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It is not fully understood why we cooperate with strangers on a daily basis. In an increasingly global world, where interaction networks and relationships between individuals are becoming more complex, different hypotheses have been put forward to explain the foundations of human cooperation on a large scale and to account for the true motivations that are behind this phenomenon. In this context, population structure has been suggested to foster cooperation in social dilemmas, but theoretical studies of this mechanism have yielded contradictory results so far; additionally, the issue lacks a proper experimental test in large systems. We have performed the largest experiments to date with humans playing a spatial Prisoner’s Dilemma on a lattice and a scale-free network (1,229 subjects). We observed that the level of cooperation reached in both networks is the same, comparable with the level of cooperation of smaller networks or unstructured populations. We have also found that subjects respond to the cooperation that they observe in a reciprocal manner, being more likely to cooperate if, in the previous round, many of their neighbors and themselves did so, which implies that humans do not consider neighbors’ payoffs when making their decisions in this dilemma but only their actions. Our results, which are in agreement with recent theoretical predictions based on this behavioral rule, suggest that population structure has little relevance as a cooperation promoter or inhibitor among humans.

Significance Human populations are both extremely cooperative and highly structured. Mathematical models have shown that fixed network interaction structures can lead to cooperation under certain conditions, by allowing cooperators to cluster together. Here, we provide empirical evidence of this phenomenon. We explore how different fixed social network structures can promote cooperation using economic game experiments. We find that people cooperate at high stable levels, as long as the benefits created by cooperation are larger than the number of neighbors in the network. This empirical result is consistent with a rule predicted by mathematical models of evolution. Our findings show the important role social networks can play in human cooperation and provide guidance for promoting cooperative behavior. The evolution of cooperation in network-structured populations has been a major focus of theoretical work in recent years. When players are embedded in fixed networks, cooperators are more likely to interact with, and benefit from, other cooperators. In theory, this clustering can foster cooperation on fixed networks under certain circumstances. Laboratory experiments with humans, however, have thus far found no evidence that fixed network structure actually promotes cooperation. Here, we provide such evidence and help to explain why others failed to find it. First, we show that static networks can lead to a stable high level of cooperation, outperforming well-mixed populations. We then systematically vary the benefit that cooperating provides to one’s neighbors relative to the cost required to cooperate ( b / c ), as well as the average number of neighbors in the network ( k ). When b / c > k , we observe high and stable levels of cooperation. Conversely, when b / c ≤ k or players are randomly shuffled, cooperation decays. Our results are consistent with a quantitative evolutionary game theoretic prediction for when cooperation should succeed on networks and, for the first time to our knowledge, provide an experimental demonstration of the power of static network structure for stabilizing human cooperation.

Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called 'spatial selection': cooperators prevail against defectors by clustering in physical or other spaces.

Blockchains are distributed ledgers, operated within peer-to-peer networks. We model the proof-of-work blockchain protocol as a stochastic game and analyze the equilibrium strategies of rational, strategic miners. Mining the longest chain is a Markov perfect equilibrium, without forking, in line with Nakamoto (2008). The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying that equilibrium investment in computing capacity is excessive.

Cooperation can be sustained by institutions that punish free-riders. Such institutions, however, tend to be subverted by corruption if they are not closely watched. Monitoring can uphold the enforcement of binding agreements ensuring cooperation, but this usually comes at a price. The temptation to skip monitoring and take the institution’s integrity for granted leads to outbreaks of corruption and the breakdown of cooperation. We model the corresponding mechanism by means of evolutionary game theory, using analytical methods and numerical simulations, and find that it leads to sustained or damped oscillations. The results confirm the view that corruption is endemic and transparency a major factor in reducing it.

Despite the accumulation of research on indirect reciprocity over the past 30 years and the publication of over 100,000 related papers, there are still many issues to be addressed. Here, we look back on the research that has been done on indirect reciprocity and identify the issues that have been resolved and the ones that remain to be resolved. This manuscript introduces indirect reciprocity in the context of the evolution of cooperation, basic models of social dilemma situations, the path taken in the elaboration of mathematical analysis using evolutionary game theory, the discovery of image scoring norms, and the breakthroughs brought about by the analysis of the evolutionary instability of the norms. Moreover, it presents key results obtained by refining the assessment function, resolving the punishment dilemma, and presenting a complete solution to the social dilemma problem. Finally, it discusses the application of indirect reciprocity in various disciplines.

A growing experimental literature studies the determinants of cooperation in infinitely repeated games, tests different predictions of the theory, and suggests an empirical solution to the problem of multiple equilibria. To provide a robust description of the literature’s findings, we gather and analyze a metadata set of experiments on infinitely repeated prisoner’s dilemma games. The experimental data show that cooperation is affected by infinite repetition and is more likely to arise when it can be supported in equilibrium. However, the fact that cooperation can be supported in equilibrium does not imply that most subjects will cooperate. High cooperation rates will emerge only when the parameters of the repeated game are such that cooperation is very robust to strategic uncertainty. We also review the results regarding the effect of imperfect monitoring, changing partners, and personal characteristics on cooperation and the strategies used to support it.

The production and living conditions of reservoir resettlements are relatively poor after relocation; therefore, the Chinese government has specifically issued policies that require post-relocation support projects in resettlement areas. Existing research and practice show that game theory can be applied to the relationship between the Resettlement Development Department and other government departments (OGDs); for this reason, we construct an evolutionary game model of both sides through field study and literature research. With the analysis of the replication dynamics, evolutionary strategies and stability of the game system, the results show that the benefits of both sides are maximized and the governance effectiveness is most significant when the RDD actively plans the PReS projects and the OGD positively supports the project. This study empirically and mathematically proves the significance of cross-departmental cooperation and enriches the study of collaborative governance among multiple government departments.

In the animal world, collective action to shelter, protect and nourish requires the cooperation of group members. Among humans, many situations require the cooperation of more than two individuals simultaneously. Most of the relevant literature has focused on an extreme case, the N-person Prisoner's Dilemma. Here we introduce a model in which a threshold less than the total group is required to produce benefits, with increasing participation leading to increasing productivity. This model constitutes a generalization of the two-person stag hunt game to an N-person game. Both finite and infinite population models are studied. In infinite populations this leads to a rich dynamics that admits multiple equilibria. Scenarios of defector dominance, pure coordination or coexistence may arise simultaneously. On the other hand, whenever one takes into account that populations are finite and when their size is of the same order of magnitude as the group size, the evolutionary dynamics is profoundly affected: it may ultimately invert the direction of natural selection, compared with the infinite population limit.