The emergence of hyper-altruistic behaviour in conflictual situations

Situations where people have to decide between hurting themselves or another person are at the core of many individual and global conflicts. Yet little is known about how people behave when facing these situations in the lab. Here we report a large (N = 2.379) experiment in which participants could either take x dollars from another anonymous participant or give y dollars to the same participant. Depending on the experimental treatments, participants were also allowed to exit the game without making any decision, but paying a cost c ≥ 0. Across different protocols and parameter specifications, we found three major results: (i) when exiting is allowed and costless, subjects tend to exit the game; (ii) females are more likely than males to exit the game, but only when the cost of the exit is small; (iii) when exiting is not allowed, altruistic actions are more common than predicted by the dominant economic models. In particular, about one sixth of the subjects show hyper-altruistic tendencies, that is, they prefer giving y rather than taking x > y. In doing so, our findings shed light on human decision-making in conflictual situations and suggest that economic models should be revised in order to take into account hyper-altruistic behaviour.

Humans are spectacular in their capacity to help others and build relationships: sharing food and cooperating during hunt have played a fundamental role in the early evolution of human societies [1] and modern variants of these attitudes play a major role still nowadays: we help friends when they need, we make donations to less fortunate people, we collaborate with our partner to build a family, we cooperate with our colleagues to finish the work faster and at higher standards.
As a consequence, our social network is far more connected than that of any other animal species.While this dense spatial structure has numerous well known positive consequences, it also generates a painful paradox: with all the people we are connected with, it is often difficult to make everyone happy: sometimes the goals of two people are just not aligned; sometimes we have to choose between hurting Person A or hurting Person B; perhaps even worse, sometimes we have to choose between hurting ourselves or hurting someone else -and sometimes, this someone else is a close friend, or a close relative, or our romantic partner.
Here we formalise such no-way-out situations and then experiment them in the lab by using a particular class of economic games, in which a person has to make a decision which affects his own outcome but also the outcomes of other people, while these other people have no active role and only get what the first person decides to give.More precisely, we consider (n + 1)-player games in which Player 1 has to decide between k allocations of money, (s 1 , o 1  1 , . . ., o n 1 ) to (s k , o 1 k , . . ., o n k ), the amount s i being for himself and o j i for the j-th other person, and all other players have only one strategy, that represents the fact that they accept Player 1's choice, whatever that is.In order to have a conflict we require that there is no allocation of money that maximises the outcome of every single agent.
The simplest case with only two players and two allocations of money such that s 1 = o 2 = −s 2 = −o 1 > 0 is already interesting from both the practical and the theoretical points of view.Indeed, it models the common situation in which a person has to decide between hurting himself or hurting another person, while believing that the amount of pain (resp.pleasure) felt by the other person in one scenario equals the amount of pain (resp.pleasure) that would be felt by himself in the other scenario.From the theoretical point of view, the interest comes from the fact that all best known economic models predict that Player 1 should choose the selfish allocation (s 1 , o 1 ).This is clear if we assume that people care only about their material payoff, but it also holds for all other best known economic models.Inequity aversion models [2,3] assume that people do not care only about their material payoff, but they also care about payoff differences.Since in our two-player conflict the difference of payoffs remains constant across different choices, these models reduce to the money-maximisation model and so they also predict the selfish outcome.Analogously, also models assuming that people have a tendency to maximise the total welfare [4,5,6,7] reduce to the money-maximisation model, since in our two-player conflict the sum of payoffs remains constant across choices.Finally, also models based on regret minimisation [8,9] predict the allocation (s 1 , o 1 ), since strictly dominating strategies minimise regret.
Despite the practical importance of such conflicts, little is known about how real people behave in these situations in the ideal scenario of a lab experiment with anonymous subjects.Do they really behave as predicted by the theoretical models?Are they inclined to solve the conflict, when a way-out is made available?Are there gender differences in conflict resolution?

Method
A total of 1984 subjects living in the US were recruited using the online labour market Amazon Mechanical Turk (AMT) [10,11] and participated in one of three experiments involving money.
In Study 1, 601 subjects earned $0.30 for participation and were randomly assigned to one of six conditions.In the no-way-out condition participants were asked to decide between stealing Player 2's participation fee or donating their participation fee to Player 2. Subjects in the role of Player 2 participated in the guess-no-way-out condition and they had to guess Player 1's decision with a $0.10 reward in case they made the right guess.The free-way-out and guess-free-way-out conditions were similar, with the difference that there was a third choice available to Player 1, that is, exit the game without doing anything.In this case both subjects would keep their participation fee.Finally, the costly-way-out and guess-costly-way-out conditions differed from the free-way-out conditions in that taking the way-out costed $0.05 to Player 1.After making their decision, participants entered the demographic questionnaire, where we asked for their gender, age, and education level.The exact instructions for the no-wayout condition were as follows.Instructions for the other conditions were very similar, a part from the obvious changes.
You have been paired with another anonymous participant.You both own $0.30 for participating in this HIT.Please choose one of the following alternatives: • Donate your $0.30 to the other participant.In this case you end the game with nothing and the other participant ends the game with $0.60.
• Steal the participation fee from the other participant.In this case you end the game with $0.60 and the other participant with nothing.
Since AMT does not allow experimenters to manipulate participation fees, Study 1 actually involves deception: participants' choices did not have a real impact on their final bonus.Moreover, one may contest the use of the verb 'to steal', which, having a strong moral weight, might drive some participants away from the theoretical predictions for other reasons than their altruism.
To exclude the risk that our results were driven by either of those two causes, Study 2 replicates the no-way-out condition of Study 1 under slightly different conditions.
Specifically, in Study 2, 583 subjects kept their participation fee and were given additional $0.30 as a bonus.Then participants in the role of Player 1 were asked to decide between taking the other participant's bonus or giving their bonus to the other participant.Exact instructions were as follows.
You have been paired with another anonymous participant.You are both given additional $0.30 as a bonus.Please choose one of the following alternatives: • Give your $0.30 to the other participant.In this case you end the game with nothing and the other participant ends the game with $0.60.
• Take the participation fee from the other participant.In this case you end the game with $0.60 and the other participant with nothing.
Finally, Study 3 (600 subjects) investigates whether there is a behavioural transition when passing from two-player conflicts to three-player conflicts.Consider for instance the allocations (x, x, −2x), (x, −2x, x), and (−2x, x, x), with x > 0. While a decision maker who decides to be selfish in the two-player conflicts considered in Studies 1 and 2 has to overcome only one moral constriction (i.e., he decides to hurt someone else for his own benefit), a decision maker who decides to be selfish in a three-player scenario has to overcome two moral constrictions: not only he has to hurt someone, but he also has to decide who to hurt.In an anonymous situation, where there is no just cause to make a discrimination and hurt either of the other people at play, this additional moral constriction might work as a deterrent and decrease the percentage of people acting selfishly.
Thus, participants in Study 3 kept their participation fee and were given additional $0.30.Those in the role of Player 1 were then asked to decide between giving their money to two other people ($0.15 each) or taking one of these people's $0.30 and splitting it with the third person.Exact instructions were as follows.Instructions for the free-wayout condition were very similar, a part from the obvious changes.

You have been grouped together with other two participants, Person A and Person B.
You are all given additional $0.30 as a bonus.Please choose one of the following alternatives: • Take the $0.30 from Person A and share them with person B. In this case, Person A will finish this task with $0 and you and Person B will finish this task with $0.45.
• Take the $0.30 from Person B and share them with person A. In this case, Person B will finish this task with $0 and you and Person A will finish this task with $0.45.
• Give your $0.30 to Person A and Person B. In this case, you will finish this task with $0 and Person A and Person B will finish this task with $0.45.
After collecting the decisions, bonuses were computed and paid.These experiments have been conducted in July 2014, while the author was still employed by the University of Southampton, United Kingdom.Informed consent was obtained by all participants.These experiments were approved by the Southampton University Ethics Committee on the Use of Human Subjects in Research and carried out in accordance with the approved guidelines.
We start by analysing the choices made by the participants who played in the role of Player 1.Despite the theoretical predictions, 28% of the 101 subjects who participated in the no-way-out condition decided to donate their participation fee.Adding a free way-out had the effect that most participants chose it.Specifically, 70% of the 100 subjects who participated in the free-way-out condition decided to use the way out, while all but three of the remaining participants acted selfishly.Three people preferred to donate their participation fee.The fact that virtually nobody acted altruistically in the free-way-out condition also shows that the results of the no-way-out condition were not driven by people who did not understand the rules of the game.The costlyway-out condition gave essentially the same results as the no-way-out condition, with only 30% of the participants choosing the way out, while all but four of the remaining ones acted selfishly and stole the other participant's participation fee.In all three conditions, we found that females were more likely than males to act altruistically, although the effect was nearly significant only in the two way-out conditions (Ranksum, p = 0.5353, p = 0.0488, p = 0.0615, respectively).The fact that this effect is only marginally significant is due to the relatively small sample size: aggregating over the way-out conditions we found that females were highly more likely than males to choose the way out (67% vs 42%, p = 0.0048).See Figure 1.
Looking at the choices made by the participants who played in the role of Player 2, we found that people made statistically the right guess in the guess-no-way-out and the guess-costly-way-out conditions, while they significantly underestimated the percentage of people choosing the way-out in the guess-free-way-out conditions.Specifically, 24% of the 102 subjects in the guess-no-way-out condition bet on Player 1's giving, compared with the 28% of subjects that actually chose to give in the way-out condition (p = 0.6241); 30% of the 99 subjects in the guess-costly-way-out bet on Player 1 choosing the way out, compared with the same percentage that actually chose it in the way-out condition (p = 0.9281); and 49% of the 99 subjects in the guess-free-way-out condition bet on Player 1 choosing the way out, compared with the 70% of subjects that actually chose it (p = 0.0083).

Study 2.
While the use of the way-out (whether costly or not) can be predicted by some social preferences theories, the results of the no-way-out condition challenge all known economic models, which agree on predicting the selfish outcome.One may wonder whether these results have been driven by the use of the word stealing and/or by the fact that the participants might have been aware of the fact that their choice was actually fictitious, since in AMT experiments participation fees get automatically paid by Amazon at the end of the experiment and thus they cannot be manipulated by the experimenter.
To exclude these possibilities, Study 2 replicated the no-way-out condition of Study 1, with the following differences.Here participants kept their participation fee and were given additional $0.30 as a bonus.Participants in the role of Player 1 were then asked to decide between taking the other participant's bonus or giving their bonus to the other participant.
Figure 1: In the no-way-out condition, about 28% of subjects preferred giving $0.30 to an anonymous person, rather than taking the same amount of money from that person.Females tended to give more, though the difference was not statistically significant.In the costly-way-out condition, about 30% of subjects preferred paying $0.05 to exit the game without making any decision, rather than making a decision.Females were more likely than males to choose the way out (p = 0.0615).In the free-way-out condition, most of subjects preferred to exit the game without making any decision and without paying any cost.Females were more likely than males to choose the way out (p = 0.0488).
The p-values are not strikingly significant, but this is also due to the small sample size.Aggregating over both way-out conditions, we find p = 0.0048.
A total of 583 subjects participated in Study 2 in the role of Player 1.The results show no significant difference with the no-way-out condition in Study 1: some 21% of the participants preferred giving the money away rather than taking it from the other participant.Again, females were slightly more other-regarding than males (27% vs 18%, p = 0.0873).

Study 3.
A total of 600 subjects participated in our Study 3, where participants were asked to make a decision in a three-player conflict instead of a two-player conflict as in Study 1 and Study 2. Perhaps contrary to the expectations, we did not find any significant difference.In the no-way-out condition, 28% of the subjects opted for the altruistic action, while the remaining ones chose either of the selfish options at random.Again, we found that females were slightly more altruist than males (33% vs 24%), though, again, the difference is not statistically significant (p = 0.1675).Among the 299 subjects who participated in the way-out condition, 21 (11 males) chose the altruistic choice, regardless the existence of the way out.Among the remaining 278 subjects, 59% chose the way out.Again we found that females were significantly more likely than males to choose the way out (69% vs 52%, p = 0.0131).See Figure 2.

Discussion
The secret of the enormous success of human societies is partly due to our ability to cooperate with others and help less fortunate people [12,13,14,15].Recent lab experiments show that this ability goes far beyond the five rules of cooperation [16]: anonymous strangers cooperate also in one-shot lab experiments [17,18,19,20,21,22] and even in large groups [23].As a consequence of our cooperative and helping actions, we interact with many people every day and while there might be some situations where our choices make everyone happy, in many circumstances we find ourselves in the unpleasant situation of having to decide between hurting ourselves or hurting one or more other people.
Here we have formalised this scenario by means of simple decision problems and then we have investigated how real people behave in such situations in the context of a lab experiment with anonymous subjects.
Subjects participating in Study 1 and Study 2 were asked to decide between giving (resp.taking) a certain amount of money to (resp.from) an anonymous person.Across the two studies and a total of almost 700 subjects, we have found that about 25% of the participants preferred giving rather than taking.Moreover, adding a free way-out, that is a third strategy according to which the decision maker can exit the game without making any decisions and without paying any cost, had the effect that most (70%) of the subjects chose the way out.However, this positive effect of the way-out on conflict Figure 2: In the three-person no-way-out condition, about 28% of subjects preferred giving $0.30 to two anonymous people ($0.15 each), rather than taking the same amount of money from one of these people and sharing it with the third one.Females tended to give more, though the difference was not statistically significant.In the way-out condition, about 59% of subjects preferred to exit the game without making any decision and without paying any cost.Females were significantly more likely than males to choose the way out (p = 0.0131).
resolution vanished as soon as the participants were asked to pay a little cost ($0.05) in order to take it.Although in the no-way-out condition we have found that females tended to be more altruistic than males, the effect was not statistically significant.It became significant in the two way-out conditions, where we consistently observed that females were significantly more likely than males to solve the conflict by choosing the way-out.
While subjects participating in Studies 1 and 2 faced a two-person conflict (i.e., either hurt yourself or another person), those in Study 3 faced a three-person conflict: they were asked to either donate their money to two other people or to take one of other people's money and split it with the third person.While one could expect that this decision problem increases givings due to the fact that selfish people have to overcome two moral constrictions (first, they have to choose to hurt someone else instead of themselves, and then they have to decide who to hurt, making a discrimination without just cause) instead of only one (just choose to hurt someone else), the resulting data were very similar to those of Studies 1 and 2. In the no-way-out condition, 28% of the players acted altruistically.Adding a costless way out had the effect that most (59%) players chose it.Regarding gender differences in behaviour, we found exactly the same pattern as in Studies 1 and 2: females tended (i.e., not statistically significant) to be more altruistic than males in the no-way-out condition and were significantly more likely than males to take the way out in the way-out condition.
In sum, our results provide evidence of the three regularities: (i) a substantial proportion of people prefer harming themselves rather than harming an anonymous stranger; (ii) the majority of people prefer to avoid the conflict and exit the game, but only when the way out is costless; (iii) females are more likely than males to avoid a conflict by taking the way-out, even when it is costly.
A recent paper [24] makes a point similar to our point (i).There, Crockett et al. show that most people evaluate others' pain more than their own pain: they pay to avoid an anonymous stranger receiving an electric shock twice as much as they pay to avoid themselves receiving an electric shock.Though similar, our results are different in the way that they point out that there is no need of real physical harm to observe hyper-altruistic behaviour.In our experiment, a substantial proportion of people value others' monetary outcome more than their own, without any real physical harm involved.This is inconsistent with previous studies on social preferences, where most people value others' monetary outcomes less than their own [25], and with previous studies on empathy [26,27], which imply people value others' monetary outcomes at most as much as their own, and point out that the way people value others' monetary outcomes may not be universal: the fact that most people take the way out, when it is made available, suggests that the way people value others' monetary outcome depends on the set of available choices.
Another paper [28] makes a point similar to our point (ii), that is that most people prefer to exit the game, rather than making a decision that would harm either of the parties.There the authors show that about 28$9, rather than playing it in the role of the dictator with an endowment of $10.However, our results are stronger.Participants in ref. 28 played a two-stage game: the first stage was a normal Dictator game where participants in the role of the dictator had to decide how to allocate $10 between them and an anonymous recipient, knowing that the recipient would not have any active role.After making the decision, but before telling it to the recipient and before telling to the recipient that they were playing a Dictator game in the role of the recipient, the dictators were asked whether they wanted to stick with their decision or leave the game with $9.In this latter case, the recipient would not be informed of the fact that they were supposed to be the recipient in a Dictator game.Although 11 subjects (corresponding to 28% of the total) preferred to exit the game, only two of them had decided to keep the whole endowment for themselves in the first stage of the game.Thus it is possible that the fact that the strategy space has been changed from Stage 1 to Stage 2, and the fact that the recipient does not have complete knowledge of the decision problem, have changed some peoples preferences, who are now not really exiting the game, but just maximizing their payoff.Contrariwise, our experiment is a one-stage experiment where both parties have complete knowledge of the decision problem and so it shows that a substantial proportion of people truly have preferences for opting out.
A result similar to our point (ii), that is that most people prefer to exit the game, rather than making a decision that would harm either of the parties, was already made in [28], where the authors show that about 28% of subjects prefer to exit a dictator game with $9, rather than playing it in the role of the dictator with an endowment of $10.However, our results are stronger.Participants in [28] played a two-stage game: the first stage was a normal Dictator game where participants in the role of the dictator had to decide how to allocate $10 between them and an anonymous recipient, knowing that the recipient would not have any active role.After making the decision, but before telling it to the recipient and before telling to the recipient that they were playing a Dictator game in the role of the recipient, the dictators were asked whether they wanted to stick with their decision or leave the game with $9.In this latter case, the recipient would not be informed of the fact that they were supposed to be the recipient in a Dictator game.Although 11 subjects (corresponding to 28% of the total) preferred to exit the game, only two of them had decided to keep the whole endowment for themselves in the first stage of the game.Thus it is possible that the fact that the strategy space has been changed from Stage 1 to Stage 2, and the fact that the recipient does not have complete knowledge of the decision problem, have changed some people's preferences, who are now not really exiting the game, but just maximizing their payoff.Contrariwise, our experiment is a one-stage experiment where both parties have complete knowledge of the decision problem and so it shows that a substantial proportion of people truly have preferences for opting out.
Finally, while our point (iii) is reminiscent of the pretty well established result that females are more giving than males in the Dictator game [29,30,31,32,33,34,35,36,37,38], it goes far beyond it, suggesting that females are not only more sharing than males, but they also have a stronger tendency to find ways out and solve conflicts even at a personal cost.One might wonder how far this observation can be generalised and whether it can help us solve those conflicts between populations that are destroying many innocent lives in many places of the world.
Our results open the road to two other broad research questions.First, they challenge all best-known economic models, including inequity aversion [2,3], welfare maximisation [4,5,6,7], and regret minimisation models [8,9], which all agree on the fact that, in the no-way-out condition, every participant should take the money from the other participant(s).As a consequence, it is important to understand what psychological and economic motivations led a substantial percentage of people away from the theoretical predictions so as to take this into account in a new and more general model of human behaviour.
Second, it would be important to understand what psychological consequences such sacrificial behaviours can have on a single person.If a person is available to pay 1 cent to increase the payoff of an anonymous stranger of 1 cent, it is likely that the same person would sacrifice much more to help a closely related person.Such people may thus experience extreme forms of active sacrifice [39] in their everyday life, such as unmitigated communion, that is the extreme focus on others without the balance of a focus on self [40].
Since unmitigated communion is known to cause anxiety, depressive symptoms, lower self-esteem, and poorer physical health [41,42,43], it would be important to understand to what extent it can be captured by simple economic games such as the one we have introduced.