Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities.

Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying population dynamics in various manners. We propose and analyze an eco-evolutionary game dynamics model on a network with two communities such that players interact with other players in the same community and those in the opposite community at different rates. In our model, we consider two-person matrix games with pairwise interactions occurring on individual edges and assume that the environmental state depends on edges rather than on nodes or being globally shared in the population. We analytically determine the equilibria and their stability under a symmetric population structure assumption, and we also numerically study the replicator dynamics of the general model. The model shows rich dynamical behavior, such as multiple transcritical bifurcations, multistability, and anti-synchronous oscillations. Our work offers insights into understanding how the presence of community structure impacts the eco-evolutionary dynamics within and between niches.

Game-theoretic agent-based modelling of micro-level conflict: Evidence from the ISIS-Kurdish war.

This article delves into the dynamics of a dyadic political violence case study in Rojava, Northern Syria, focusing on the conflict between Kurdish rebels and ISIS from January 1, 2017, to December 31, 2019. We employ agent-based modelling and a formalisation of the conflict as an Iterated Prisoner's Dilemma game. The study provides a nuanced understanding of conflict dynamics in a highly volatile region, focusing on microdynamics of an intense dyadic strategic interaction between two near-equally- powered actors. The choice of using a model based on the Iterated Prisoner's Dilemma, though a classical approach, offers substantial insights due to its ability to model dyadic, equally-matched strategic interactions in conflict scenarios effectively. The investigation primarily reveals that shifts in territorial control are more critical than geographical or temporal factors in determining the conflict's course. Further, the study observes that the conflict is characterised by periods of predominantly one-sided violence. This pattern underscores that the distribution of attacks, and target choices are a more telling indicator of the conflict nature than specific behavioural patterns of the actors involved. Such a conclusion aligns with the strategic implications of the underlying model, which emphasises the outcome of interactions based on differing aggression levels. This research not only sheds light on the conflict in Rojava but also reaffirms the relevance of this type of game-theoretical approach in contemporary conflict analysis.

Committing to the wrong artificial delegate in a collective-risk dilemma is better than directly committing mistakes.

While autonomous artificial agents are assumed to perfectly execute the strategies they are programmed with, humans who design them may make mistakes. These mistakes may lead to a misalignment between the humans' intended goals and their agents' observed behavior, a problem of value alignment. Such an alignment problem may have particularly strong consequences when these autonomous systems are used in social contexts that involve some form of collective risk. By means of an evolutionary game theoretical model, we investigate whether errors in the configuration of artificial agents change the outcome of a collective-risk dilemma, in comparison to a scenario with no delegation. Delegation is here distinguished from no-delegation simply by the moment at which a mistake occurs: either when programming/choosing the agent (in case of delegation) or when executing the actions at each round of the game (in case of no-delegation). We find that, while errors decrease success rate, it is better to delegate and commit to a somewhat flawed strategy, perfectly executed by an autonomous agent, than to commit execution errors directly. Our model also shows that in the long-term, delegation strategies should be favored over no-delegation, if given the choice.

Tolerance for corruption and descriptive social norm: An experimental study of embezzlement.

Public tolerance for corruption within a society significantly influences the prevalence of corrupt practices, but less is known about how this tolerance evolves with social norms. This paper presents experimental evidences demonstrating that the descriptive social norm indicating widespread corruption can lead to increased tolerance for corruptive acts. We introduce an asymmetric information ultimatum game to simulate the interactions between embezzlers and citizens. Game theoretical analysis reveals that victims anticipating corruption will exhibit greater compliance with embezzlement when the offers are evaluated based on descriptive norms. To test the hypothesis, we employ a framing effect to induce variations in descriptive norms within a behavioral experiment. Although the treatment effect is significant only in the subgroup of student cadres, this subgroup demonstrated increased beliefs about embezzlement, greater tolerance for corruption, and a heightened propensity to embezzle when exposed to framings with hierarchical implications. This paper contributes to the corruption literature by examining the effects of descriptive norms on victims' responses to embezzlement. It offers a more comprehensive perspective on how social standards shape public opinions and corrupt actions, enhancing our understanding of the self-reinforcing nature of corruption.

Evolutionarily stable payoff matrix in hawk-dove games.

BACKGROUND: Classical matrix game models aim to find the endpoint of behavioural evolution for a set of fixed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players' strategies but also the payoff matrix evolves according to natural selection. RESULTS: We start out from the hawk-dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifies fighting ability and determines the probability of winning and the cost of losing escalated hawk-hawk fights. We define evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payoff matrix. CONCLUSIONS: We find that the maximal possible cost of escalating fights remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the final evolutionarily stable phenotype maximizes the payoff of hawk-hawk fights. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.

WIPO initiative of transforming traditional resources and sharing rights: An evolutionary game analysis and a Chinese context.

WIPO-GRTKF specifies, for the first time, how traditional resources embodied by traditional knowledge, genetic resources, and folklore can be defined, and what the relationship between original rights, and rights arising from the transformation and utilisation of traditional resources can be understood. Committed to promoting innovation, shared benefits and balanced interests, WIPO tries to achieve a balance between preventing users from violating holders' original rights through the acquisition of patent, trademark and copyright, and incentivizing all stakeholders to transform traditional resources to improve the greater good. The document triggers a new round of disputes among interest groups over how to share rights arising from the transformation and utilisation of traditional resources. Using an evolutionary game model to simulate how holders and users transform traditional resources, and share rights, we find that when the two sides choose to cooperate to apply for transformation and give consent to use, their benefits are maximised and strategies stabilised. We suggest that in the transforming process, holders' rights and users' interests be given equal emphasis, and an autonomous and open mode combining statutory licensing, and justified utilisation of original rights be employed. We advocate for a hybrid legislative arrangement that integrates the incentive of IPRs as private rights, and the safeguard of public rights. In the dual subject system, both users and holders enjoy multiple rights in the process of protecting and transforming traditional resources. The Chinese approach to transforming traditional resources and sharing their rights will contribute to sustainable development of traditional resource industry across the globe.

Research on multilateral collaboration strategies in agricultural seed quality assurance.

Seeds, as the initial products in agricultural systems, play a pivotal role in ensuring quality, fundamental to national food security and sustainable agricultural development. This study introduces a concept integrating public governance and evolutionary game theory to construct a quadripartite evolutionary game model involving seed companies, certification agencies, farmers, and governmental departments. It considers the strategic choices of these stakeholders under varying economic motivations and market mechanisms, as well as the influence of external regulation and incentives on game strategies. The existence conditions for evolutionarily stable strategy combinations are determined using the Lyapunov first method, and MATLAB is employed for numerical simulation analysis to validate the game analysis under initial conditions. The simulation results reveal two potential equilibrium points corresponding to different strategic choices among stakeholders. The study finds that producing high-quality seeds and the refusal of certification agencies to engage in rent-seeking are crucial for ensuring seed quality. Additionally, the cost-benefit ratio of seed companies, the speculative cost of certification agencies, and the rights-protection cost of farmers are key determinants in the evolution of seed quality assurance strategies. This research also holds practical significance in enhancing seed quality assurance mechanisms and fostering sustainable development in agriculture.

Evolution of Cooperation in Spatio-Temporal Evolutionary Games with Public Goods Feedback.

In biology, evolutionary game-theoretical models often arise in which players' strategies impact the state of the environment, driving feedback between strategy and the surroundings. In this case, cooperative interactions can be applied to studying ecological systems, animal or microorganism populations, and cells producing or actively extracting a growth resource from their environment. We consider the framework of eco-evolutionary game theory with replicator dynamics and growth-limiting public goods extracted by population members from some external source. It is known that the two sub-populations of cooperators and defectors can develop spatio-temporal patterns that enable long-term coexistence in the shared environment. To investigate this phenomenon and unveil the mechanisms that sustain cooperation, we analyze two eco-evolutionary models: a well-mixed environment and a heterogeneous model with spatial diffusion. In the latter, we integrate spatial diffusion into replicator dynamics. Our findings reveal rich strategy dynamics, including bistability and bifurcations, in the temporal system and spatial stability, as well as Turing instability, Turing-Hopf bifurcations, and chaos in the diffusion system. The results indicate that effective mechanisms to promote cooperation include increasing the player density, decreasing the relative timescale, controlling the density of initial cooperators, improving the diffusion rate of the public goods, lowering the diffusion rate of the cooperators, and enhancing the payoffs to the cooperators. We provide the conditions for the existence, stability, and occurrence of bifurcations in both systems. Our analysis can be applied to dynamic phenomena in fields as diverse as human decision-making, microorganism growth factors secretion, and group hunting.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph.

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

Safe Food Supply Chain as Health Network: An Evolutionary Game Analysis of Behavior Strategy for Quality Investment.

There is a natural relation between human health and the quality of their food and drinks, and elevating the quality input level of food production for all enterprises within the food supply chain system forms the foundation for preventing various potential food safety risks that may be encountered. Unlike the previous research on quality investment of food production by enterprises, this paper probes into the evolutionary routes of the behavior strategy selection of subjects in the food supply chain and the preconditions for the equilibrium points of the social co-governance system. It takes the approach of establishing a tripartite evolutionary game model of food suppliers, food manufacturers and consumers on the basis of the social co-governance framework, in view of the above, this paper focuses on the influence of the reputation mechanism and the market contracts among supply chain subjects on the selection of a behavior strategy for quality investment by enterprises under the condition of lawful regulation by government. The results show that every subject selects their own behavior strategy on the basis of the balance of their respective interests. The net disbursement incurred by enterprises for quality investment and the costs of participation in governance by consumers constitute the dominant factors that influence both enterprises' selection of a behavior strategy and the level of social co-governance. Compared with the increase in economic punishment imposed on suppliers for production of risky food raw materials, it is more efficient to control food safety risks by lowering the costs of quality investment by suppliers. Accordingly, this paper proposes advice on policy in an attempt to provide inspiration for preventing and controlling food safety risks.

Deterministic theory of evolutionary games on temporal networks.

Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for studying evolutionary dynamics of any [Formula: see text] pairwise games in structured populations where individuals are connected and organized by temporally activated edges. In the limit of weak selection, we derive replicator-like equations with a transformed payoff matrix characterizing how the mean frequency of each strategy varies over time, and then obtain critical conditions for any strategy to be evolutionarily stable on temporal networks. Interestingly, the re-scaled payoff matrix is a linear combination of the original payoff matrix with an additional one describing local competitions between any pair of different strategies, whose weights are solely determined by network topology and selection intensity. As a particular example, we apply the deterministic theory to analysing the impacts of temporal networks in the mini-ultimatum game, and find that temporally networked population structures result in the emergence of fairness. Our work offers theoretical insights into the subtle effects of network temporality on evolutionary game dynamics.

Game analysis on PPP model operation of abandoned mines ecological restoration under the innovation of central government's reward and punishment system in China.

There is a huge funding gap in the abandoned mines ecological restoration in China. It is of great research value to explore how PPP model can better introduce social capital into the low-profit ecological restoration of abandoned mines. Based on the innovation perspective of the central government's reward and punishment system, this paper constructs an evolutionary game model of "local government-social capital", analyzes the interaction and behavior mechanism of core stakeholders in the operation process of abandoned mines ecological restoration PPP mode, and discusses the influence of evolutionary equilibrium strategy and parameters change on evolutionary strategy under different scenarios by Matlab simulation. The research shows that the abandoned mines ecological restoration needs the support of the central government. When the local government lightly punishes the low-quality service of social capital, the central government needs to pay higher costs to promote all parties to actively participate in the operation and supervision of the PPP project. The revenue and cost of government supervision, the operating subsidy for social capital and the cost saved by social capital in providing bad service are the key factors affecting the evolution of the game between government and social capital. Punishment can effectively spur social capital to keep the contract and operate in the project, but the punishment effect will be ineffective without government supervision. Finally, some suggestions are put forward, such as establishing a long-term supervision mechanism and a reasonable income mechanism for PPP projects, increasing penalties for violations, attracting third parties to reduce supervision costs and strengthening communication between the two parties, so as to make the project take into account the economic performance of social capital and the social welfare of government departments, and achieve dual Pareto improvement.

Ambush strategy enhances organisms' performance in rock-paper-scissors games.

We study a five-species cyclic system wherein individuals of one species strategically adapt their movements to enhance their performance in the spatial rock-paper-scissors game. Environmental cues enable the awareness of the presence of organisms targeted for elimination in the cyclic game. If the local density of target organisms is sufficiently high, individuals move towards concentrated areas for direct attack; otherwise, they employ an ambush tactic, maximising the chances of success by targeting regions likely to be dominated by opponents. Running stochastic simulations, we discover that the ambush strategy enhances the likelihood of individual success compared to direct attacks alone, leading to uneven spatial patterns characterised by spiral waves. We compute the autocorrelation function and measure how the ambush tactic unbalances the organisms' spatial organisation by calculating the characteristic length scale of typical spatial domains of each species. We demonstrate that the threshold for local species density influences the ambush strategy's effectiveness, while the neighbourhood perception range significantly impacts decision-making accuracy. The outcomes show that long-range perception improves performance by over 60%, although there is potential interference in decision-making under high attack triggers. Understanding how organisms' adaptation their environment enhances their performance may be helpful not only for ecologists, but also for data scientists, aiming to improve artificial intelligence systems.

Research on the mechanism of consumer participation in value co-creation by innovative enterprises: An evolutionary game analysis framework.

The profound changes brought about by informatization and digitalization have given rise to the user-centered innovation concept, and value co-creation by enterprises has become an inevitable trend. It has become a pressing issue for scholars to analyze the mechanism of consumer participation in the value co-creation of innovative enterprises. In this paper, by establishing an evolutionary game model between consumers and innovative enterprises, we analyze in depth the mechanism of consumer participation in the value co-creation of innovative enterprises. The results show that the initial cooperation probability between consumers and innovative enterprises directly affects their strategic choices; the establishment of reward mechanisms makes consumers more inclined to choose active participation in value co-creation strategies; as the probability of non-cooperation between the two parties being reported increases, the probability of consumers and innovative enterprises choosing cooperation also increases. Studying the mechanism of consumer participation in the value co-creation of innovative enterprises has essential theoretical and practical significance for enterprises to achieve value creation, enhance competitiveness, and promote innovation. This study not only enriches and develops relevant theories but also provides guidance and support for the practice of enterprises, promoting sustainable development and successful co-creation.

An evolutionary game analysis of algorithmic indirect copyright infringement from the perspective of collusion between UGC platforms and direct infringers.

User-generated content (UGC) is developing rapidly as an emerging platform form, however, the problem of indirect copyright infringement by algorithms is becoming more and more prominent, and infringement governance has become a key act in the development of UGC platforms. When infringement occurs, recommendation algorithms expand the scope and results of infringement, while platforms choose to conspire with direct infringers for their own interests, making it difficult for infringed persons to defend their rights. In order to analyse the influence of different factors in the platform ecosystem on the subject's behavioural strategies, a "platform-infringer" evolutionary game model is constructed, and numerical simulation is used to verify the correctness of the stable results. Based on the simulation results, it is concluded that the factors of uncertain revenue, punishment and reputation loss have important influence on the decision-making behaviour of the subject of infringement governance, and accordingly, the proposed measures on the publishers, platforms and the legal level of the government are conducive to the evolution of the system to the point of positive regulation and stability of rights protection, with a view to promoting the healthier and more stable development of the UGC platforms.

The impact of mobility costs on cooperation and welfare in spatial social dilemmas.

From over-exploitation of resources to urban pollution, sustaining well-being requires solving social dilemmas of cooperation. Often such dilemmas are studied assuming that individuals occupy fixed positions in a network or lattice. In spatial settings, however, agents can move, and such movements involve costs. Here we investigate how mobility costs impact cooperation dynamics. To this end, we study cooperation dilemmas where individuals are located in a two-dimensional space and can be of two types: cooperators-or cleaners, who pay an individual cost to have a positive impact on their neighbours-and defectors-or polluters, free-riding on others' effort to sustain a clean environment. Importantly, agents can pay a cost to move to a cleaner site. Both analytically and through agent-based simulations we find that, in general, introducing mobility costs increases pollution felt in the limit of fast movement (equivalently slow strategy revision). The effect on cooperation of increasing mobility costs is non-monotonic when mobility co-occurs with strategy revision. In such scenarios, low (yet non-zero) mobility costs minimise cooperation in low density environments; whereas high costs can promote cooperation even when a minority of agents initially defect. Finally, we find that heterogeneity in mobility cost affects the final distribution of strategies, leading to differences in who supports the burden of having a clean environment.

Smart transition pathways and development incentive mechanism of China's smart community elderly care industry under market dominance: Considering a multi-subjective behavior game.

Against the backdrop of an aging population, China is actively experimenting with an innovative elderly care model, so smart community elderly care has recently received widespread attention. However, the results of the implementation of the model have not yet met the expectation due to the variety of interests among the relevant participants. In this study, we identified the most core stakeholders in smart community elderly care, developed a four-party evolutionary game model including local governments, communities, service supply enterprises and households with elderly members. By applying the system dynamics method, we simulate the evolutionary paths and explore the complex interactions at the multiparticipant level in order to facilitate the transition of community elderly care services from traditional to smart, and then propose managerial insights for accelerating the construction of smart community elderly care. The results suggest that: (1) the four players in the game influence each other and are intimately related, and the benign interaction between them will further stimulate the vitality of the smart community elderly care industry; (2) appropriate improvement in policy support will strongly promote smart community elderly care, and the incentive effect on the demand side (households with elderly members) is more significant; (3) when households' preference for smart services increases, and the perceived value to communities and enterprises reaches a certain threshold, communities and enterprises will actively adopt smart solution and technology as well as develop stable portfolio strategy; (4) measures such as simultaneously increasing the level of smart and resource synergy will promote the system evolution toward smart services, and the system is more sensitive to the internal behavior of the enterprise than the external behavior between community and enterprise.

A game-theoretic approach for modelling pedestrian-vehicle conflict resolutions in uncontrolled traffic environments.

The interactions of motorised vehicles with pedestrians have always been a concern in traffic safety. The major threat to pedestrians comes from the high level of interactions imposed in uncontrolled traffic environments, where road users have to compete over the right of way. In the absence of traffic management and control systems in such traffic environments, road users have to negotiate the right of way while avoiding conflict. Furthermore, the high level of movement freedom and agility of pedestrians, as one of the interactive parties, can lead to exposing unpredictable behaviour on the road. Traffic interactions in uncontrolled mixed traffic environments will become more challenging by fully/partially automated driving systems' deployment, where the intentions and decisions of interacting agents must be predicted/detected to avoid conflict and improve traffic safety and efficiency. This study aims to formulate a game-theoretic approach to model pedestrian interactions with passenger cars and light vehicles (two-wheel and three-wheel vehicles) in uncontrolled traffic settings. The proposed models employ the most influencing factors in the road user's decision and choice of strategy to predict their movements and conflict resolution strategies in traffic interactions. The models are applied to two data sets of video recordings collected in a shared space in Hamburg and a mid-block crossing area in Surat, India, including the interactions of pedestrians with passenger cars and light vehicles, respectively. The models are calibrated using the identified conflicts between users and their conflict resolution strategies in the data sets. The proposed models indicate satisfactory performances considering the stochastic behaviour of road users - particularly in the mid-block crossing area in India - and have the potential to be used as a behavioural model for automated driving systems.

Dynamics of a Cournot game with bounded rational firms and various scale effects.

In this paper, we focus on a dynamic Cournot game in the market with a nonlinear (isoelastic) demand function. In our model, there are N competing firms featured by nonlinear cost functions, which enhances our model's resemblance to real-world scenarios. Firstly, we focus on the homogeneous case where firms' marginal costs change at equal rates. We establish analytical expressions of the market supply at equilibrium and perform comparative static analysis. In addition, we investigate the local stability under different economies of scale and show that there could be multiple stable equilibria if firms face economies of scale. The heterogeneous case where firms' marginal costs change at distinct rates is much more complex, thus we investigate the duopoly game with only two firms involved. Methods of symbolic computations such as triangular decomposition and partial cylindrical algebraic decomposition are employed in the analytical investigations of the equilibrium, which is nearly impossible by using the pencil-and-paper approach since the closed-form equilibrium is quite complicated. According to the computational results, we derive that two stable positive equilibria may coexist if both firms face economies of scale. Additionally, we conduct preliminary numerical simulations and find two different types of complex dynamics of the model considered in this paper: complex trajectories such as periodic and chaotic orbits may appear; the topological structure of the basins of attraction may be complex.

Medical equipment effectiveness evaluation model based on cone-constrained DEA and attention-based bi-LSTM.

This study constructs a composite indicator system covering the core dimensions of medical equipment input and output. Based on this system, an innovative cone-constrained data envelopment analysis (DEA) model is designed. The model integrates the advantages of the analytic hierarchy process (AHP) with an improved criterion importance through intercriteria correlation (CRITIC) method to determine subjective and objective weights and employs game theory to obtain the final combined weights, which are further incorporated as constraints to form the cone-constrained DEA model. Finally, a bidirectional long short-term memory (Bi-LSTM) model with an attention mechanism is introduced for integration, aiming to provide a novel and practical model for evaluating the effectiveness of medical equipment. The proposed model has essential reference value for optimizing medical equipment management decision-making and investment strategies.