LETTERS Social diversity promotes the emergence of cooperation in public goods games Francisco C. Santos 1 , Marta D. Santos 2 & Jorge M. Pacheco 2 Humans often cooperate in public goods games 1–3 and situations ranging from family issues to global warming 4,5 . However, evolu- tionary game theory predicts 4,6 that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments 7 . Here we show how social diversity provides an escape from this apparent para- dox. Up to now, individuals have been treated as equivalent in all respects 4,8 , in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution 9 , cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment 10–12 . Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications. The N-person prisoner’s dilemma constitutes the most used meta- phor to study public goods games (PGGs): cooperators (C) contrib- ute an amount c (‘cost’) to the public good; defectors (D) do not contribute. The total contribution is multiplied by an enhancement factor r and the result is equally distributed between all N members of the group. Hence, Ds get the same benefit of the Cs at no cost. Collective action to shelter, protect and nourish, which abounds in the animal world, provides examples of PGGs, because the coopera- tion of group members is required. Ultimately, the success (and survival) 5 of the human species relies on the capacity of humans for large-scale cooperation. In the absence of enforcement mechan- isms 7,13,14 , conventional evolutionary game theory predicts that the temptation to defect leads individuals to forgo the public good 4 in the N-person prisoner’s dilemma. Whenever interactions are not repeated, and reward and punishment 4,8,13 can be ruled out, several mechanisms were explored that promote cooperation. Individuals were either constrained to interact only with their neighbours on spatial lattices 4,8,15 , or given the freedom to opt out of particip- ating 4,15 , leading to a coexistence of cooperators and defectors, even on spatial lattices. Here we investigate what happens in the absence of reputation and punishment and when participation is compulsory. Unlike previous studies involving PGGs 4,8,15 , individuals now interact along the social ties defined by a heterogeneous graph 16–18 . This reflects the fact that individuals have different roles in social communities. Empirical studies show that social graphs have a marked degree of heterogeneity combined with small-world effects 19–21 , as illustrated in Fig. 1b. Hence we introduce diversity in the study of cooperation under PGGs in the context of evolutionary graph theory 22 , and in the pre- sence of spatial and network reciprocity 18,23,24 . 1 Institut de Recherches Interdisciplinaires et de De ´veloppements en Intelligence Artificielle (IRIDIA), Computer and Decision Engineering Department, Universite ´ Libre de Bruxelles, B-1050 Brussels, Belgium. 2 ATP-group, Centro de Fisica Teo ´rica e Computacional (CFTC) and Departamento de Fı ´sica da Universidade de Lisboa, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. c ε β α δ γ a b Figure 1 | Population structure and local neighbourhoods. a, Regular graphs studied so far, which mimic spatially extended systems. b, Scale-free graphs 9 in which small-world effects coexist with a large heterogeneity in neighbourhood size. c, The focal individual (largest sphere) belongs to different groups (neighbourhoods) of different sizes in a heterogeneous graph. Given his/her connectivity k 5 4, we identify five neighbourhoods, each centred on one of the members of the focal individual’s group, such that individual fitness derives from the payoff accumulated in all five neighbourhoods (a, b, c, d and e). Vol 454 | 10 July 2008 | doi:10.1038/nature06940 213 ©2008 Macmillan Publishers Limited. All rights reserved