Evolution of global cooperation driven by risks

Impacts of preferences on the emergence of cooperation

Behavior decision making, where individuals can efficiently express their preferences for all options, has a great impact on cooperation. Hereby, we institute a minimal model in well-mixed populations where whether and how to sanction defectors are decided by cooperators via different decision-making mechanisms. The results illustrate that whether cooperation can outbreak depends on the cooperators' preferences for sanction and complying with the electoral outcome. We highlight the role of individuals' preferences in the emergence of cooperation and show that there exists an intermediate degree of the cooperators' preference for sanction at which the cooperators' preference for complying with the electoral outcome has a negligible impact on cooperation. We point out whether conformity facilitates the emergence of cooperation depends on the cooperators' preference for sanction. We find, compared with individual decision making, whether collective decision making is more conducive to promoting cooperation crucially depends on cooperators' preferences as well as the consensus required for employing sanction.

Insurance optimizes complex interactive and cooperative behaviors in public goods games

Global cooperation is urgently needed to prevent risks of world-wide extreme events and disasters for sustainable development. In human societies, however, there exists bias toward interacting with partners with similar characteristics, but not contributing globally. We study how complex interactive behaviors evolve under risks through proposing a threshold public goods game model. In the model, individuals either play games with participants who own the same phenotype, or contribute to the collective target of global public goods. We further introduce an insurance compensation mechanism into the model to probe the evolution of global cooperation. It is found that the introduction of the insurance remarkably promotes the emergence of global cooperative behavior and inhibits the tendency to play games only with individuals of the same phenotype. Besides, contrary to models without insurance, global cooperation is strengthened with the increase of imitation intensities. In addition, high risk and high threshold are in favor of global cooperation.

Coevolution of nonlinear group interactions and strategies in well-mixed and structured populations

In microbial populations and human societies, the rule of nonlinear group interactions strongly affects the intraspecific evolutionary dynamics, which leads to the variation of the strategy composition eventually. The consequence of such variation may retroact to the rule of the interactions. This correlation indicates that the rule of nonlinear group interactions may coevolve with individuals' strategies. Here, we develop a model to investigate such coevolution in both well-mixed and structured populations. In our model, positive and negative correlations between the rule and the frequency of cooperators are considered, with local and global information. When the correlation refers to the global information, we show that in well-mixed populations, the coevolutionary outcomes cover the scenarios of defector dominance, coexistence, and bi-stability. Whenever the population structure is considered, its impact on the coevolutionary dynamics depends on the type of the correlation: with a negative (positive) correlation, population structure promotes (inhibits) the evolution of cooperation. Furthermore, when the correlation is based on the more accessible local information, we reveal that a negative correlation pushes cooperators into a harsh situation whereas a positive one lowers the barriers for cooperators to occupy the population. All our analytical results are validated by numerical simulations. Our results shed light on the power of the coevolution of nonlinear group interactions and evolutionary dynamics on generating various evolutionary outcomes, implying that the coevolutionary framework may be more appropriate than the traditional cases for understanding the evolution of cooperation in both structureless and structured populations.

Evolution of cooperation with interactive identity and diversity

Interactive identity and interactive diversity are generally regarded as two typical interaction patterns in living systems. The former describes that in each generation every individual behaves identically to all of its opponents, and the latter allows each individual to behave diversely to its distinct opponents. Most traditional research on the evolution of cooperation, however, has been confined to populations with a uniform interaction pattern. Here we study the cooperation conundrum in a diverse population comprising players with interactive identity and with interactive diversity. We find that in homogeneous networks a small fraction of players taking interactive diversity are enough to stabilize cooperation for a wide range of payoff values even in a noisy environment. When assigned to heterogeneous networks, players in high-degree nodes taking interactive diversity significantly strengthen systems' resilience against the shifty environment and enlarge the survival region of cooperation. However, they fail to establish a homogeneous strategy 'cloud' in the neighborhood and thus can not coordinate players in low-degree nodes to reach a socially optimal cooperation level. The most favorable outcome emerges when players in high-degree nodes take interactive identity and meanwhile others adopt interactive diversity. Our findings reveal the significance of the two typical interaction patterns and could be a good heuristic in coordinating them to achieve the social optimum in cooperation.

Coevolutionary dynamics of phenotypic diversity and contingent cooperation

Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.

Phenotypic variation is commonly observed from human cells to the intestinal pathogen Salmonella enterica serovar Typhimurium to the wrinkly-spreader morphs. Such phenotypic diversity proves effective in promoting cooperation, or confers survival advantage against unfavorable environmental changes. Prior studies show that interactions based on phenotypic similarity can promote cooperation. Yet in these models, the level of phenotypic diversity is prescribed such that individuals each possess the same number of available phenotypes, and thereby no evolution of phenotypic diversity per se. We here take into consideration important aspects of the diversity of phenotype and contingent cooperation and show that phenotypic diversity coevolves with cooperation under a variety of conditions. Our work provides a potential mechanism for the evolution of cooperation, and individuals, especially cooperators, endowed with diverse phenotypes constitute the backbone in inducing the coevolution.

Evolutionary dynamics of general group interactions in structured populations

The evolution of populations is influenced by many factors, and the simple classical models have been developed in a number of important ways. Both population structure and multiplayer interactions have been shown to significantly affect the evolution of important properties, such as the level of cooperation or of aggressive behavior. Here we combine these two key factors and develop the evolutionary dynamics of general group interactions in structured populations represented by regular graphs. The traditional linear and threshold public goods games are adopted as models to address the dynamics. We show that for linear group interactions, population structure can favor the evolution of cooperation compared to the well-mixed case, and we see that the more neighbors there are, the harder it is for cooperators to persist in structured populations. We further show that threshold group interactions could lead to the emergence of cooperation even in well-mixed populations. Here population structure sometimes inhibits cooperation for the threshold public goods game, where depending on the benefit to cost ratio, the outcomes are bistability or a monomorphic population of defectors or cooperators. Our results suggest, counterintuitively, that structured populations are not always beneficial for the evolution of cooperation for nonlinear group interactions.

Solving the collective-risk social dilemma with risky assets in well-mixed and structured populations

In the collective-risk social dilemma, players lose their personal endowments if contributions to the common pool are too small. This fact alone, however, does not always deter selfish individuals from defecting. The temptations to free ride on the prosocial efforts of others are strong because we are hardwired to maximize our own fitness regardless of the consequences which might have for the public good. Here we show that the addition of risky assets to the personal endowments, both of which are lost if the collective target is not reached, can contribute to solving the collective-risk social dilemma. In infinite well-mixed populations, risky assets introduce new stable and unstable mixed steady states, whereby the stable mixed steady state converges to full cooperation as either the risk of collective failure or the amount of risky assets increases. Similarly, in finite well-mixed populations, the introduction of risky assets enforces configurations where cooperative behavior thrives. In structured populations cooperation is promoted as well, but the distribution of assets among the groups is crucial. Surprisingly, we find that the completely rational allocation of assets only to the most successful groups is not optimal, and this regardless of whether the risk of collective failure is high or low. Instead, in low-risk situations bounded rational allocation of assets works best, while in high-risk situations the simplest uniform distribution of assets among all the groups is optimal. These results indicate that prosocial behavior depends sensitively on the potential losses individuals are likely to endure if they fail to cooperate.

Aspiration dynamics of multi-player games in finite populations

On studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer. In the latter case, individuals adjust their strategies based on a comparison of their pay-offs from the evolutionary game to a value they aspire, called the level of aspiration. Unlike imitation processes of pairwise comparison, aspiration-driven updates do not require additional information about the strategic environment and can thus be interpreted as being more spontaneous. Recent work has mainly focused on understanding how aspiration dynamics alter the evolutionary outcome in structured populations. However, the baseline case for understanding strategy selection is the well-mixed population case, which is still lacking sufficient understanding. We explore how aspiration-driven strategy-update dynamics under imperfect rationality influence the average abundance of a strategy in multi-player evolutionary games with two strategies. We analytically derive a condition under which a strategy is more abundant than the other in the weak selection limiting case. This approach has a long-standing history in evolutionary games and is mostly applied for its mathematical approachability. Hence, we also explore strong selection numerically, which shows that our weak selection condition is a robust predictor of the average abundance of a strategy. The condition turns out to differ from that of a wide class of imitation dynamics, as long as the game is not dyadic. Therefore, a strategy favoured under imitation dynamics can be disfavoured under aspiration dynamics. This does not require any population structure, and thus highlights the intrinsic difference between imitation and aspiration dynamics.

Extrapolating weak selection in evolutionary games

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By “qualitatively valid” we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies . In particular, rank changes are almost certain for , which jeopardizes the predictive power of results derived for weak selection.

In evolutionary game dynamics in finite populations, selection intensity plays a key role in determining the impact of the game on reproductive success. Weak selection is often employed to obtain analytical results in evolutionary game theory. We investigate the validity of weak selection predictions for stronger intensities of selection. We prove that in general qualitative results obtained under weak selection fail to extend even to moderate selection strengths for games with either more than two strategies or more than two players. In particular, we find that even in pairwise interactions qualitative changes with changing selection intensity arise almost certainly in the case of a large number of strategies.