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

A new electoral bottom-up model of institutional governance

The sustainable governance of Global Risky Commons (GRC)-global commons in the presence of a sizable risk of overall failure-is ubiquitous and requires a global solution. A prominent example is the mitigation of the adverse effects of global warming. In this context, the Collective Risk Dilemma (CRD) provides a convenient baseline model which captures many important features associated with GRC type problems by formulating them as problems of cooperation. Here we make use of the CRD to develop, for the first time, a bottom-up institutional governance framework of GRC. We find that the endogenous creation of local institutions that require a minimum consensus amongst group members-who, in turn, decide the nature of the institution (reward/punishment) via an electoral process-leads to higher overall cooperation than previously proposed designs, especially at low risk, proving that carrots and sticks implemented through local voting processes are more powerful than other designs. The stochastic evolutionary game theoretical model framework developed here further allows us to directly compare our results with those stemming from previous models of institutional governance. The model and the methods employed here are relevant and general enough to be applied to a variety of contemporary interdisciplinary problems.

Co-evolution of risk and cooperation in climate policies under wealth inequality

Worldwide cooperation is necessary to mitigate the effects of climate change. Many previous investigations employed the so-called collective risk dilemma, where the risk of losing everything whenever a target is not met was fixed from the outset, rendering predictions dependent on snapshot values assumed for this parameter, whose importance was found to be paramount. Here, we couple risk with the overall success of mitigation, investigating the co-evolution of risk and cooperation in a world where countries are partitioned in two different wealth classes, allowing us to further assess the impact of wealth inequality and homophily on the co-evolutionary dynamics. We show that the stochastic dynamics is dominated by a global attractor, typically located in a region of low risk, where most developed countries cooperate most of the time while developing countries cooperate to a lesser extent. This scenario assumes no homophily which, when moderate, can contribute to increase overall cooperation, more so when combined with the presence of a small fraction of developing countries that opt for an unconditional cooperative behavior.

Evolution of conditional cooperation in collective-risk social dilemma with repeated group interactions

The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world, individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviours affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.

Combination of institutional incentives for cooperative governance of risky commons

Finding appropriate incentives to enforce collaborative efforts for governing the commons in risky situations is a long-lasting challenge. Previous works have demonstrated that both punishing free-riders and rewarding cooperators could be potential tools to reach this goal. Despite weak theoretical foundations, policy makers frequently impose a punishment-reward combination. Here, we consider the emergence of positive and negative incentives and analyze their simultaneous impact on sustaining risky commons. Importantly, we consider institutions with fixed and flexible incentives. We find that a local sanctioning scheme with pure reward is the optimal incentive strategy. It can drive the entire population toward a highly cooperative state in a broad range of parameters, independently of the type of institutions. We show that our finding is also valid for flexible incentives in the global sanctioning scheme, although the local arrangement works more effectively.

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Pure reward in a local scheme is more effective both for fixed and flexible incentives

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It can drive the entire population toward a highly cooperative state

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Increasing the efficiency of the institution can induce the success of pure reward

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A local scheme promotes group success more effectively than a global scheme

Timing Uncertainty in Collective Risk Dilemmas Encourages Group Reciprocation and Polarization

Social dilemmas are often shaped by actions involving uncertain returns only achievable in the future, such as climate action or voluntary vaccination. In this context, uncertainty may produce non-trivial effects. Here, we assess experimentally — through a collective risk dilemma — the effect of timing uncertainty, i.e. how uncertainty about when a target needs to be reached affects the participants' behaviors. We show that timing uncertainty prompts not only early generosity but also polarized outcomes, where participants' total contributions are distributed unevenly. Furthermore, analyzing participants' behavior under timing uncertainty reveals an increase in reciprocal strategies. A data-driven game-theoretical model captures the self-organizing dynamics underpinning these behavioral patterns. Timing uncertainty thus casts a shadow on the future that leads participants to respond early, whereas reciprocal strategies appear to be important for group success. Yet, the same uncertainty also leads to inequity and polarization, requiring the inclusion of new incentives handling these societal issues.

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Timing uncertainty influences experimental observations in the collective risk game

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It induces subjects to contribute earlier and in a polarized manner

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Successful players adopt reciprocal strategies, responding in kind to past actions

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Coordination gets more difficult under high timing uncertainty

Behavioural patterns behind the demise of the commons across different cultures

Common-pool resources require a dose of self-restraint to ensure sustainable exploitation, but this has often proven elusive in practice. To understand why, and characterize behaviours towards ecological systems in general, we devised a social dilemma experiment in which participants gain profit from harvesting a virtual forest vulnerable to overexploitation. Out of 16 Chinese and 15 Spanish player groups, only one group from each country converged to the forest's maximum sustainable yield. All other groups were overzealous, with about half of them surpassing or on the way to surpass a no-recovery threshold. Computational-statistical analyses attribute such outcomes to an interplay between three prominent player behaviours, two of which are subject to decision-making 'inertia' that causes near blindness to the resource state. These behaviours, being equally pervasive among players from both nations, imply that the commons fall victim to behavioural patterns robust to confounding factors such as age, education and culture.

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.

Strategy intervention for the evolution of fairness

The 'irrational' preference for fairness has attracted increasing attention. Although previous studies have focused on the effects of spitefulness on the evolution of fairness, they did not consider non-monotonic rejections shown in behavioral experiments. In this paper, we introduce a non-monotonic rejection in an evolutionary model of the Ultimatum Game. We propose strategy intervention to study the evolution of fairness in general structured populations. By sequentially adding five strategies into the competition between a fair strategy and a selfish strategy, we arrive at the following conclusions. First, the evolution of fairness is inhibited by altruism, but it is promoted by spitefulness. Second, the non-monotonic rejection helps fairness overcome selfishness. Particularly for group-structured populations, we analytically investigate how fairness, selfishness, altruism, and spitefulness are affected by population size, mutation, and migration in the competition among seven strategies. Our results may provide important insights into understanding the evolutionary origin of fairness.

Risk-aware multi-armed bandit problem with application to portfolio selection

Sequential portfolio selection has attracted increasing interest in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision-making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk awareness into the classic multi-armed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of the financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.

The promotion of cooperation by the poor in dynamic chicken games

The evolution of cooperative behavior is one of the most important issues in game theory. Previous studies have shown that cooperation can evolve only under highly limited conditions, and various modifications have been introduced to games to explain the evolution of cooperation. Recently, a utility function basic to game theory was shown to be dependent on current wealth as a conditional (state) variable in a dynamic version of utility theory. Here, we introduce this dynamic utility function to several games. Under certain conditions, poor players exhibit cooperative behavior in two types of chicken games (the hawk-dove game and the snowdrift game) but not in the prisoner’s dilemma game and the stag hunt game. This result indicates that cooperation can be exhibited by the poor in some chicken games. Thus, the evolution of cooperation may not be as limited as has been suggested in previous studies.

Impact of migration on the multi-strategy selection in finite group-structured populations

For large quantities of spatial models, the multi-strategy selection under weak selection is the sum of two competition terms: the pairwise competition and the competition of multiple strategies with equal frequency. Two parameters σ₁ and σ₂ quantify the dependence of the multi-strategy selection on these two terms, respectively. Unlike previous studies, we here do not require large populations for calculating σ₁ and σ₂, and perform the first quantitative analysis of the effect of migration on them in group-structured populations of any finite sizes. The Moran and the Wright-Fisher process have the following common findings. Compared with well-mixed populations, migration causes σ₁ to change with the mutation probability from a decreasing curve to an inverted U-shaped curve and maintains the increase of σ₂. Migration (probability and range) leads to a significant change of σ₁ but a negligible one of σ₂. The way that migration changes σ₁ is qualitatively similar to its influence on the single parameter characterizing the two-strategy selection. The Moran process is more effective in increasing σ₁ for most migration probabilities and the Wright-Fisher process is always more effective in increasing σ₂. Finally, our findings are used to study the evolution of cooperation under direct reciprocity.

The evolution of optimal resource allocation and mating systems in hermaphroditic perennial plants

By incorporating the effects of inbreeding depression (ID) on both juveniles and adults survivorship, we developed a new theoretical model for hermaphroditic perennial plants. Our model showed that the effect of the selfing rate on the evolutionarily stable strategy (ESS) reproductive allocation depends on three parameters: (1) the self-fertilized juvenile relative survivorship (SFJRS), (2) the self-fertilized adult relative survivorship (SFARS) and (3) the growth rate of self-fertilized adult, where the SFJRS is the survivorship of self-fertilized juveniles divided by the survivorship of outcrossed juveniles, and likewise for the SFARS. However, the ESS sex allocation decreases as the selfing rate increases. This relationship seems independent of the SFJRS, the SFARS, and the growth rate of self-fertilized adults. Additionally, our model showed that the complete outcrossing is an ESS when the fraction of juvenile inbreeding depression (FJID) is less than 1/2 − τ, where τ is the self-fertilized adults mortality rate caused by ID. In contrast, the complete selfing also acts as an ESS when the FJID is greater than 1/2 − τ. These results could explain the diversity of mating strategies and related resource allocations for plants.