Social Cooperation and Disharmony in Communities Mediated through Common Pool Resource Exploitation

The paradigm of tax-reward and tax-punishment strategies in the advancement of public resource management dynamics

In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system's path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.

Mine or Ours? Neural Basis of the Exploitation of Common-Pool Resources

Why do people often exhaust unregulated common (shared) natural resources but manage to preserve similar private resources? To answer this question, in this study we combine a neurobiological, economic and cognitive modeling approach. Using functional magnetic resonance imaging on 50 participants, we show that a sharp decrease of common and private resources is associated with deactivation of the ventral striatum, a brain region involved in the valuation of outcomes. Across individuals, when facing a common resource, ventral striatal activity is anticorrelated with resource preservation (less harvesting), whereas with private resources the opposite pattern is observed. This indicates that neural value signals distinctly modulate behavior in response to the depletion of common vs private resources. Computational modeling suggested that overharvesting of common resources was facilitated by the modulatory effect of social comparison on value signals. These results provide an explanation of people’s tendency to over-exploit unregulated common natural resources.

Adaptation strategies and collective dynamics of extraction in networked commons of bistable resources

When populations share common-pool resources (CPRs), individuals decide how much effort to invest towards resource extraction and how to allocate this effort among available resources. We investigate these dual aspects of individual choice in networked games where resources undergo regime shifts between discrete quality states (viable or depleted) depending on collective extraction levels. We study the patterns of extraction that emerge on various network types when agents are free to vary extraction from each CPR separately to maximize their short-term payoffs. Using these results as a basis for comparison, we then investigate how results are altered if agents fix one aspect of adaptation (magnitude or allocation) while letting the other vary. We consider two constrained adaptation strategies: uniform adaptation, whereby agents adjust their extraction levels from all CPRs by the same amount, and reallocation, whereby agents selectively shift effort from lower- to higher-quality resources. A preference for uniform adaptation increases collective wealth on degree-heterogeneous agent-resource networks. Further, low-degree agents retain preferences for these constrained strategies under reinforcement learning. Empirical studies have indicated that some CPR appropriators ignore—while others emphasize—allocation aspects of adaptation; our results demonstrate that structural patterns of resource access can determine which behavior is more advantageous.

A toy model for the epidemic-driven collapse in a system with limited economic resource

ABSTRACT

Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann-Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine.

GRAPHIC ABSTRACT

Myopic reallocation of extraction improves collective outcomes in networked common-pool resource games

When individuals extract benefits from multiple resources, the decision they face is twofold: besides choosing how much total effort to exert for extraction, they must also decide how to allocate this effort. We focus on the allocation aspect of this choice in an iterated game played on bipartite networks of agents and common-pool resources (CPRs) that degrade linearly in quality as extraction increases. When CPR users attempt to reallocate their extraction efforts among resources to maximize their own payoffs in the very next round (that is, myopically), collective wealth is increased. Using a heterogeneous mean-field approach, we estimate how these reallocations affect the payoffs of CPR users of different degrees within networks having different levels of degree heterogeneity. Focusing specifically on Nash equilibrium initial conditions, which represent the patterns of over-exploitation that result from rational extraction, we find that networks with greater heterogeneity among CPR degrees show greater improvements over equilibrium due to reallocation. When the marginal utility of extraction diminishes, these reallocations also reduce wealth inequality. These findings emphasize that CPR users' adaptive reallocations of effort-a behavior that previously-studied network evolutionary game models typically disallow by construction-can serve to direct individuals' self-interest toward the collective good.

Best response dynamics improve sustainability and equity outcomes in common-pool resources problems, compared to imitation dynamics

Shared resource extraction among profit-seeking individuals involves a tension between individual benefit and the collective well-being represented by the persistence of the resource. Many game theoretic models explore this scenario, but these models tend to assume either best response dynamics (where individuals instantly switch to better paying strategies) or imitation dynamics (where individuals copy successful strategies from neighbours), and do not systematically compare predictions under the two assumptions. Here we propose an iterated game on a social network with payoff functions that depend on the state of the resource. Agents harvest the resource, and the strategy composition of the population evolves until an equilibrium is reached. The system is then repeatedly perturbed and allowed to re-equilibrate. We compare model predictions under best response and imitation dynamics. Compared to imitation dynamics, best response dynamics increase sustainability of the system, the persistence of cooperation while decreasing inequality and debt corresponding to the Gini index in the agents' cumulative payoffs. Additionally, for best response dynamics, the number of strategy switches before equilibrium fits a power-law distribution under a subset of the parameter space, suggesting the system is in a state of self-organized criticality. We find little variation in most mean results over different network topologies; however, there is significant variation in the distributions of the raw data, equality of payoff, clustering of like strategies and power-law fit. We suggest the primary mechanisms driving the difference in sustainability between the two strategy update rules to be the clustering of like strategies as well as the time delay imposed by an imitation processes. Given the strikingly different outcomes for best response versus imitation dynamics for common-pool resource systems, our results suggest that modellers should choose strategy update rules that best represent decision-making in their study systems.

Homophily Based on Few Attributes Can Impede Structural Balance

Homophily between agents and structural balance in connected triads of agents are complementary mechanisms thought to shape social groups leading to, for instance, consensus or polarization. To capture both processes in a unified manner, we propose a model of pair and triadic interactions. We consider N fully connected agents, where each agent has G underlying attributes, and the similarity between agents in attribute space (i.e., homophily) is used to determine the link weight between them. For structural balance we use a triad-updating rule where only one attribute of one agent is changed intentionally in each update, but this also leads to accidental changes in link weights and even link polarities. The link weight dynamics in the limit of large G is described by a Fokker-Planck equation from which the conditions for a phase transition to a fully balanced state with all links positive can be obtained. This "paradise state" of global cooperation is, however, difficult to achieve requiring G>O(N^{2}) and p>0.5, where the parameter p captures a willingness for consensus. Allowing edge weights to be a consequence of attributes naturally captures homophily and reveals that many real-world social systems would have a subcritical number of attributes necessary to achieve structural balance.

Questionnaire data analysis using information geometry

The analysis of questionnaires often involves representing the high-dimensional responses in a low-dimensional space (e.g., PCA, MCA, or t-SNE). However questionnaire data often contains categorical variables and common statistical model assumptions rarely hold. Here we present a non-parametric approach based on Fisher Information which obtains a low-dimensional embedding of a statistical manifold (SM). The SM has deep connections with parametric statistical models and the theory of phase transitions in statistical physics. Firstly we simulate questionnaire responses based on a non-linear SM and validate our method compared to other methods. Secondly we apply our method to two empirical datasets containing largely categorical variables: an anthropological survey of rice farmers in Bali and a cohort study on health inequality in Amsterdam. Compare to previous analysis and known anthropological knowledge we conclude that our method best discriminates between different behaviours, paving the way to dimension reduction as effective as for continuous data.

Cooperation dynamics of generalized reciprocity in state-based social dilemmas

We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone." Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation, and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation by dictating the degree of cooperation displayed both at the microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.

Punishment and inspection for governing the commons in a feedback-evolving game

Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of the common state, punishing the latter group seems to be an adequate reaction. This conclusion, however, is less straightforward when we acknowledge the fact that resources are finite and even a renewable resource has limited growing capacity. To clarify the possible consequences, we consider a coevolutionary model where beside the payoff-driven competition of cooperator and defector players the level of a renewable resource depends sensitively on the fraction of cooperators and the total consumption of all players. The applied feedback-evolving game reveals that beside a delicately adjusted punishment it is also fundamental that cooperators should pay special attention to the growing capacity of renewable resources. Otherwise, even the usage of tough punishment cannot save the community from an undesired end.

Our proposed model considers not only the fundamental dilemma of individual and collective benefits but also focuses on their impacts on the environmental state. In general, there is a strong interdependence between individual actions and the actual shape of environment that can be described by means of a co-evolutionary model. Such approach recognizes the fact that even if our common-pool resources are partly renewable, they have limited growth capacities hence a depleted environment is unable to recover and reach a sustainable level again. This scenario would have a dramatic consequence on our whole society, therefore we should avoid it by punishing those who are not exercising restrain. We provide analytical and numerical evidences which highlight that punishment alone may not necessarily be a powerful tool to maintain a healthy shape of environment for the benefit of future generations. Cooperator actors, who are believed to take care of present state of our environment, should also consider carefully the growth capacity of renewable resources.