Agricultural landscapes are quintessential socio-ecological systems, places where social and environmental factors co-exist and interact in inherently complex ways. When modellers try to reproduce these systems, farmers’ behaviour is of paramount importance. Crop choice, the application of certain agricultural practices and the adoption of innovations are actions that ripple through the economy, social sustainability and environmental sustainability of an agricultural landscape. Agent-based models, computational representations that focus on the atomistic parts of a system and describe their behaviour and interactions in a bottom-up approach, have become the tool of choice for capturing these dynamics. Yet while models involving farmers’ behaviour are now quite numerous, relatively few studies explicitly account for social interactions. GeSoN was designed precisely to fill this gap, recreating the farmers’ social context relevant to their decision-making process.

The theoretical heart of the model is the bounded rationality framework, first articulated by Herbert Simon. Bounded rationality states that, when making decisions, humans do not set out complex optimisation procedures; instead, they mediate between constraints regarding time, knowledge and cognitive abilities. Four distinct facets of human decision-making must be considered: humans encounter difficulties in evaluating and planning long behavioural sequences given their limited cognitive capacity and the inherent complexity of their environment; people tend to set aspirational levels related to specific goals; they work on goals sequentially rather than simultaneously; and their search strategy is aimed at satisfaction rather than optimisation. A vital aspect of the framework is ecological rationality, the insight that decisions are strongly influenced by the environment, both physical and social, relevant to agents’ goals and needs. This stands in deliberate contrast to the Expected Utility Theory, whose assumptions of selfishness, stable transitive preferences and unlimited cognitive capacity have been refuted by numerous empirical studies in different domains.

To model the interaction amongst farmers, the researchers turned to opinion dynamics, a branch of social network analysis that studies the evolution of individuals’ views as the result of interactions within a network. The approach assumes people influence each other, describes the interaction process from an individual point of view and produces results emergent from those interactions, pooled for the population. GeSoN belongs to the family of models in which opinions are continuous variables, usually ranging between 0 and 1, following the seminal work of Deffuant and colleagues and of Hegselmann and Krause. The major constraint applied is bounded confidence: influence during an interaction occurs only when a specific condition regarding the similarity between opinions is met. The underlying assumption is that opposite opinions have little or no influence on each other, a principle grounded in the observation that people with similar attitudes are more likely to interact and that there is a lack of understanding between persons with substantially different views.

What sets GeSoN apart is its multi-layer network structure, built on the concept of geographical specificity. The model generates connections between farmers using different criteria, forming a multi-criteria web of channels through which farmers interact. The first and major component is the Geographical Network, which represents the influence over the landscape of so-called nodal farmers, those that create the highest number of connections with others and hence significantly influence the agricultural landscape. This network uses a modified gravity model, an empirical economic model originally inspired by Newton’s law of gravitation and primarily applied to international trade studies. The two main assumptions are that closer farmers are more likely to interact and that larger farms, in terms of farm size, have more influence over their neighbours than smaller ones. The strength of the link connecting Farmer i with Farmer j is computed as the size of Farmer j divided by the physical distance between the two farms. After computing the force connecting them, all farmers hold a ranked list of the other farmers in the landscape, ordered by that force, and choose a predetermined number of neighbours from the top of the list when interactions take place.

Two further layers complete the structure. The Associative network simulates the presence, in a landscape, of groups of cooperating farmers, such as members of the same cooperative, a producer organisation or similar farmers in terms of agricultural production. This layer matters because farmers are strongly affected in their decision-making by being part of such groups. The Virtual network captures the non-agricultural connections between farmers, like friendship or parenthood, incorporating a determined level of stochasticity into the structure. Both of these layers are exogenous and predetermined at the beginning of a simulation. Together, the three layers evolve beyond the purely mathematical random connection rules of the seminal Watts-Strogatz and French-DeGroot models, forming a genuine socio-economical network in which economic and social criteria shape agents’ connections.

Once the links are formed, opinions travel through them. In GeSoN, opinions such as risk aversion and sustainability concerns are modelled as continuous variables ranging from 0 to 1, with 1 excluded. Crucially, every farmer carries not only a personal opinion but also a level of uncertainty, modelled as a continuous variable ranging from 0 to 0.6, with the farmer’s opinion sitting at the uncertainty’s central point. The minimum distance required to enable the influence of one opinion over another is represented by the uncertainty associated with the influenced agent’s opinion. The magnitude of influence is controlled by a mobility parameter, fixed for all agents and set at the beginning of the simulation. The governing formula is a weighted mean of the influenced farmer’s opinion and the central part of the influencing farmer’s shared opinion, with weights given by the mobility parameter and its inverse, both scaled by a factor indicating the difference in the farmers’ uncertainties. This factor makes the influence between farmers with unequal uncertainties asymmetrical: when two farmers with high and low uncertainty respectively interact, the effect is stronger on the farmer with high uncertainty. Time is discrete, and farmers upload their opinions only after every other farmer has interacted with their respective neighbours, ensuring that the starting order of farmers makes no difference to the results.

The researchers demonstrated the model’s behavioural capabilities with a prototype implementation in Python, running simulations over both real and simulated landscapes. In a scenario based on the real Danish landscape of Himmerland, with 190 farmers whose locations and sizes were extracted from the EU’s Land Parcel Identification System database, initial opinions drawn from a uniform distribution evolved over 100 time steps into a double peak distribution, with the more prominent peak slowly forming from around the sixtieth time step. In a striking comparison, two simulations with identical input values but different network structures produced substantially different results: applying all three networks showed polarisation of opinions around two values, roughly 0.3 and 0.7, while applying just the Geographical Network showed consensus around the mean opinion value of about 0.5. This indicates that a single simple network would give erroneous results if the other networks were active in the real world. A second experiment on a simulated landscape of 214 farmers revealed further emergent behaviour, with two peaks forming rapidly and the larger peak drifting towards higher values, driven by the peculiar initial spatial configuration in which clusters of small farms remained uninfluential and uninfluenced.

The model’s peculiarity lies in the conjunction of bounded confidence opinion dynamics with the bounded rationality behavioural framework and geographical specificity, together with a multifactorial asymmetrical interaction function unique to this model. In the seminal Deffuant-Weisbuch model, by contrast, the formula governing the interaction is symmetrical and uncertainty is not taken directly into consideration. The asymmetrical function has a double consequence: farmer interactions are independent, so exchanges are not guaranteed to be mutual, and the influence one farmer has on another may differ in magnitude. This allows for the formation of different roles during a simulation, with farmers holding the most connections and low uncertainty playing the role of leaders or nodal farmers. The prototype results, characterised by consensus, polarisation and fragmentation, display non-linearities indicating the emergence of interesting, complex dynamics.

GeSoN has clear limitations at this stage of development. Farmers are the only type of agent represented, although agricultural advisors, food processing industries and institutions may mediate interactions in real scenarios and are planned for future developments. Farmers’ emotions were intentionally left outside the system boundaries, as were the agricultural land market and other sources of influence such as economic and environmental shocks. The continuous representation of opinions also ignores the intricacies related to one’s personal views. Nonetheless, the model presents flexibility and adaptability to be incorporated into more complex simulation systems, and the team plans to integrate it as a module of the ALMaSS agent-based modelling platform, where farmers’ decision-making is handled through the CONSUMAT conceptual framework. The practical payoff could be considerable: ex-ante policy analysis could benefit from the model in predicting farmers’ responses to specific measures, and predicting the adoption rate of voluntary enrolment measures in the EU agricultural policy framework could lead to higher efficiency and effectiveness, avoiding sub-optimal budget allocation when adoption cannot be precisely foreseen. As the model matures within richer simulations, the different configurations of inputs, diverse populations of farmers and varied agricultural landscapes are expected to generate complex emergent properties that can inform the real world.

Subject of Research: Socio-ecological simulation

Article Title: GeSoN: A Geo-Social Network model applying bounded rationality to farmers in socio-ecological simulations

Article References: Paparella, A., Cembalo, L., & Topping, C. (2023). GeSoN: A Geo-Social Network model applying bounded rationality to farmers in socio-ecological simulations. Food and Ecological Systems Modelling Journal, 4, Article e100714. https://doi.org/10.3897/fmj.4.100714

Image Credits: AI Generated

DOI: 10.3897/fmj.4.100714

Keywords: agent-based modelling, bounded rationality, opinion dynamics, socio-ecological systems, agricultural networks, farmer behaviour, gravity model, bounded confidence, GeSoN, Geo-Social, Network, model

The editorial behind the collection, authored by Chengyi Tu of Zhejiang Sci-Tech University and Hongzhong Deng of the National University of Defense Technology, was curated to advance our comprehension of how emergent phenomena are born from strategic interactions. Crucially, the editors sought to move beyond the conventional assumption of complete rationality that has long dominated classical game theory. Instead, they encouraged models that reflect the nuanced realities of limited information, bounded rationality, and dynamic network structures. The resulting compilation of five articles offers a diverse yet cohesive exploration of these themes, and the underlying mathematical principles reveal a common truth: complex systems are driven by the continuous interplay of strategic adaptation and structural constraints.

The contributions can be grouped into three thematic areas: the evolutionary foundations of cooperation, the dynamics of social and organizational adaptation, and strategic optimization in competitive environments. Each area tackles the same fundamental question from a different angle—how do macroscopic patterns emerge from microscopic behaviors when agents interact strategically? The answer, it turns out, involves network reciprocity, threshold effects, memory dynamics, and diversity, concepts that recur across biology, sociology, and economics with remarkable consistency.

In the first thematic area, Nicholas MacLaren and colleagues provide a foundational perspective by investigating the Social Brain Hypothesis through the lens of evolutionary game theory. In their article, Cooperation and the social brain hypothesis in primate social networks, the authors combine data on primate brain size with theoretical models of cooperation on networks. They utilize a gift-giving game framework to demonstrate that species with larger brain sizes tend to form social network structures that more effectively foster cooperation. This work highlights the critical role of network reciprocity in the evolution of social complexity, offering empirical support for the idea that cognitive capacity and social structure co-evolve to solve collective action problems. The finding suggests that the evolution of large brains in primates was not merely about individual intelligence but about the ability to navigate social networks in ways that sustain cooperation.

Moving from biological to human social systems, two articles employ dynamical modeling to understand adaptation and policy impact. In the first, Cao and colleagues construct a tripartite evolutionary game model involving government bodies, pharmaceutical enterprises, and research institutions to examine how policy tool combinations drive the construction of public health technology R&D alliances. Their analysis of supply-side, demand-side, and environmental policy tools reveals that demand-side government procurement is the most effective incentive for fostering alliances. Crucially, they identify non-linear threshold effects, showing that excessive intervention can paradoxically reduce participation—a classic complex system phenomenon where more is not always better. This finding has profound implications for policymakers who might assume that increasing subsidies or regulations will always increase collaboration.

In the second article on social adaptation, Hailu and colleagues apply advanced mathematical control theory to organizational psychology. By modeling employees as indifferent, resistant, or adaptive to reform initiatives in public service organizations, they use fractional order derivatives to capture the memory effects and dynamics of opinion change. Their application of optimal control theory suggests that targeted training and clear communication are the most effective strategies to minimize resistance, providing a rigorous quantitative basis for change management. The use of fractional calculus is particularly noteworthy because it allows the model to incorporate historical dependencies—how past experiences shape current attitudes—which is essential for understanding how organizational culture evolves over time.

The final two articles explore optimization and performance in competitive physical and virtual arenas. Gullholm and colleagues offer a fascinating intersection of sports analytics and game theory in their study of fantasy football dream teams under budget constraints. By analyzing dream teams in Fantasy Premier League under various constraints, they find that top-performing teams exhibit a high degree of diversity across multiple variables—a feature not found in randomly assembled teams. This finding suggests a game theoretic advantage to diversity, paralleling biological principles where diversity enhances system robustness and evolutionary fitness. The implication is that diversity is not merely a social virtue but a strategic advantage in competitive environments.

In the realm of physical performance, Marcojos and colleagues contribute a study on modified training drills in improving the dribbling agility of futsal athletes. While more empirical in nature, this study addresses the complex physical systems aspect of the Research Topic. It demonstrates how specific, modified interventions can optimize the adaptive capacity of agents operating in highly dynamic environments. The study is a reminder that the principles of strategic adaptation apply not only to cognitive and social systems but also to the physical systems that underpin human performance.

Together, these five articles illustrate the immense versatility of game theory and evolutionary dynamics as analytical lenses. Whether explaining the roots of primate cooperation, optimizing public health alliances, managing organizational resistance, or assembling competitive sports teams, the underlying mathematical principles reveal a common truth: complex systems are driven by the continuous interplay of strategic adaptation and structural constraints. The editors hope this collection inspires further interdisciplinary research that bridges the gap between theoretical models and real-world complexities, and the breadth of the contributions suggests that this bridge is already being crossed in ways that could reshape how we understand everything from the evolution of the social brain to the design of effective public policy.

Subject of Research: Game theory and evolutionary dynamics in complex systems

Article Title: Editorial: Game theory and evolutionary dynamics: unraveling complex systems

Article References: Tu, C., & Deng, H. (2026). Editorial: Game theory and evolutionary dynamics: unraveling complex systems. Frontiers in Complex Systems, 4, Article 1794474. https://doi.org/10.3389/fcpxs.2026.1794474

Image Credits: AI Generated

DOI: 10.3389/fcpxs.2026.1794474

Keywords: game theory, evolutionary dynamics, complex systems, cooperation, network reciprocity, bounded rationality, public health policy, organizational change, sports analytics, Frontiers in Complex Systems, Editorial, Game

The research team, led by Wa Ode Dian Purnamasari of the University of Muhammadiyah Buton and colleagues at the University of Muhammadiyah Malang, spent September through December 2024 embedded in the coconut economy of seven producing districts. Their sample was substantial: 489 copra processors, 182 coconut shell charcoal producers, marketing intermediaries, and a panel of ten institutional experts drawn from government agencies, extension services, academia, and farmer organizations. Statistical power analysis confirmed the sample far exceeded the minimum of 146 respondents needed for a medium effect size. Crucially, the study observed naturally occurring market behavior rather than staging artificial experiments, giving the results an ecological validity that laboratory studies of economic decision-making often lack.

The economics alone are striking. Using the Hayami value-added framework, the team calculated that turning coconut shell waste, a by-product most producers simply discarded, into charcoal generated an average value of IDR 1,002.52 per kilogram of raw material, with a value-added ratio of 54.87 percent. In plain terms, more than half of the charcoal’s final worth came from the processing itself rather than from the underlying raw material. Profit rates averaged a remarkable 98.06 percent, though the researchers note that nearly all of this value accumulated as entrepreneurial profit rather than wages: labor compensation amounted to just IDR 19.39 per kilogram, or under two percent of the value added.

The conversion efficiency tells its own story. Each kilogram of coconut shell yielded roughly 0.31 kilograms of charcoal on average, while the labor coefficient of 0.0019 workdays per kilogram shows the process depends more on operational efficiency than on muscle power. Charcoal sold at IDR 6,000 per kilogram across all three districts studied, Lasalimu, South Lasalimu, and Kapontori, with value added remarkably consistent between IDR 996 and IDR 1,011 per kilogram. Yet despite this proven profitability, charcoal processing remained concentrated in only a handful of districts, a pattern the researchers attribute not to resource scarcity but to what behavioral economists call bounded rationality: producers stick with familiar, simpler copra production because new processing systems carry perceived risk, informational demands, and operational complexity.

The marketing analysis exposed an equally compelling paradox. Two channels dominated copra trade. In the longer channel, produce flowed from farmers through collectors and wholesalers before reaching industrial buyers, leaving producers with 75 percent of the final price and generating a cumulative margin of IDR 3,500 per kilogram. In the shorter channel, selling directly to wholesalers lifted the farmer’s share to 85.71 percent and cut the price-spread efficiency index from 25 percent to 14.29 percent. By every conventional measure, the shorter chain was better. And yet many producers stubbornly clung to collectors, accepting lower returns in exchange for immediate cash payments, informal credit access, supply aggregation, and flexible transaction arrangements that formal institutions failed to provide.

To understand why, the researchers turned to multicriteria decision analysis. Because the archived study record preserved only the final ordering of five marketing criteria rather than the original pairwise-comparison matrices, the team applied the rank-order centroid method, a transparent technique that converts rank positions into normalized weights. The results placed selling price first at 0.4567, followed by demand stability at 0.2567, accessibility at 0.1567, payment speed at 0.0900, and product absorption capacity at 0.0400. The researchers caution that part of the apparent dominance of the top two criteria reflects the mathematics of the rank-order centroid formula itself, which assigns declining weights by rank position, rather than a measured intensity of expert preference. Even so, the ordinal ranking was rock-solid: across twenty sensitivity scenarios perturbing each weight by up to twenty percent, not a single rank reversal occurred.

The strategic dimension came through a group-level SWOT-AHP synthesis. Strengths dominated the strategic landscape with a weight of 0.4658, followed by opportunities at 0.2771, weaknesses at 0.1611, and threats at 0.0960. Combining these groups into four classic TOWS orientations produced a clear winner: the aggressive Strength-Opportunity strategy, emphasizing value-added processing, institutional strengthening, technology dissemination, and market expansion, scored 0.3715. Strength-Threat strategies followed at 0.2809, then Weakness-Opportunity at 0.2191 and Weakness-Threat at 0.1286. All sixteen perturbation scenarios preserved this exact order, with Spearman rank correlations of 1.000 against the baseline, a level of local stability that few strategic assessments can claim.

The authors are refreshingly candid about the limits of interpretation. They stress that their behavioral conclusions are preference-based and conceptual rather than a psychometric validation of bounded rationality, institutional trust, or prospect theory, since no validated scales for those constructs were administered. The five criteria instead serve as observable proxies: price as monetary payoff, demand stability as uncertainty reduction, accessibility as transaction friction, payment speed as liquidity certainty, and absorption capacity as transaction-completion security. A further limitation concerns reproducibility, because the ten individual expert pairwise-comparison matrices were not retained in the archived record, meaning an equivalent reciprocal matrix reported in the paper reproduces the consensus vector mathematically but cannot recover original expert-level consistency or disagreement.

For policymakers, the implications are potentially transformative. The study suggests that simply opening shorter market channels or broadcasting better price information will not shift producer behavior unless institutions can replicate the non-price benefits, cash certainty, credit, and security, that intermediaries have long provided. Interventions that strengthen cooperatives, guarantee transparent payments, and reduce institutional uncertainty may outperform pure price incentives. Similarly, spreading coconut shell charcoal processing, a genuine waste-to-value opportunity, may require demonstration plots, peer mentoring, and gradual adoption schemes rather than technology handouts, because the barrier is behavioral as much as technical.

Perhaps the deepest lesson is methodological. Behavioral economics has long been criticized for building its edifice on laboratory games played by university students in wealthy countries. This study shows what the field gains when it ventures into rural markets where decisions are entangled in patron-client ties, liquidity constraints, and generations of social relationships. There, the rational actor model bends visibly: profitable opportunities go unexploited not because producers are irrational, but because certainty, familiarity, and trust are themselves valuable goods. In Buton’s coconut economy, the most efficient market structure on paper is not necessarily the one people will choose, and any reform that forgets this is likely to fail.

Subject of Research: Behavioral decision-making and marketing institution preferences in Indonesian coconut agroindustry development using SWOT-AHP and value-added analysis

Article Title: Behavioral decision-making and marketing institution preferences in coconut agroindustry development: evidence from SWOT-AHP and value-added analysis in Indonesia

Article References: Purnamasari, W. O. D., Sutawi, Ariadi, B. Y., & Zarliani, W. O. A. (2026). Behavioral decision-making and marketing institution preferences in coconut agroindustry development: evidence from SWOT-AHP and value-added analysis in Indonesia. Frontiers in Behavioral Economics, 5, Article 1900046. https://doi.org/10.3389/frbhe.2026.1900046

Image Credits: AI Generated

DOI: 10.3389/frbhe.2026.1900046

Keywords: behavioral economics, bounded rationality, coconut agroindustry, Indonesia, marketing institutions, SWOT-AHP, value-added analysis, rural development, marketing channels, coconut shell charcoal, farmer's share, Buton Regency

Agent-based modeling has experienced broad popularity because it allows researchers to implement autonomous agents, such as humans, households, or companies, as individual entities with varying decision-making processes. Each agent makes decisions based on its own circumstances, enabling the exploration of how macro-level phenomena emerge from micro-level interactions. This makes ABM particularly promising for understanding human-environment dynamics under different policy scenarios. However, the methodology comes with unsolved challenges, including calibration and validation procedures, computational efficiency, transparency, and reusability, and, most importantly, adequate representation of human behavior. Many ABMs are implemented using oversimplified approaches to modeling human decisions, and modelers are often unaware of the abundance of behavioral theories accumulated in the social sciences over centuries, or lack the competence to put them into code adequately.

The MOZAIC framework addresses the formalization challenge directly. Social science theories are formulated primarily in natural language, which necessarily leaves room for interpretation when they are translated into computational models. Even the term “formalization” can be interpreted in several ways, referring to graphical representations such as decision trees or flow charts, ontological systems, specific cognitive architectures, mathematical formulae, or pseudocode and code. Existing efforts toward standardized model descriptions, such as the ODD protocol and its extensions, improve transparency and communication but do not address the formalization of the underlying theories themselves. The authors argue for mathematical formalization as one concrete realization of a common standard beyond source code and natural-language descriptions, reaping benefits such as explicit and self-contained assumptions, generality, and standardization.

Mathematics, the authors note, can itself be considered a language. They cite mathematician George Pólya, who characterized mathematical notation as a “langue bien faite,” a language well adapted to its purpose, concise and precise, with rules that, unlike the rules of ordinary grammar, suffer no exception. Where their use is feasible and suitable, mathematical definitions are precise on one hand and flexible in their level of contextualization on the other. Filling in all the details, they can be as precise as computer code, whereas when stating more abstract properties, they can remain at a more general level, like graphical representations, but may avoid ambiguities. Crucially, the framework requires no mathematical knowledge beyond high school, as it employs only basic concepts such as functions to describe important parts of a model accurately.

MOZAIC guides the formalization process in four steps. First, the behavioral context and theory selection: the model’s context must be delineated, requiring gathering empirical information and finding relevant scientific studies related to human behavior in the system under study, leading to the selection of a theory to be formalized. Second, the definition of elementary model components: agents, environment, and interaction structures are specified in mathematical language, including state variables relevant to decision making. Third, the definition of decision model components: possible decision options, a set of decision criteria, and how to evaluate them are specified. Fourth, the mathematical formalization of the theory itself: the social science theory is formalized by defining how the model components from the previous steps are assembled to form the decision model, delivering a decision-making process for agents. In practice, the authors emphasize, there will be a back-and-forth between steps rather than a strict linear progression.

To demonstrate the framework’s usefulness, the team applied MOZAIC to the case of mobility tool ownership decision making within the Mobility Transition Model (MoTMo), an agent-based model developed to simulate mobility behavior in Germany over multiple decades. The purpose of MoTMo is to provide information on long-term dynamics to support informed decision making by policymakers, stakeholders, and citizens. The model should reproduce the past evolution of the number of privately owned vehicles in the study regions, as well as insights about the population’s mobility choices obtained from the “Mobilität in Deutschland” survey studies. The focus on car ownership is motivated by emissions data: motorized individual transport accounts for 75.3 percent of passenger transport emissions in Germany, and the most significant factor in using this mode is availability, defined by car ownership status.

From a pool of roughly thirty theories representing a broad spectrum of human behavioral drivers and usage across scientific disciplines, the authors formalized five example theories: rational actor, bounded rationality, habitual decision making, prospect theory, and descriptive norms. The rational actor theory, or homo economicus, assumes an agent is perfectly informed, acts in self-interest, and makes consistent decisions based on well-defined preferences, formalized through utility maximization. Bounded rationality modifies this by acknowledging limitations in cognitive capacity, information availability, or time. The authors provided two formalizations of bounded rationality: one introducing a gratification threshold so that agents strive for satisfaction rather than maximization, and another removing financial information from the utility evaluation, reflecting evidence that people often underestimate the financial burden of car ownership.

Habitual decision making highlights the role of established behavioral patterns, formalized by allowing agents to enter the decision-making process only when their needs are no longer satisfied or when they experience a mobility milestone, such as obtaining a driving license, a traffic accident, a change of residence, or the birth of a child. Prospect theory, developed by Daniel Kahneman and Amos Tversky, adapts rational actor assumptions to reflect systematic cognitive biases, including loss aversion. In the mobility context, selling a car is interpreted as a loss, so agents who currently own a car will only decide to give it up if the utility of the alternative exceeds that of the car by at least a loss aversion barrier. Descriptive norm theory, based on the work of Robert Cialdini and colleagues, formalizes a fundamentally different mechanism: agents decide on the basis of observable behavior in the population, for example following the majority decision of neighbors within a given radius, skipping the utility evaluation step entirely.

The resulting Mathematical Building Blocks (MBBs) offer mathematical descriptions of the elements and structures of the theories, allowing for comparison and aiming to be reusable in other ABMs by filling in context-specific details. The authors found that the rational actor theory is easy to formalize because mathematical descriptions already exist extensively in economics, making its widespread use understandable. Bounded rationality, by contrast, comes with a broad definition that allows and requires significant subjective interpretation, limiting comparability and highlighting the need to accurately state assumptions. Prospect theory seems promising in guiding how to bound rationality based on empirical findings, while habitual theory does not specify how a new decision is taken when habits are interrupted, meaning a combination with a different decision mechanism is needed. The descriptive norm approach structurally differs from the other theories because it skips the evaluation of available options from an agent’s perspective.

The MBBs are complementary to work on reusable building blocks (RBBs) and the AGENTBLOCKS library, which provides atomic blocks of code of specific mechanisms relevant to many ABMs in a given domain. The authors propose mathematical definitions as formal descriptions that are independent of programming languages, positioned as a stepping stone between social science theories, which are formulated in natural language and general, and model code, which is formal and case-specific. Mathematical definitions are more specific and applicable than graphical illustrations and more general and transferable than implemented code. The authors acknowledge limitations, including that the formalizations are based on a simplified model, that utility functions may not be appropriate for all theories, and that reading mathematical formulae requires concentration and experience. Future work should address the implementation and evaluation of the MBBs within ABM code, potentially creating AGENTBLOCKS based on these MBBs, and applying the MOZAIC framework to more complex models. The authors hope that collaborative, interdisciplinary definitions of MBBs with modelers, social scientists, and mathematicians could facilitate community standards for formalizing social science theories in agent-based modeling.

Subject of Research: A mathematical framework for formalizing behavioral theories in agent-based models of mobility

Article Title: MOZAIC: A mathematical approach to formalizing behavioral theories – applied to an agent-based model of mobility

Article References: Schutera, S., Scholz, G., & Wolf, S. (2026). MOZAIC: A mathematical approach to formalizing behavioral theories – applied to an agent-based model of mobility. Frontiers in Social Psychology, 4, Article 1772740. https://doi.org/10.3389/frsps.2026.1772740

Image Credits: AI Generated

DOI: 10.3389/frsps.2026.1772740

Keywords: agent-based modeling, MOZAIC, behavioral theories, mathematical formalization, mobility, decision making, social simulation, car ownership, bounded rationality, prospect theory, mathematical, approach

Tourism seasonality is not a minor scheduling nuisance. When demand concentrates around school holidays, summer weather, and headline attractions, destinations suffer overcrowding, strained infrastructure, environmental stress, degraded visitor experiences, and unstable seasonal labour markets, while hotels and restaurants sit half-empty for much of the year. Researchers have long argued that seasonality is a structural feature of destination systems rather than a marketing failure. The central challenge, as Dalir frames it, is not attracting more visitors but redistributing the attention, movement, and spending of the visitors a destination already receives across time and space.

The theoretical heart of the study lies in a distinction borrowed from Herbert Simon’s bounded rationality: the difference between the full choice set — everything objectively available to a traveller at a moment of decision — and the perceived choice set, the small subset a person actually notices and evaluates. Digital platforms appear to expand choice, but they also mediate how choice is encountered. Rankings, recommendation lists, review summaries, filters, and AI-generated itineraries determine which alternatives become cognitively accessible. An off-season festival or a charming peripheral museum may fail not because it lacks value, but because it never enters the traveller’s field of attention. AI, in this framing, is not a neutral information tool but a decision-mediating infrastructure that shapes what becomes visible before any preference is formed.

To test how different forms of algorithmic mediation play out at scale, Dalir built an agent-based model in NetLogo 6.4.0 simulating a destination ecosystem populated by heterogeneous visitor agents and supply agents — attractions, restaurants, accommodations, and souvenir shops. The model was calibrated with multiple data sources, including secondary destination data, online platform data, stakeholder input, and a survey of 400 respondents distributed through Prolific, of which 310 valid responses informed behavioural parameters such as spending, price sensitivity, and revisit probabilities. Visitors evaluate options using a bounded-rational random utility function in which congestion-adjusted quality, price, travel costs, and memory-based expectations combine, and each AI intervention adds a mechanism-specific cognitive term weighted by the visitor’s trust in AI — so effects vary across people rather than assuming uniform responsiveness.

Three AI conditions were compared against a business-as-usual baseline, each intervening at a different point in the decision process. Predictive nudging raises the salience of congestion and timing information, steering visitors toward less crowded options while leaving the choice set intact. Recommender-system filtering, the most aggressive intervention, restricts AI-adopting visitors to a top-k list of attractions ranked by predicted preference fit — directly shrinking the perceived choice set. Fairness-oriented visibility enhancement boosts the attractiveness of low-visibility, underrepresented, or off-peak alternatives without narrowing anything. The full experiment comprised 800 simulation runs, 200 per condition, generating 1,600 season-specific observations that were analysed with two-way ANOVA using intervention condition and season as factors.

The headline results are striking in both directions. All three AI interventions significantly increased spending and visitor numbers compared with business as usual, with large effect sizes. For spending, the intervention main effect was F(3, 1592) = 157.55, p < .001, with a partial eta-squared of .229. Recommender-system filtering produced the highest overall spending mean of roughly 818,793 simulation currency units, followed by predictive nudging at 809,527 and fairness-oriented visibility enhancement at 780,010. Visitor numbers rose from a baseline mean of about 338 to roughly 404–405 under all three interventions. On raw economic performance, AI looks like an unambiguous win.

But the seasonality result is where the study delivers its most important punch. The interaction between intervention and season — the statistical test of whether AI effects differ between high and low season — was not significant for either spending (p = .312) or visitor numbers (p = .655). In fact, the seasonal spending gap widened under every AI condition, growing from 94,597 under business as usual to as much as 127,297 under predictive nudging. AI lifted both seasons, but it lifted them roughly equally, leaving the structural imbalance untouched. The interventions, Dalir concludes, are performance-enhancing rather than seasonality-reducing. The reason is that seasonality is not merely an information problem; it is anchored in climate, school calendars, annual leave, work routines, event schedules, and accommodation availability — conditions that sit outside the platform interface and that no recommendation engine can rewrite.

The mechanism-level analysis reveals why the three designs behave so differently. The recommender condition showed the highest influence rate at 0.547 and cut the perceived choice set from about 25.6 options to 12.3, providing direct evidence of filtering at work. Predictive nudging had the lowest influence rate at 0.169, but every AI-influenced decision under it was attributable to congestion avoidance, confirming its value as a flow-coordination tool. Fairness-oriented visibility enhancement, with an influence rate of 0.396, kept the perceived choice set equal to the full set while spreading attention more evenly. Distributionally, the trade-offs are stark: recommender filtering concentrated demand around highly ranked attractions even as it maximised spending, while fairness-oriented enhancement activated more attractions with lower dispersion — the best profile for provider visibility and destination resilience, even though it was not the strongest earner.

The robustness analysis adds a subtle warning about design parameters. Varying the recommender choice-set size across k = 3, 5, 10, and 15 showed that influence peaks at moderate filtering levels and declines when choice sets become either too narrow or too broad — a non-linear threshold dynamic suggesting an optimal filtering range. Excessive filtering suppresses exploration and reinforces concentration; weak filtering fails to reduce cognitive burden. In other words, settings that look like technical dials are actually behavioural and governance choices with system-level consequences, and small parameter changes near critical regions can produce disproportionate effects on how demand and economic opportunity are distributed.

The broader message extends well beyond tourism. AI-enabled platforms should not be evaluated solely on accuracy, personalisation quality, engagement, or conversion, because systems that perform well by user-level metrics can still generate uneven consequences for providers, destinations, and ecosystems. For destination managers, the implication is to deploy AI with explicit objectives — revenue growth, congestion reduction, low-season stimulation, or provider resilience each demand a different design — and to track dashboards that monitor seasonal gaps and exposure concentration, not just visitor counts. For platforms and policymakers, the study argues for hybrid architectures combining filtering, nudging, and visibility mechanisms, transparency around ranking criteria, and exposure-diversity audits. AI can support more balanced tourism systems, the study concludes, but only when its decision architecture is deliberately designed to redistribute attention, visibility, and demand. Left to its own optimisation logic, it will happily make the busy season busier.

Subject of Research: Agent-based simulation of how AI-mediated decision mechanisms in tourism platforms affect visitor choice, spending, and seasonality

Article Title: Can AI Solve Eco-Economic Challenges? Simulating the Impact of AI Systems on Seasonality Using Agent-Based Modelling

Article References: Dalir, S. (2026). Can AI Solve Eco-Economic Challenges? Simulating the Impact of AI Systems on Seasonality Using Agent-Based Modelling. Information Systems Frontiers. https://doi.org/10.1007/s10796-026-10818-z

Image Credits: AI Generated

DOI: 10.1007/s10796-026-10818-z

Keywords: artificial intelligence, tourism seasonality, agent-based modelling, smart tourism, recommender systems, digital choice architecture, bounded rationality, predictive nudging, algorithmic bias, destination management, platform ecosystems, simulation

The starting point of the model is a dual-channel supply chain, a structure that has become ubiquitous in the era of direct-to-consumer sales. A manufacturer operates a direct channel, selling to consumers itself, while simultaneously supplying a retailer who competes for the same customers under a wholesale contract. Economists have long studied such arrangements with static game-theoretic tools, typically computing a Stackelberg equilibrium in which the manufacturer, as the leader, sets a wholesale price and the two channels then respond. Shen and colleagues preserve this static Stackelberg benchmark to fix the contractual wholesale price, but they then depart from tradition in two important directions that transform a well-behaved equilibrium problem into a rich nonlinear dynamical system.

The first departure is the quantum-inspired coupling of prices. Rather than treating the direct-channel price and the retail price as separate decision variables adjusted by independent learning rules, the authors introduce a strategic coupling mapping with an intensity parameter gamma, which generates the observable prices from an underlying entangled structure. The idea descends from the quantum game theory literature that began with the landmark 1999 work of Eisert, Wilkens, and Lewenstein in Physical Review Letters, where strategies were encoded in quantum states and entanglement was shown to alter equilibrium outcomes dramatically. In the pricing context, the coupling parameter plays an analogous role: it measures how strongly the two channels’ pricing decisions are interwoven, so that a change in one channel’s price is not merely a competitive signal but part of a jointly generated strategic state. As gamma varies, the effective landscape of the pricing game changes, and with it the stability of any long-run price configuration.

The second departure brings consumer psychology into the dynamics. Shoppers do not respond only to the price they see today; they carry internal reference prices, benchmarks formed from past experience against which current offers are judged as gains or losses. This reference-price effect, documented empirically since Winer’s 1986 brand-choice model and formalized in work by Hardie, Johnson, and Fader and by Briesch and colleagues, is captured here through exponential smoothing: consumers maintain channel-specific reference prices that are updated each period as a weighted average of the previous reference and the current observed price. The memory embedded in these reference prices means that demand today depends on the entire history of pricing, not just the present moment. Combined with multiplicative bounded-rationality learning, in which each channel adjusts its price in proportion to the marginal profitability of a price change rather than solving for the exact optimum, the model becomes a four-dimensional nonlinear discrete-time dynamical system with its own independently computed dynamic fixed point, distinct from the static Stackelberg benchmark.

With the machinery in place, the authors subject the system to a full local stability analysis via the Jacobian matrix, the standard tool for determining whether small perturbations around a fixed point decay or grow. The results trace a familiar but compelling narrative in nonlinear dynamics. For moderate values of the coupling intensity and learning speeds, the system converges to its dynamic fixed point: prices settle into a stable configuration and the market behaves as classical theory would hope. But as the strategic coupling intensifies, the fixed point loses stability through a flip bifurcation, the canonical first step on the period-doubling route to chaos. Prices begin to oscillate between two values, then four, then eight, and eventually the oscillations become aperiodic and irregular, wandering across a strange attractor. The authors also document multi-band attractors, in which the chaotic trajectory alternates among disjoint bands, and irregular bounded oscillations that never settle yet never diverge, a signature of complex but constrained market behavior.

What makes these findings more than a mathematical curiosity is their economic interpretation. Period-doubling in a pricing model corresponds to a market that cycles between promotional and premium pricing with increasing unpredictability, precisely the pattern that plagues firms locked in price wars across competing channels. The reference-price memory acts as an amplifier of this instability: because consumers anchor on past prices, aggressive discounting today depresses the reference price and thus the perceived value of future full-price sales, feeding back into the channels’ next adjustments. The quantum-inspired coupling, meanwhile, changes the geometry of the strategic interaction and shifts the thresholds at which stability breaks down. Sensitivity analysis around the contractual wholesale price shows that the qualitative flip-bifurcation mechanism is preserved regardless of where the wholesale benchmark sits, suggesting that the instability is an intrinsic feature of the coupled learning process rather than an artifact of a particular contract.

The second half of the paper confronts the practical question: once chaos has taken hold, can it be controlled? Chaos control has a distinguished pedigree, beginning with the celebrated Ott-Grebogi-Yorke method of 1990 and Pyragas’s delayed-feedback scheme of 1992, both of which demonstrated that chaotic systems can be stabilized using small, carefully timed interventions. Shen and colleagues compare two controllers adapted to the pricing game. The first is a local state-feedback controller, which measures the current deviation of prices from the dynamic fixed point and applies a corrective adjustment proportional to that deviation. The second is a delayed-feedback controller in the Pyragas tradition, which instead compares present prices with their values one period earlier and acts to eliminate the difference, requiring no knowledge of where the fixed point actually lies, an attractive property when the target is only implicitly defined.

Both controllers succeed. In numerical experiments conducted in MATLAB, with code available from the corresponding author upon reasonable request and no external datasets used, each scheme drives the chaotic baseline regime back to the dynamic fixed point. The evidence is presented in the language of control theory: tracking errors, the gap between actual and target prices, fall below a prescribed threshold; the control inputs themselves decay toward zero, indicating that the interventions become vanishingly small once order is restored; and the spectral radii of the controlled system, which measure how rapidly perturbations shrink, drop below one, the mathematical criterion for asymptotic stability. In economic terms, either controller can convert a market trapped in erratic price oscillations into one that converges smoothly to a coherent pricing pattern, and the comparison offers firms or regulators a menu of interventions with different information requirements.

The study situates itself within a rapidly growing literature on quantum game models of economic competition. Recent years have seen quantum treatments of Cournot and Bertrand duopolies, triopolies with heterogeneous players, public-enterprise competition, and mixed duopolies with nonlinear demand, published largely in Quantum Information Processing by groups including Shi and Xu, Zhang and colleagues, Zhu and Zhou, Deng and colleagues, and the Wei group, alongside the present authors’ own 2025 model of dual channels under channel cooperation and service. What distinguishes the new contribution is the combination of three ingredients, quantum-inspired coupling, dual-channel structure with a contractual wholesale benchmark, and consumer reference-price memory, in a single dynamical framework, together with a systematic chaos-control analysis. Earlier dual-channel work, from Chiang, Chhajed, and Hess’s strategic analysis of direct marketing to Cai’s channel-selection models and Chen and Zhou’s omni-channel complexity study, had explored either reference effects or nonlinear dynamics, but rarely both, and none had introduced quantum coupling into this setting.

The implications reach beyond the mathematics. For managers of dual-channel firms, the results offer a caution: aggressive price-adjustment speeds and tightly coupled strategic responses, each individually rational, can jointly push a market past a stability threshold into behavior that no equilibrium analysis predicts. For researchers, the paper demonstrates that quantum game theory is maturing from an abstract formalism into a modeling toolkit capable of capturing strategic interdependence in ways that classical games cannot, and that behavioral memory and nonlinear dynamics belong in the same conversation. The authors acknowledge no external funding beyond support from the Key Project in Natural Science Research of the Anhui Provincial Department of Education, and they declare no conflicts of interest. Whether real pricing data will confirm the bifurcation thresholds their model identifies remains an open question, but the framework now exists to ask it, and the answer could reshape how firms think about the fine line between healthy competition and chaotic price warfare.

Subject of Research: Nonlinear dynamics and chaos control in a quantum-coupled dual-channel pricing game with consumer reference-price memory

Article Title: Quantum-coupled dual-channel pricing dynamics with reference-price memory

Article References: Shen, J., Shi, L., & Zhu, K. (2026). Quantum-coupled dual-channel pricing dynamics with reference-price memory. Quantum Information Processing, 25(10), Article 335. https://doi.org/10.1007/s11128-026-05360-5

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05360-5

Keywords: quantum game theory, dual-channel supply chain, reference price, chaos control, bifurcation, nonlinear dynamics, bounded rationality, Stackelberg game, delayed feedback, price war, flip bifurcation, Quantum Information Processing

The study, led by Tobias Brosch, director of the Consumer Decision and Sustainable Behavior Lab at UNIGE’s Faculty of Psychology and Educational Sciences and the Swiss Center for Affective Sciences, together with postdoctoral researcher Mario Herberz, is published in the Journal of Environmental Psychology. Rather than running a single experiment, the team conducted a systematic review and meta-analysis, a statistical technique that pools the results of many independent studies to reveal patterns no individual investigation could detect on its own. The researchers analysed 71 studies examining the impact of specific climate communication strategies, drawing on data from a total of 216,000 participants in Switzerland and abroad. This scale makes it the first large-scale synthesis of its kind in the domain of climate action messaging.

The scope of the analysis was deliberately broad. The 71 studies encompassed 15 distinct communication approaches, spanning the full spectrum of what campaigners currently deploy in the field. At one end sat purely informational strategies, which aim to fill knowledge gaps by presenting scientific facts about global warming, its causes and its consequences. At the other end sat emotionally oriented approaches, including storytelling and messages designed to evoke a sense of wonder or awe at the beauty of nature. In between lay strategies grounded in the principle of bounded rationality, a concept from behavioural economics which holds that human decision-making is limited by attention, time and cognitive capacity. These approaches do not try to persuade through argument but instead facilitate choices by highlighting specific, personally relevant aspects of climate change, such as its consequences for health or household finances.

The headline finding is, in one sense, reassuring for communicators: almost all of these strategies are likely to have a positive effect. According to Brosch, the synthesis shows that the vast majority of approaches improve people’s intentions and behaviours, as well as their support for climate policies. In other words, the question facing campaign designers is rarely whether a given message will help, but how much it will help. Given that the studies reviewed mainly measured the effects of messages to which people were exposed only once, the authors note that this is particularly encouraging, since repeated exposure, as occurs in sustained campaigns, can be expected to strengthen the impact of effective messages over time.

But the meta-analysis also revealed a clear hierarchy among the strategies, and this is where the practical implications become sharpest. Campaigns that evoke a strong emotional response were found to be significantly more effective than those that simply present facts and scientific evidence. Two emotional routes stood out in particular. The first is storytelling, in which narratives carry the audience through experiences rather than at them, allowing listeners to feel the stakes of climate change rather than merely read about them. The second is the evocation of wonder or awe at the beauty of nature, an emotion that appears to connect people to the very thing at stake in climate action: landscapes, ecosystems and species worth preserving.

A third, closely related family of high-performing messages draws on moral, ethical or even religious considerations. These framings highlight humanity’s connection to something greater than itself, a natural world that people have a responsibility to preserve for future generations and for its own sake. The effectiveness of such messages suggests that climate communication resonates most deeply when it engages the values and identities that people already hold, rather than attempting to construct persuasion from raw data. Facts, in this picture, are not useless; they are simply insufficient on their own to overcome the psychological distance that many people feel from a global, slow-moving problem.

One strategy family, however, failed to deliver. Messages built on individual and collective responsibility, exemplified by slogans such as ‘success depends largely on you’, showed little or no effect on intentions, behaviour or policy support. Worse, the researchers note that such messages may even foster reactance, the well-documented psychological phenomenon in which people respond to perceived pressure or blame by digging in their heels and doing the opposite of what is asked. Guilt-oriented appeals that place the entire burden of a planetary problem on a single person’s shoulders appear, at least in the aggregated evidence, to be a dead end for campaigners.

The synthesis also yielded a more modest but actionable insight: messages are more effective when they include images. Visual content, whether photographs of melting ice or sweeping natural landscapes, appears to amplify the persuasive power of accompanying text. This aligns with the broader emotional findings, since imagery is a particularly direct route to affective response. For public authorities and organisations with limited communication budgets, the combination of narrative, emotional framing and strong visuals represents the most evidence-backed recipe currently available.

The timing of these findings matters. As Brosch observes, the scientific evidence on climate change is now well established, and the central challenge is no longer generating knowledge but turning knowledge into action. The gap between what people know and what they do, sometimes called the knowledge-action gap, has persisted for decades despite ever-clearer reports from the scientific community. The Geneva results suggest that closing this gap requires communicators to stop treating audiences as information deficits to be filled and start treating them as emotional, moral and social beings whose behaviour is shaped by feelings, stories and values. At a time when the stakes of climate inaction continue to rise, the researchers conclude that there is considerable scope to improve climate communication, and the evidence now points clearly toward where that improvement should begin: with the heart as much as the head.

Subject of Research: The effectiveness of different communication strategies in promoting climate action

Article Title: To promote climate action, emotion matters more than information

Article References: To promote climate action, emotion matters more than information. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: climate change, climate communication, meta-analysis, emotion, storytelling, behavior change, environmental psychology, University of Geneva, bounded rationality, public campaigns, knowledge-action gap, policy support