proceed to the splitting phase.
Player 1, the higher-ranked one, offers an amount x 1 , between 0 and 40 units (the total pot to be shared) that is subsequently accepted or rejected by player 2, the lower-ranked one. In case of rejection, one of the players will be awarded the whole pot with probability proportional to their rank difference. In view of the fact that the expected payoff for player 2 case of rejection is W 2 =4k, player 2 should reject if offered a smaller amount. On the other hand, the expected payoff for player 1 in case of rejection is W 1 =4(10-k), so she must at least secure that amount with her offer. This leads to a prediction for the splitting phase that player 1 should offer 4k and this should be accepted.
Regarding the cooperation phase, it is clear that there is a multiplicity of equilibria, as any s 1 , s 2 such that s 1 + s 2 is at least 20 gives access to the second phase, that would lead to a non-negative additional contribution to the payoff. In any event, the most relevant conclusion for our analysis in the main text is that the offer is predicted to be 4k, and so should the acceptance threshold be.