Valerio Capraro

A Model of Human Cooperation in Social Dilemmas

Social dilemmas are situations in which collective interests are at odds with private interests: pollution, depletion of natural resources, and intergroup conflicts, are at their core social dilemmas. Because of their multidisciplinarity and their importance, social dilemmas have been studied by economists, biologists, psychologists, sociologists, and political scientists. These studies typically explain tendency to cooperation by dividing people in proself and prosocial types, or appealing to forms of external control or, in iterated social dilemmas, to long-term strategies. But recent experiments have shown that cooperation is possible even in one-shot social dilemmas without forms of external control and the rate of cooperation typically depends on the payoffs. This makes impossible a predictive division between proself and prosocial people and proves that people have attitude to cooperation by nature. The key innovation of this article is in fact to postulate that humans have attitude to cooperation by nature and consequently they do not act a priori as single agents, as assumed by standard economic models, but they forecast how a social dilemma would evolve if they formed coalitions and then they act according to their most optimistic forecast. Formalizing this idea we propose the first predictive model of human cooperation able to organize a number of different experimental findings that are not explained by the standard model. We show also that the model makes satisfactorily accurate quantitative predictions of population average behavior in one-shot social dilemmas.

Heuristics guide the implementation of social preferences in one-shot Prisoner's Dilemma experiments.

Cooperation in one-shot anonymous interactions is a widely documented aspect of human behaviour. Here we shed light on the motivations behind this behaviour by experimentally exploring cooperation in a one-shot continuous-strategy Prisoners Dilemma (i.e. one-shot two-player Public Goods Game). We examine the distribution of cooperation amounts, and how that distribution varies based on the benefit-to-cost ratio of cooperation (b/c). Interestingly, we find a trimodal distribution at all b/c values investigated. Increasing b/c decreases the fraction of participants engaging in zero cooperation and increases the fraction engaging in maximal cooperation, suggesting a role for efficiency concerns. However, a substantial fraction of participants consistently engage in 50% cooperation regardless of b/c. The presence of these persistent 50% cooperators is surprising, and not easily explained by standard models of social preferences. We present evidence that this behaviour is a result of social preferences guided by simple decision heuristics, rather than the rational examination of payoffs assumed by most social preference models. We also find a strong correlation between play in the Prisoners Dilemma and in a subsequent Dictator Game, confirming previous findings suggesting a common prosocial motivation underlying altruism and cooperation.

Social heuristics and social roles: intuition favors altruism for women but not for men

Are humans intuitively altruistic, or does altruism require self-control? A theory of social heuristics, whereby intuitive responses favor typically successful behaviors, suggests that the answer may depend on who you are. In particular, evidence suggests that women are expected to behave altruistically, and are punished for failing to be altruistic, to a much greater extent than men. Thus, women (but not men) may internalize altruism as their intuitive response. Indeed, a meta-analysis of 13 new experiments and 9 experiments from other groups found that promoting intuition relative to deliberation increased giving in a Dictator Game among women, but not among men (Study 1, N = 4,366). Furthermore, this effect was shown to be moderated by explicit sex role identification (Study 2, N = 1,831): the more women described themselves using traditionally masculine attributes (e.g., dominance, independence) relative to traditionally feminine attributes (e.g., warmth, tenderness), the more deliberation reduced their altruism. Our findings shed light on the connection between gender and altruism, and highlight the importance of social heuristics in human prosociality.

Benevolent Characteristics Promote Cooperative Behaviour among Humans

Cooperation is fundamental to the evolution of human society. We regularly observe cooperative behaviour in everyday life and in controlled experiments with anonymous people, even though standard economic models predict that they should deviate from the collective interest and act so as to maximise their own individual payoff. However, there is typically heterogeneity across subjects: some may cooperate, while others may not. Since individual factors promoting cooperation could be used by institutions to indirectly prime cooperation, this heterogeneity raises the important question of who these cooperators are. We have conducted a series of experiments to study whether benevolence, defined as a unilateral act of paying a cost to increase the welfare of someone else beyond ones own, is related to cooperation in a subsequent one-shot anonymous Prisoners dilemma. Contrary to the predictions of the widely used inequity aversion models, we find that benevolence does exist and a large majority of people behave this way. We also find benevolence to be correlated with cooperative behaviour. Finally, we show a causal link between benevolence and cooperation: priming people to think positively about benevolent behaviour makes them significantly more cooperative than priming them to think malevolently. Thus benevolent people exist and cooperate more.

Group Size Effect on Cooperation in One-Shot Social Dilemmas

Social dilemmas are central to human society. Depletion of natural resources, climate protection, security of energy supply, and workplace collaborations are all examples of social dilemmas. Since cooperative behaviour in a social dilemma is individually costly, Nash equilibrium predicts that humans should not cooperate. Yet experimental studies show that people do cooperate even in anonymous one-shot interactions. In spite of the large number of participants in many modern social dilemmas, little is known about the effect of group size on cooperation. Does larger group size favour or prevent cooperation? We address this problem both experimentally and theoretically. Experimentally, we find that there is no general answer: it depends on the strategic situation. Specifically, we find that larger groups are more cooperative in the Public Goods game, but less cooperative in the N-person Prisoners dilemma. Theoretically, we show that this behaviour is not consistent with either the Fehr & Schmidt model or (a one-parameter version of) the Charness & Rabin model, but it is consistent with the cooperative equilibrium model introduced by the second author.

Rethinking Spontaneous Giving: Extreme Time Pressure and Ego-Depletion Favor Self-Regarding Reactions

Previous experimental studies suggest that cooperation in one-shot anonymous interactions is, on average, spontaneous, rather than calculative. To explain this finding, it has been proposed that people internalize cooperative heuristics in their everyday life and bring them as intuitive strategies in new and atypical situations. Yet, these studies have important limitations, as they promote intuitive responses using weak time pressure or conceptual priming of intuition. Since these manipulations do not deplete participants’ ability to reason completely, it remains unclear whether cooperative heuristics are really automatic or they emerge after a small, but positive, amount of deliberation. Consistent with the latter hypothesis, we report two experiments demonstrating that spontaneous reactions in one-shot anonymous interactions tend to be egoistic. In doing so, our findings shed further light on the cognitive underpinnings of cooperation, as they suggest that cooperation in one-shot interactions is not automatic, but appears only at later stages of reasoning.

Cooperative Equilibria in Iterated Social Dilemmas

The implausibility of the extreme rationality assumptions of Nash equilibrium has been attested by numerous experimental studies with human players. In particular, the fundamental social dilemmas such as the Traveler’s dilemma, the Prisoner’s dilemma, and the Public Goods game demonstrate high rates of deviation from the unique Nash equilibrium, dependent on the game parameters or the environment in which the game is played. These results inspired several attempts to develop suitable solution concepts to more accurately explain human behaviour. In this line, the recently proposed notion of cooperative equilibrium [5, 6], based on the idea that players have a natural attitude to cooperation, has shown promising results for single-shot games. In this paper, we extend this approach to iterated settings. Specifically, we define the Iterated Cooperative Equilibrium (ICE) and show it makes statistically precise predictions of population average behaviour in the aforementioned domains. Importantly, the definition of ICE does not involve any free parameters, and so it is fully predictive.

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.

Do Good Actions Inspire Good Actions in Others

Actions such as sharing food and cooperating to reach a common goal have played a fundamental role in the evolution of human societies. Despite the importance of such good actions, little is known about if and how they can spread from person to person to person. For instance, does being recipient of an altruistic act increase your probability of being cooperative with a third party? We have conducted an experiment on Amazon Mechanical Turk to test this mechanism using economic games. We have measured willingness to be cooperative through a standard Prisoners dilemma and willingness to act altruistically using a binary Dictator game. In the baseline treatments, the endowments needed to play were given by the experimenters, as usual; in the control treatments, they came from a good action made by someone else. Across four different comparisons and a total of 572 subjects, we have never found a significant increase of cooperation or altruism when the endowment came from a good action. We conclude that good actions do not necessarily inspire good actions in others. While this is consistent with the theoretical prediction, it challenges the majority of other experimental studies.

Discrete homology theory for metric spaces

htmlabstractWe define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz maps from an n n -dimensional cube to a fixed metric space. We prove that the resulting homology theory satisfies a discrete analogue of the Eilenberg–Steenrod axioms, and prove a discrete analogue of the Mayer–Vietoris exact sequence. Moreover, this discrete homology theory is related to the discrete homotopy theory of a metric space through a discrete analogue of the Hurewicz theorem. We study the class of groups that can arise as discrete homology groups and, in this setting, we prove that the fundamental group of a smooth, connected, metrizable, compact manifold is isomorphic to the discrete fundamental group of a ‘fine enough’ rectangulation of the manifold. Finally, we show that this discrete homology theory can be coarsened, leading to a new non-trivial coarse invariant of a metric space.