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Understanding large-scale cooperation among unrelated individuals is one of the greatest challenges of the 21st century. Since human cooperation evolves on social networks, the theoretical framework of multilayer networks is perfectly suited for studying this fascinating aspect of our biology. To that effect, we here study the cooperation in evolutionary games on interdependent networks, such that players in one network layer play the snowdrift game (SDG), and the prisoner's dilemma game (PDG) in the other layer. Importantly, players are able to share information across two layers, which in turn affects their strategy choices. Monte Carlo simulations reveal that the transfer of information about the strategy of the corresponding player in the other network layer alone is enough to significantly promote the overall level of cooperation. However, while the cooperation is markedly enhanced in the layer where the PDG is played, the opposite is true, albeit to a lesser extent, for the layer where the SDG is played. The net increase in cooperation is thus due to a doubly effect of information sharing. We show further that the more complete the information transfer, the more the overall level of cooperation is promoted, and that this holds as long as the information channels between the player do not vary over time. We discuss potential implications of these findings for future human experiments concerning the cooperation on multilayer networks.

Rewarding cooperation is in many ways expected behaviour from social players. However, strategies that promote antisocial behaviour are also surprisingly common, not just in human societies, but also among eusocial insects and bacteria. Examples include sanctioning of individuals who behave prosocially, or rewarding of free-riders who do not contribute to collective enterprises. We therefore study the public goods game with antisocial and prosocial pool rewarding in order to determine the potential negative consequences on the effectiveness of positive incentives to promote cooperation. Contrary to a naive expectation, we show that the ability of defectors to distribute rewards to their like does not deter public cooperation as long as cooperators are able to do the same. Even in the presence of antisocial rewarding, the spatial selection for cooperation in evolutionary social dilemmas is enhanced. Since the administration of rewards to either strategy requires a considerable degree of aggregation, cooperators can enjoy the benefits of their prosocial contributions as well as the corresponding rewards. Defectors when aggregated, on the other hand, can enjoy antisocial rewards, but due to their lack of contributions to the public good they ultimately succumb to their inherent inability to secure a sustainable future. Strategies that facilitate the aggregation of akin players, even if they seek to promote antisocial behaviour, thus always enhance the long-term benefits of cooperation.

Evolutionary game dynamics on networks typically consider the competition among simple strategies such as cooperation and defection in the Prisoner’s Dilemma and summarize the effect of population structure as network reciprocity. However, it remains largely unknown regarding the evolutionary dynamics involving multiple powerful strategies typically considered in repeated games, such as the zero-determinant (ZD) strategies that are able to enforce a linear payoff relationship between them and their co-players. Here, we consider the evolutionary dynamics of always cooperate (AllC), extortionate ZD (extortioners), and unbending players in lattice populations based on the commonly used death-birth updating. Out of the class of unbending strategies that can foster reciprocal cooperation and fairness among extortionate players, we consider a particular candidate, pre-optimized through the machine-learning method of particle swarm optimization (PSO), called PSO Gambler. We derive analytical results under weak selection and rare mutations, including pairwise fixation probabilities and long-term frequencies of strategies. In the absence of the third unbending type, extortioners can achieve a half-half split in equilibrium with unconditional cooperators for sufficiently large extortion factors. However, the presence of unbending players fundamentally changes the dynamics and tilts the system to favor unbending cooperation. Most surprisingly, extortioners cannot dominate at all regardless of how large their extortion factor is, and the long-term frequency of unbending players is maintained almost as a constant. Our analytical method is applicable to studying the evolutionary dynamics of multiple strategies in structured populations. Our work provides insights into the interplay between network reciprocity and direct reciprocity, revealing the role of unbending strategies in enforcing fairness and suppressing extortion.

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.

We study the coupled dynamics between strategy updating and partner switching on adaptive multilayer networks whose structure is split into an interaction layer for accumulating payoff and a learning layer for updating strategy. Two different types of adaptive multilayer network dynamics are modeled to study the evolution of cooperation. First, the selected individual either varies his strategy updating environment or switches his interaction partners during the partner switching process. It is proved that an increasing ratio of interaction network reconfiguration facilitates the coevolution of cooperation, indicating that interaction network acts a profound role in promoting the coevolution cooperation. Furthermore, we consider a type that the selected player simultaneously updates his strategy updating network and interaction network during the rewiring process. For a low frequent partner switching process, it is found that the evolution of cooperation is hindered whenever the two layers do not coincide. However, when the frequency of partner switching process increases, breaking the symmetry between interaction network and learning network resolves the social dilemma and enhances the evolution of cooperation. Moreover, a comparison between two adaptive multilayer network dynamics shows that the former type that only permits one layer to evolve every step on the adaptive multilayer networks suppresses the evolution of cooperation.

Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio, ( b / c ) ∗ , which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that ( b / c ) ∗ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes ( b / c ) ∗ small to facilitate cooperation. In contrast, ( b / c ) ∗ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes ( b / c ) ∗ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery.

How does natural selection lead to cooperation between competing individuals? The Prisoner's Dilemma captures the essence of this problem. Two players can either cooperate or defect. The payoff for mutual cooperation, R, is greater than the payoff for mutual defection, P. But a defector versus a cooperator receives the highest payoff, T, where as the cooperator obtains the lowest payoff, S. Hence, the Prisoner's Dilemma is defined by the payoff ranking T > R > P > S. In a well-mixed population, defectors always have a higher expected payoff than cooperators, and therefore natural selection favors defectors. The evolution of cooperation requires specific mechanisms. Here we discuss five mechanisms for the evolution of cooperation: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity (or graph selection). Each mechanism leads to a transformation of the Prisoner's Dilemma payoff matrix. From the transformed matrices, we derive the fundamental conditions for the evolution of cooperation. The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations.

Network reciprocity has been successfully put forward (since M. A. Nowak and R. May's, 1992, influential paper) as the simplest mechanism-requiring no strategical complexity-supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents' interactions localized, while network reciprocity is the property of the underlying evolutionary process to favor cooperation in sparse rather than dense networks. In theoretical models, the property holds under imitative evolutionary processes, whereas cooperation disappears in any network if imitation is replaced by the more rational best-response rule of strategy update. In social experiments, network reciprocity has been observed, although the imitative behavior did not emerge. What did emerge is a form of conditional cooperation based on direct reciprocity-the propensity to cooperate with neighbors who previously cooperated. To resolve this inconsistency, network reciprocity has been recently shown in a model that rationally confronts the two main behaviors emerging in experiments-reciprocal cooperation and unconditional defection-with rationality introduced by extending the best-response rule to a multi-step predictive horizon. However, direct reciprocity was implemented in a non-standard way, by allowing cooperative agents to temporarily cut the interaction with defecting neighbors. Here, we make this result robust to the way cooperators reciprocate, by implementing direct reciprocity with the standard tit-for-tat strategy and deriving similar results.

In this work, we explore the role of learning dynamics and social norms in human cooperation on networks. We study the model recently introduced in [Physical Review E, 97, 042321 (2018)] that integrates the well-studied Experience Weighted Attraction learning model with some features characterizing human norm psychology, namely the set of cognitive abilities humans have evolved to deal with social norms. We provide further evidence that this extended model-that we refer to as Experience Weighted Attraction with Norm Psychology-closely reproduces cooperative patterns of behavior observed in large-scale experiments with humans. In particular, we provide additional support for the finding that, when deciding to cooperate, humans balance between the choice that returns higher payoffs with the choice in agreement with social norms. In our experiment, agents play a prisoner's dilemma game on various network structures: (i) a static lattice where agents have a fixed position; (ii) a regular random network where agents have a fixed position; and (iii) a dynamic lattice where agents are randomly re-positioned at each game iteration. Our results show that the network structure does not affect the dynamics of cooperation, which corroborates results of prior laboratory experiments. However, the network structure does seem to affect how individuals balance between their self-interested and normative choices.

To achieve food security and meet the demands of the ever-growing human populations, farming systems have assumed unsustainable practices to produce more from a finite land area. This has been cause for concern mainly due to the often-irreversible damage done to the otherwise productive agricultural landscapes. Agro-ecology is proclaimed to be deteriorating due to eroding integrity of connected ecological mosaics and vulnerability to climate change. This has contributed to declining species diversity, loss of buffer vegetation, fragmentation of habitats, and loss of natural pollinators or predators, which eventually leads to decline in ecosystem services. Currently, a hierarchy of conservation initiatives is being considered to restore ecological integrity of agricultural landscapes. However, the challenge of identifying a suitable conservation strategy is a daunting task in view of socio-ecological factors that may constrain the choice of available strategies. One way to mitigate this situation and integrate biodiversity with agricultural landscapes is to implement offset mechanisms, which are compensatory and balancing approaches to restore the ecological health and function of an ecosystem. This needs to be tailored to the history of location specific agricultural practices, and the social, ecological and environmental conditions. The offset mechanisms can complement other initiatives through which farmers are insured against landscape-level risks such as droughts, fire and floods. For countries in the developing world with significant biodiversity and extensive agriculture, we should promote a comprehensive model of sustainable agricultural landscapes and ecosystem services, replicable at landscape to regional scales. Arguably, the model can be a potential option to sustain the integrity of biodiversity mosaic in agricultural landscapes.