arXiv subjects

Attila Szolnoki

Publications and source records attributed to Attila Szolnoki.

At least 19 recordsLinked to original sources

arXiv2026

Coordinated incentives in AI-generated misinformation governance

With the rapid diffusion of AI-generated content, AI-driven misinformation is becoming increasingly pervasive and difficult to govern, undermining information credibility and social trust. This study models the strategic interdependence among a government regulator, an AI enterprise, and users through a three-party evolutionary game that incorporates heterogeneous rewards and punishments. From the resulting replicator equations, we characterize the evolutionary stability of competing governance and production strategies. The analysis indicates that neither unilateral regulation nor market incentives alone can effectively curb misinformation. Instead, an evolutionarily stable regime of real-information production arises only when regulatory rewards and punishment intensity, enterprise reputation loss, and user adoption incentives collectively surpass critical thresholds. The findings highlight the need for coordinated and adaptive policy mixes that align regulatory instruments with enterprise behavior and user uptake while managing governance costs.

physics.soc-ph↗

arXiv2026

Evolutionary dynamics in public goods games with general frequency-dependent returns

The public goods game serves as a significant paradigm for investigating the emergence and maintenance of cooperation in conflicting situations. In the traditional public goods game, the multiplication factor characterizing the synergy effect of common efforts is typically assumed to be constant. In real-world scenarios, however, investment returns are often dynamic and vary with the strategic composition of the interaction group. To date, the evolutionary dynamics of the public goods game with such frequency-dependent returns have remained not fully understood. In this work, we introduce a general frequency-dependent multiplication factor that depends on the strategy composition within the game group. Through theoretical analysis, we derive the mathematical conditions under which cooperation is favored. Our results show that whether cooperation has an evolutionary advantage over defection depends on the investment return rate in the full-contribution state of the game group, irrespective of the return rates in other states. An increase in this rate leads to a higher abundance of cooperators. Furthermore, we introduce a general frequency-dependent multiplication factor into the public goods game with peer punishment, and systematically explore its effects on the cooperation dilemma and the second-order free-rider problem. Our results highlight that the abundance of cooperators or punishers is governed solely by the investment return values in the full-cooperation and full-punishment compositions of the group. A higher return rate in the full-cooperation state facilitates the promotion of cooperation, whereas a higher return rate in the full-punishment state favors the emergence of punishment. Our theoretical findings are verified by individual-based simulations.

q-bio.PE↗

arXiv2026

Payoff-Driven Coevolution and Oscillatory Dynamics in Hypergraph

We study a coevolutionary public goods game on a dynamic hypergraph, where an individual's payoff directly determines the number of hyperedges it can join. In the proposed mechanism, nodes adjust their participation according to the group payoffs of hyperedges, and hyperedges that remain occupied only by defectors for a sufficiently long time collapse and are rebuilt by selecting new members based on the current payoffs of nodes. This adaptive rule captures the performance-driven reorganization of group interactions in evolving collective systems. Using Monte Carlo simulations, we show that the cooperation fraction and average hyperdegree may converge to steady states with stochastic fluctuations or exhibit persistent oscillations, depending on the parameter regime. The steady-state outcomes are strongly nonmonotonic with respect to the structural adaptation parameters: cooperation is sustained only when the rate of link formation is properly balanced. If structural adaptation is too fast, frequent contacts between cooperators and defectors destroy cooperative clusters; if it is too slow, cooperators lack sufficient structural support to expand. This differs from the conventional expectation in static settings that larger benefit parameters always facilitate cooperation. We further introduce spectral entropy to quantify the regularity of the oscillatory dynamics and identify limit-cycle behavior in the phase space in certain regimes. These results suggest that adaptive higher-order restructuring can both promote and destabilize cooperation, offering insight into oscillatory cooperation and recurrent prosperity-decline cycles in real group-structured systems.

physics.soc-ph↗

arXiv2026

Cooperation in Public Goods Games over Uniform Random Hypergraphs with Game Transitions

The evolution of cooperation is a central enigma in evolutionary game theory. Traditionally, the combination of pairwise networks and repeated Public Goods Games with a single state fails to adequately describe realistic group interaction scenarios. On the one hand, pairwise networks lack clear group definitions. On the other hand, a participant's decision affects not only competitors' fitness but also the state of the surrounding environment. To address this problem, we propose a Public Goods Game with game transition mechanisms based on Uniform Random Hypergraphs. In our model, game groups formed by hyperedges transition between two types of games, one with abundant public resources and the other with scarce public resources. The transition probability is closely related to the strategies of players within the hyperedges. By developing a Monte Carlo simulation framework that incorporates payoff accumulation, strategy imitation, and game state transitions, we aim to reveal the coevolutionary patterns of strategies and game states in group interactions. Our study highlights a nonlinear relationship between defection sensitivity and cooperation frequency under game transitions, as well as the asymmetric effects of the two sensitivities in state-dependent transitions. These observations open new directions for how to approach social dilemmas.

physics.soc-ph↗

arXiv2026

The survival of the weakest in a biased donation game

Cooperating first then mimicking the partner's act has been proven to be effective in utilizing reciprocity in social dilemmas. However, the extent to which this, called Tit-for-Tat strategy, should be regarded as equivalent to unconditional cooperators remains controversial. Here, we introduce a biased Tit-for-Tat (T) strategy that cooperates differently toward unconditional cooperators (C) and fellow T players through independent bias parameters. The results show that, even under strong dilemmas in the donation game framework, this three-strategy system can exhibit diverse phase diagrams on the parameter plane. In particular, when T-bias is small and C-bias is large, a ``hidden T phase'' emerges, in which the weakest T strategy dominates. The dominance of the weakened T strategy originates from a counterintuitive mechanism characterizing non-transitive ecological systems: T suppresses its relative fitness to C, rapidly eliminates the cyclic dominance clusters, and subsequently expands slowly to take over the entire population. Analysis in well-mixed populations confirms that this phenomenon arises from structured populations. Our study thus reveals the subtle role of bias regulation in cooperative modes by emphasizing the ``survival of the weakest'' effect in a broader context.

cs.GT↗

arXiv2026

Coevolutionary dynamics of cooperation, risk, and cost in collective risk games

Addressing both natural and societal challenges requires collective cooperation. Studies on collective-risk social dilemmas have shown that individual decisions are influenced by the perceived risk of collective failure. However, existing feedback evolving game models often focus on a single feedback mechanism, such as the coupling between cooperation and risk or between cooperation and cost. In many real-world scenarios, however, the level of cooperation, the cost of cooperating, and the collective risk are dynamically interlinked. Here, we present an evolutionary game model that considers the interplay of these three variables. Our analysis shows that the worst-case scenario, characterized by full defection, maximum risk, and the highest cost of cooperation, remains a stable evolutionary attractor. Nevertheless, cooperation can emerge and persist because the system also supports stable equilibria with non-zero cooperation. The system exhibits multistability, meaning that different initial conditions lead to either sustained cooperation or a tragedy of the commons. These findings highlight that initial levels of cooperation, cost, and risk collectively determine whether a population can avert a tragic outcome.

nlin.AO↗

arXiv2026

Evolutionary Dynamics of Variable Games in Structured Populations

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic properties in structured populations, derive theoretical conditions for cooperation, and identify the optimal game distribution for promoting cooperation. To address these issues, we propose the variable game framework in a structured population, where the game interactions between different individuals change over time. By means of the Markov chain and the pair approximation method, we derive theoretical conditions under which cooperation is favored by natural selection and when it is favored over defection under weak selection. Furthermore, we respectively formulate and solve two optimization problems to determine the optimal game distribution that most effectively fosters the evolution of cooperation by maximizing the gradient of cooperation selection and minimizing the fitness difference between defectors and cooperators. The theoretical predictions regarding both the conditions for cooperation and optimal game distribution are further validated by numerical calculations and extensive Monte Carlo simulations. Our findings offer novel insights into the mechanisms driving cooperative behavior in complex systems and provide theoretical guidance for designing optimal game environments that facilitate the evolution of cooperation.

cs.GT↗

arXiv2026

Supervised tax compliance and evasion from a spatial evolutionary game perspective

Taxation constitutes a fundamental component of modern national economic systems, exerting profound impacts on both societal functioning and governmental operations. In this paper, we employ an interdependent network approach to model the coevolution between citizens and regulators within a taxation system that fundamentally constitutes a public goods game framework with complex interactive dynamics. In a game layer, citizens engage in public goods games, facing the social dilemma of tax compliance (cooperation) versus evasion (defection). Tax compliance supports the sustainability of public finances while tax evasion presents markedly stronger short-term incentives. In a regulatory layer, fair regulators punish tax evaders, while corrupt regulators keep silent due to bribes. Governmental regulatory interventions introduce critical institutional constraints that alter the traditional equilibrium of the game. Importantly, there exists a strategy update not only among citizens but also among regulators. Our results indicate that strengthening penalties can effectively curb tax evasion, and the influence of bribery on both tax compliance rates and the proportion of fair regulators is nonlinear. Additionally, increasing regulators' salaries and intensifying the crackdown on corrupt regulators can foster the emergence of fair regulators, thereby reducing tax evasion among citizens. The results offer practical policy implications, suggesting that balanced deterrence and institutional fairness are essential to sustaining compliance, and point to the need for future empirical validation and model extensions.

physics.soc-ph↗

arXiv2026

Effects of Stochastic Games on Evolutionary Dynamics in Structured Populations

Continuously changing environments have a paramount role in the evolution of cooperative behavior. Previous works have shown that the transitions among different games, as the feedback between behaviors and environments, can promote cooperative behavior significantly. Quantitative analysis, however, is limited to homogeneous populations, while realistic populations in nature are often more complex and highly heterogeneous. We hereby provide an analytical treatment of when the evolution of cooperation can be supported in stochastic games, applying to arbitrary spatial heterogeneity and payoff structure. We highlight that the rule and frequency of game changes can have surprisingly diverse effects on evolutionary outcomes, depending on the governing social dilemmas. While stochastic games favor the evolution of cooperation in donation games, this is not the case for public goods games and snowdrift games. Hence, our framework and model results offer a more subtle insight into the long-standing enigma.

physics.soc-ph↗

arXiv2026

Punishment in bipartite societies

From ant-acacia mutualism to performative conflict resolution among Inuit, dedicated punishments between distinct subsets of a population are widespread and can reshape the evolutionary trajectory of cooperation. Existing studies have focused on punishments within a homogeneous population, paying little attention to cooperative dynamics in a situation where belonging to a subset is equally important to the actual strategy represented by an actor. To fill this gap, we here study a bipartite population where cooperator agents in a public goods game penalize exclusively those defectors who belong to the alternative subset. We find that cooperation can emerge and remain stable under symmetric intergroup punishment. In particular, at low punishment intensity and at a small value of the enhancement factor of the dilemma game, intergroup punishment promotes cooperation more effectively than a uniformly applied punishment. Moreover, intergroup punishment in bipartite populations tends to be more favorable for overall social welfare. When this incentive is balanced, cooperators can collectively restrain defectors of the alternative set via aggregate interactions in a randomly formed working group, offering a more effective incentive. Conversely, breaking the symmetry of intergroup punishment inhibits cooperation, as the imbalance creates an Achilles' heel in the enforcement structure. Our work, thus, reveals symmetry in intergroup punishment as a unifying principle behind cooperation across human and biological systems.

q-bio.PE↗

arXiv2026

Shaping the learning signal in a combined Q-learning rule to improve structured cooperation

Q-learning provides a standard reinforcement learning framework for studying cooperation by specifying how agents update action values from repeated local interactions outcomes. Although previous work has shown that reputation can promote cooperation in such systems, most models introduce reputation by modifying payoffs, encoding it directly in the state or changing partner selection, which makes it difficult to isolate the role of the learning signal itself. Here, we construct the reinforcement signal as a weighted combination of reputation and game payoffs, leaving the game and network structure unchanged. We find that increasing the weight on reputation generally promotes cooperation by consolidating clusters, but this effect is conditional on the learning dynamics. Specifically, this promoting effect vanishes in two regimes: when the learning rate is extremely small, which prevents effective information propagation and when the discount factor approaches one, as distant future expectations obscure the immediate reputational advantage. Outside these limiting cases, the efficacy of reputation in promoting cooperation is attenuated by higher learning rates but amplified by larger discount factors. These results advance the understanding of cooperative dynamics by demonstrating that cooperation can be stabilized through the reputational shaping of learning signals alone, providing critical insights into the interplay between social information and individual learning parameters.

physics.soc-ph↗

arXiv2025

Evolutionary Cooperation with Game Transitions via Markov Decision Chain in Networked Population

Individual cooperative strategy influences the surrounding dynamic population, which in turn affects cooperative strategy. To better model this phenomenon, we develop a Markov decision chain based game transitions model and examine the dynamic transitions in game states of individuals within a network and their impact on the strategy's evolution. Additionally, we extend single-round strategy imitation to multiple rounds to better capture players' potential non-rational behavior. Using intensive simulations, we explore the effects of transition probabilities and game parameters on game transitions and cooperation. Our study finds that strategy-driven game transitions promote cooperation, and increasing the transition rates of Markov decision chains can significantly accelerate this process. By designing different Markov decision chains, these results provide simulation based guidance for practical applications in swarm intelligence, such as strategic collaboration.

physics.soc-ph↗

arXiv2025

Evolutionary Dynamics Based on Reputation in Networked Populations with Game Transitions

The environment undergoes perpetual changes that are influenced by a combination of endogenous and exogenous factors. Consequently, it exerts a substantial influence on an individual's physical and psychological state, directly or indirectly affecting the evolutionary dynamics of a population described by a network, which in turn can also alter the environment. Furthermore, the evolution of strategies, shaped by reputation, can diverge due to variations in multiple factors. To explore the potential consequences of the mentioned situations, this paper studies how game and reputation dynamics alter the evolution of cooperation. Concretely, game transitions are determined by individuals' behaviors and external uncontrollable factors. The cooperation level of its neighbors reflects individuals' reputation, and further, a general fitness function regarding payoff and reputation is provided. Within the context of the donation game, we investigate the relevant outcomes associated with the aforementioned evolutionary process, considering various topologies for distinct interactions. Additionally, a biased mutation is introduced to gain a deeper insight into the strategy evolution. We detect a substantial increase in the cooperation level through intensive simulations, and some important phenomena are observed, e.g., the unilateral increase of the value of prosocial behavior limits promotion in cooperative behavior in square-lattice networks.

physics.soc-ph↗

arXiv2025

Reputation assimilation mechanism for sustaining cooperation

Keeping a high reputation, by contributing to common efforts, plays a key role in explaining the evolution of collective cooperation among unrelated agents in a complex society. Nevertheless, it is not necessarily an individual feature, but may also reflect the general state of a local community. Consequently, a person with a high reputation becomes attractive not just because we can expect cooperative acts with higher probability, but also because such a person is involved in a more efficient group venture. These observations highlight the cumulative and socially transmissible nature of reputation. Interestingly, these aspects were completely ignored by previous works. To reveal the possible consequences, we introduce a spatial public goods game in which we use an assimilated reputation simultaneously characterizing the individual and its neighbors' reputation. Furthermore, a reputation-dependent synergy factor is used to capture the high (or low) quality of a specific group. Through extensive numerical simulations, we investigate how cooperation and extended reputation co-evolve, thereby revealing the dynamic influence of the assimilated reputation mechanism on the emergence and persistence of cooperation. By fostering social learning from high-reputation individuals and granting payoff advantages to high-reputation groups via an adaptive multiplier, the assimilated reputation mechanism promotes cooperation, ultimately to the systemic level.

physics.soc-ph↗

arXiv2025

Inter-role reciprocity in evolutionary trust game on square lattices

Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating trustors and trustees. For even lattice sizes, it creates two disjoint diagonal sub-lattices for strategy learning, while game interactions can take place on the original lattice. This setup ensures a minimal spatial structure that allows interactions across roles and learning within roles. By simulations on this setup, we detect an inter-role spatial reciprocity mechanism, through which trust can emerge. In particular, a moderate return ratio allows investing trustors and trustworthy trustees to form inter-role clusters and thus save trust. If the return is too high, it harms the survival of trustees; if too low, it harms trustors. The proposed simulation framework is also applicable to any bipartite game to uncover potential inter-role spatial mechanisms across various scenarios.

physics.soc-ph↗

arXiv2025

Strategic competition in informal risk sharing mechanism versus collective index insurance

The frequent occurrence of natural disasters has posed significant challenges to society, necessitating the urgent development of effective risk management strategies. From the early informal community-based risk sharing mechanisms to modern formal index insurance products, risk management tools have continuously evolved. Although index insurance provides an effective risk transfer mechanism in theory, it still faces the problems of basis risk and pricing in practice. At the same time, in the presence of informal community risk sharing mechanisms, the competitiveness of index insurance deserves further investigation. Here we propose a three-strategy evolutionary game model, which simultaneously examines the competitive relationship between formal index insurance purchasing (I), informal risk sharing strategies (S), and complete non-insurance (A). Furthermore, we introduce a method for calculating insurance company profits to aid in the optimal pricing of index insurance products. We find that basis risk and risk loss ratio have significant impacts on insurance adoption rate. Under scenarios with low basis risk and high loss ratios, index insurance is more popular; meanwhile, when the loss ratio is moderate, an informal risk sharing strategy is the preferred option. Conversely, when the loss ratio is low, individuals tend to forego any insurance. Furthermore, accurately assessing the degree of risk aversion and determining the appropriate ratio of risk sharing are crucial for predicting the future market sales of index insurance.

q-fin.RM↗

arXiv2025

Context-sensitive norm enforcement reduces sanctioning costs in spatial public goods games

Uniform punishment policies can sustain cooperation in social dilemmas but impose severe costs on enforcers, creating a second-order free-rider problem that undermines the very mechanism designed to prevent exploitation. We show that the remedy is not a harsher stick but a smarter one. In a four-strategy spatial public-goods game we pit conventional punishers, who levy a fixed fine, against norm-responsive punishers that double both fine and cost only when at least half of their current group already cooperates. Extensive large scale Monte Carlo simulations on lattices demonstrate that context-sensitive punishment achieves complete defector elimination at fine levels 15\% lower than uniform enforcement, despite identical marginal costs per sanctioning event. The efficiency gain emerges because norm-responsive punishers conserve resources in defector-dominated regions while concentrating intensified sanctions at cooperative-defector boundaries, creating self-reinforcing fronts that amplify the spread of prosocial behavior. These findings reveal that enforcement efficiency can be dramatically improved by targeting punishment at cooperative-defector interfaces rather than applying uniform sanctions, offering quantitative guidelines for designing adaptive regulatory mechanisms that maximize compliance while minimizing institutional costs.

physics.soc-ph↗

arXiv2025

Evolutionary Dynamics with Self-Interaction Learning in Networked Systems

The evolution of cooperation in networked systems helps to understand the dynamics in social networks, multi-agent systems, and biological species. The self-persistence of individual strategies is common in real-world decision making. The self-replacement of strategies in evolutionary dynamics forms a selection amplifier, allows an agent to insist on its autologous strategy, and helps the networked system to avoid full defection. In this paper, we study the self-interaction learning in the networked evolutionary dynamics. We propose a self-interaction landscape to capture the strength of an agent's self-loop to reproduce the strategy based on local topology. We find that proper self-interaction can reduce the condition for cooperation and help cooperators to prevail in the system. For a system that favors the evolution of spite, the self-interaction can save cooperative agents from being harmed. Our results on random networks further suggest that an appropriate self-interaction landscape can significantly reduce the critical condition for advantageous mutants, especially for large-degree networks.

cs.SI↗