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Complex adaptive networks exhibit remarkable resilience, driven by the dynamic interplay of structure (interactions) and function (state). While static-network analyses offer valuable insights, understanding how structure and function co-evolve under external interventions is critical for explaining system-level adaptation. Using a unique dataset of clandestine criminal networks, we combine empirical observations with computational modeling to test the impact of various interventions on network adaptation. Our analysis examines how networks with specialized roles adapt and form emergent structures to optimize cost-benefit trade-offs. We find that emergent sparsely connected networks exhibit greater resilience, revealing a security-efficiency trade-off. Notably, interventions can trigger a "criminal opacity amplification" effect, where criminal activity increases despite reduced network visibility. While node isolation fragments networks, it strengthens remaining active ties. In contrast, deactivating nodes (analogous to social reintegration) can unintentionally boost criminal coordination, increasing activity or connectivity. Failed interventions often lead to temporary functional surges before reverting to baseline. Surprisingly, stimulating connectivity destabilizes networks. Effective interventions require precise calibration to node roles, connection types, and external conditions. These findings challenge conventional assumptions about connectivity and intervention efficacy in complex adaptive systems across diverse domains.

The world is currently grappling with challenges on both local and global scales, many of which demand coordinated behavioral changes. However, breaking away from the status is often difficult due to deeply ingrained social norms. In such cases, social systems may require seemingly exogenous interventions to set off endogenous, largely irreversible processes that drive change -- social tipping. While studies have looked at targeted interventions, real-life constraints faced by policymakers, like minimizing costs while ensuring a quick and fair transition, remain understudied. To address this complexity, we introduce a game-theoretic framework that accounts for individual heterogeneity and networks of local influence. We implement various heuristics based on information about individual preferences and commonly used local network properties. Results show that where the change is initiated in the population and the direction in which it propagates is essential to the effectiveness of interventions. We identify optimal strategies under different scenarios, such as varying levels of resistance to change, preference heterogeneity, and homophily. These results provide insights that can be experimentally tested and help policymakers to better direct incentives.

A common assumption in the literature on information diffusion is that populations are homogeneous regarding individuals' information acquisition and propagation process: Individuals update their informed and actively communicating state either through imitation (simple contagion) or peer influence (complex contagion). Here, we study the impact of the mixing and placement of individuals with different update processes on how information cascades in social networks. We consider Simple Spreaders, which take information from a random neighbor and communicate it, and Threshold-based Spreaders, which require a threshold number of active neighbors to change their state to active communication. Even though, in a population made exclusively of Simple Spreaders, information reaches all elements of any (connected) network, we show that, when Simple and Threshold-based Spreaders coexist and occupy random positions in a social network, the number of Simple Spreaders systematically amplifies the cascades only in degree heterogeneous networks (exponential and scale-free). In random and modular structures, this cascading effect originated by Simple Spreaders only exists above a critical mass of these individuals. In contrast, when Threshold-based Spreaders are assorted preferentially in the nodes with a higher degree, the cascading effect of Simple Spreaders vanishes, and the spread of information is drastically impaired. Overall, the study highlights the significance of the strategic placement of different roles in networked structures, with Simple Spreaders driving widespread cascades in heterogeneous networks and Threshold-based Spreaders playing a critical regulatory role in information spread with a tunable effect based on the threshold value., Comment: 12 pages, 5 figures

The interplay between criminal organizations and law enforcement disruption strategies is crucial in criminology. Criminal enterprises, like legitimate businesses, balance visibility and security to thrive. This study uses evolutionary game theory to analyze criminal networks' dynamics, resilience to interventions, and responses to external conditions. We find strong hysteresis effects, challenging traditional deterrence-focused strategies. Optimal thresholds for organization formation or dissolution are defined by these effects. Stricter punishment doesn't always deter organized crime linearly. Network structure, particularly link density and skill assortativity, significantly influences organization formation and stability. These insights advocate for adaptive policy-making and strategic law enforcement to effectively disrupt criminal networks.

Policymaking for complex challenges such as pandemics necessitates the consideration of intricate implications across multiple domains and scales. Computational models can support policymaking, but a single model is often insufficient for such multidomain and scale challenges. Multi-models comprising several interacting computational models at different scales or relying on different modeling paradigms offer a potential solution. Such multi-models can be assembled from existing computational models (i.e., integrated modeling) or be designed conceptually as a whole before their computational implementation (i.e., integral modeling). Integral modeling is particularly valuable for novel policy problems, such as those faced in the early stages of a pandemic, where relevant models may be unavailable or lack standard documentation. Designing such multi-models through an integral approach is, however, a complex task requiring the collaboration of modelers and experts from various domains. In this collaborative effort, modelers must precisely define the domain knowledge needed from experts and establish a systematic procedure for translating such knowledge into a multi-model. Yet, these requirements and systematic procedures are currently lacking for multi-models that are both multiscale and multi-paradigm. We address this challenge by introducing a procedure for developing multi-models with an integral approach based on clearly defined domain knowledge requirements derived from literature. We illustrate this procedure using the case of school closure policies in the Netherlands during the COVID-19 pandemic, revealing their potential implications in the short and long term and across the healthcare and educational domains. The requirements and procedure provided in this article advance the application of integral multi-modeling for policy support in multiscale and multidomain contexts.

Recently, social debates have been marked by increased polarization of social groups. Such polarization not only implies that groups cannot reach a consensus on fundamental questions but also materializes in more modular social spaces/networks that further amplify the risks of polarization in less polarizing topics. How can network adaptation bridge different communities when individuals reveal homophilic or heterophilic social rewiring preferences? Here, we consider information diffusion processes that capture a continuum from simple to complex contagion processes. We use a computational model to understand how fast and to what extent individual rewiring preferences bridge initially weakly connected communities and how likely it is for them to reach a consensus. We show that homophilic and heterophilic rewiring have different impacts depending on the type of opinion spread. First, in the case of complex opinion diffusion, we show that even polarized social networks can reach a population-wide consensus without reshaping their underlying network. When polarized social structures amplify opinion polarization, heterophilic rewiring preferences play a key role in creating bridges between communities and facilitating a population-wide consensus. Secondly, in the case of simple opinion diffusion, homophilic rewiring preferences are more capable of fostering consensus and avoiding a co-existence (dynamical polarization) of opinions. Hence, across a broad profile of simple and complex opinion diffusion processes, only a mix of heterophilic and homophilic rewiring preferences avoids polarization and promotes consensus., Comment: 10 pages. 4 figures

Complex adaptive systems (CASs), from ecosystems to economies, are open systems and inherently dependent on external conditions. While a system can transition from one state to another based on the magnitude of change in external conditions, the rate of change -- irrespective of magnitude -- may also lead to system state changes due to a phenomenon known as a rate-induced transition (RIT). This study presents a novel framework that captures RITs in CASs through a local model and a network extension where each node contributes to the structural adaptability of others. Our findings reveal how RITs occur at a critical environmental change rate, with lower-degree nodes tipping first due to fewer connections and reduced adaptive capacity. High-degree nodes tip later as their adaptability sources (lower-degree nodes) collapse. This pattern persists across various network structures. Our study calls for an extended perspective when managing CASs, emphasizing the need to focus not only on thresholds of external conditions but also the rate at which those conditions change, particularly in the context of the collapse of surrounding systems that contribute to the focal system's resilience. Our analytical method opens a path to designing management policies that mitigate RIT impacts and enhance resilience in ecological, social, and socioecological systems. These policies could include controlling environmental change rates, fostering system adaptability, implementing adaptive management strategies, and building capacity and knowledge exchange. Our study contributes to the understanding of RIT dynamics and informs effective management strategies for complex adaptive systems in the face of rapid environmental change., Comment: 25 pages, 4 figures, 1 box, supplementary information

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives respectively for a structured population of individuals whose conflicting interactions are characterized by a prisoner's dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world, and scale-free networks.

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 towards 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.

Global change is reshaping ecosystems and societies. Strategic choices that were best yesterday may be sub-optimal tomorrow; and environmental conditions that were once taken for granted may soon cease to exist. In this setting, how people choose behavioral strategies has important consequences for environmental dynamics. Economic and evolutionary theories make similar predictions for strategic behavior in a static environment, even though one approach assumes perfect rationality and the other assumes no cognition whatsoever; but predictions differ in a dynamic environment. Here we explore a middle ground between economic rationality and evolutionary myopia. Starting from a population of myopic agents, we study the emergence of a new type that forms environmental forecasts when making strategic decisions. We show that forecasting types can have an advantage in changing environments, even when the act of forecasting is costly. Forecasting types can invade but not overtake the population, producing a stable coexistence with myopic types. Moreover, forecasters provide a public good by reducing the amplitude of environmental oscillations and increasing mean payoff to forecasting and myopic types alike. We interpret our results for understanding the evolution of different modes of decision-making. And we discuss implications for the management of environmental systems of great societal importance., Comment: revised ms; results unchanged

Recent attempts at cooperating on climate change mitigation highlight the limited efficacy of large-scale agreements, when commitment to mitigation is costly and initially rare. Bottom-up approaches using region-specific mitigation agreements promise greater success, at the cost of slowing global adoption. Here, we show that a well-timed switch from regional to global negotiations dramatically accelerates climate mitigation compared to using only local, only global, or both agreement types simultaneously. This highlights the scale-specific roles of mitigation incentives: local incentives capitalize on regional differences (e.g., where recent disasters incentivize mitigation) by committing early-adopting regions, after which global agreements draw in late-adopting regions. We conclude that global agreements are key to overcoming the expenses of mitigation and economic rivalry among regions but should be attempted once regional agreements are common. Gradually up-scaling efforts could likewise accelerate mitigation at smaller scales, for instance when costly ecosystem restoration initially faces limited public and legislative support.

While the benefits of common and public goods are shared, they tend to be scarce when contributions are provided voluntarily. Failure to cooperate in the provision or preservation of these goods is fundamental to sustainability challenges, ranging from local fisheries to global climate change. In the real world, such cooperative dilemmas occur in multiple interactions with complex strategic interests and frequently without full information. We argue that voluntary cooperation enabled across multiple coalitions (akin to polycentricity) not only facilitates greater generation of non-excludable public goods, but may also allow evolution toward a more cooperative, stable, and inclusive approach to governance. Contrary to any previous study, we show that these merits of multi-coalition governance are far more general than the singular examples occurring in the literature, and are robust under diverse conditions of excludability, congestability of the non-excludable public good, and arbitrary shapes of the return-to-contribution function. We first confirm the intuition that a single coalition without enforcement and with players pursuing their self-interest without knowledge of returns to contribution is prone to cooperative failure. Next, we demonstrate that the same pessimistic model but with a multi-coalition structure of governance experiences relatively higher cooperation by enabling recognition of marginal gains of cooperation in the game at stake. In the absence of enforcement, public-goods regimes that evolve through a proliferation of voluntary cooperative forums can maintain and increase cooperation more successfully than singular, inclusive regimes., Comment: 16 pages (2 figures) plus supplementary material (1 figure)

The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the diffusion of human behaviours, innovations, and knowledge. Based on that evidence, we propose a model that considers multiple, potentially asymmetric, and competing contagion processes and analyse its respective population-wide dynamics, bringing together ideas from complex contagion, opinion dynamics, evolutionary game theory, and language competition by shifting the focus from individuals to the properties of the diffusing processes. We show that our model spans a dynamical space in which the population exhibits patterns of consensus, dominance, and, importantly, different types of polarisation, a more diverse dynamical environment that contrasts with single simple contagion processes. We show how these patterns emerge and how different population structures modify them through a natural development of spatial correlations: structured interactions increase the range of the dominance regime by reducing that of dynamic polarisation, tight modular structures can generate structural polarisation, depending on the interplay between fundamental properties of the processes and the modularity of the interaction network., Comment: 18 Pages, 5 Figures

How individuals adapt their behavior in cultural evolution remains elusive. Theoretical studies have shown that the update rules chosen to model individual decision making can dramatically modify the evolutionary outcome of the population as a whole. This hints at the complexities of considering the personality of individuals in a population, where each one uses its own rule. Here, we investigate whether and how heterogeneity in the rules of behavior update alters the evolutionary outcome. We assume that individuals update behaviors by aspiration-based self-evaluation and they do so in their own ways. Under weak selection, we analytically reveal a simple property that holds for any two-strategy multi-player games in well-mixed populations and on regular graphs: the evolutionary outcome in a population with heterogeneous update rules is the weighted average of the outcomes in the corresponding homogeneous populations, and the associated weights are the frequencies of each update rule in the heterogeneous population. Beyond weak selection, we show that this property holds for public goods games. Our finding implies that heterogeneous aspiration dynamics is additive. This additivity greatly reduces the complexity induced by the underlying individual heterogeneity. Our work thus provides an efficient method to calculate evolutionary outcomes under heterogeneous update rules.