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In this paper, we provide a novel approach to achieving a desired outcome in a coordination game: the original 2 × 2 game is embedded in a 2 × 3 game where one of the players may use a third action. For a large set of payoff values, only one of the Nash equilibria of the original 2 × 2 game is stable under replicator dynamics. We show that this Nash equilibrium attracts all initial conditions in the interior of the state space for the modified 2 × 3 game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium. This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies). [ABSTRACT FROM AUTHOR]

In 1965, T.S. Motzkin and E. G. Straus established an elegant connection between the clique number of a graph and the global maxima of a quadratic program defined on the standard simplex. Over the years, this seminal finding has inspired a number of studies aimed at characterizing the properties of the (local and global) solutions of the Motzkin–Straus program. The result has also been generalized in various ways and has served as the basis for establishing new bounds on the clique number and developing powerful clique-finding heuristics. Despite the extensive work done on the subject, apart from a few exceptions, the existing literature pays little or no attention to the Karush–Kuhn–Tucker (KKT) points of the program. In the conviction that these points might reveal interesting structural properties of the graph underlying the program, this paper tries to fill in the gap. In particular, we study the generalized KKT points of a parameterized version of the Motzkin–Straus program, which are defined via a relaxation of the usual first-order optimality conditions, and we present a number of results that shed light on the symmetries and regularities of certain substructures associated with the underlying graph. These combinatorial structures are further analyzed using barycentric coordinates, thereby providing a link to a related quadratic program that encodes local structural properties of the graph. This turns out to be particularly useful in the study of the generalized KKT points associated with a certain class of graphs that generalize the notion of a star graph. Finally, we discuss the associations between the generalized KKT points of the Motzkin–Straus program and the so-called replicator dynamics, thereby offering an alternative, dynamical-system perspective on the results presented in the paper. [ABSTRACT FROM AUTHOR]

Evolutionary game theory offers an interesting avenue of exploration for populations that are subdivided into smaller groups based on shared traits. Despite being self-contained, interactions between individuals within each group are crucial. These interactions lead to a game with a block-diagonal payoff matrix having blocks of order two or three. A constant negative payoff is assigned to each player, while the background fitness function is inversely proportional to the density of players in the given territory. Through the lens of reaction–diffusion systems, we examine the circumstances necessary for diffusion-driven instability or Turing instability. We derive a set of necessary conditions for Turing instability around the interior equilibrium state. These results reveal that Turing instability occurs when some diagonal elements are positive, or diagonal cofactors of 3-order blocks are negative in the payoff matrix of the game. In summary, this article explores the dynamics of group interactions in population games and identifies key conditions that lead to instability. [ABSTRACT FROM AUTHOR]

Networked evolutionary game theory is a well-established framework for modeling the evolution of social behavior in structured populations. Most of the existing studies in this field have focused on 2-strategy games on heterogeneous networks or n-strategy games on regular networks. In this paper, we consider n-strategy games on arbitrary networks under the pairwise comparison updating rule. We show that under the limit of weak selection, the short-run behavior of the stochastic evolutionary process can be approximated by replicator equations with a transformed payoff matrix that involves both the average value and the variance of the degree distribution. In particular, strongly heterogeneous networks can facilitate the evolution of the payoff-dominant strategy. We then apply our results to analyze the evolutionarily stable strategies in an n-strategy minimum-effort game and two variants of the prisoner’s dilemma game. We show that the cooperative equilibrium becomes evolutionarily stable when the average degree of the network is low and the variance of the degree distribution is high. Agent-based simulations on quasi-regular, exponential, and scale-free networks confirm that the dynamic behaviors of the stochastic evolutionary process can be well approximated by the trajectories of the replicator equations. [ABSTRACT FROM AUTHOR]

One of the central results of evolutionary matrix games is that a state corresponding to an evolutionarily stable strategy (ESS) is an asymptotically stable equilibrium point of the standard replicator dynamics. This relationship is crucial because it simplifies the analysis of dynamic phenomena through static inequalities. Recently, as an extension of classical evolutionary matrix games, matrix games under time constraints have been introduced (Garay et al. in J Theor Biol 415:1–12, 2017; Křivan and Cressman in J Theor Biol 416:199–207, 2017). In this model, after an interaction, players do not only receive a payoff but must also wait a certain time depending on their strategy before engaging in another interaction. This waiting period can significantly impact evolutionary outcomes. We found that while the aforementioned classical relationship holds for two-dimensional strategies in this model (Varga et al. in J Math Biol 80:743–774, 2020), it generally does not apply for three-dimensional strategies (Varga and Garay in Dyn Games Appl, 2024). To resolve this problem, we propose a generalization of the replicator dynamics that considers only individuals in active state, i.e., those not waiting, can interact and gain resources. We prove that using this generalized dynamics, the classical relationship holds true for matrix games under time constraints in any dimension: a state corresponding to an ESS is asymptotically stable. We believe this generalized replicator dynamics is more naturally aligned with the game theoretical model under time constraints than the classical form. It is important to note that this generalization reduces to the original replicator dynamics for classical matrix games. [ABSTRACT FROM AUTHOR]

Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of utility functions of the decisions over time, as well as in the disease transmission rates. This approach leads to a system of stochastic differential Eqs of a susceptible-infected-recovered (SIR) model coupled with a stochastic replicator Eq. We explore the dynamics of these Eqs and identify new behaviors emerging from stochastic influences. Interestingly, incorporating stochasticity into the utility functions for vaccination and nonvaccination leads to a decision-making model that reflects the bounded rationality of humans. Noise, like social norms, is a two-sided sword that depends on the degree of bounded rationality of each group. We also perform a stochastic optimal control as a discount to the cost of vaccination to counteract bounded rationality.

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential/multiplicative weights algorithm for online learning. Even though these models share the same continuous-time limit—the replicator dynamics—we show that second-order effects play a crucial role and may lead to drastically different behaviors in each model, even in very simple, symmetric 2 × 2 games. Specifically, we study the resulting discrete-time dynamics in a class of parametrized congestion games, and we show that (i) in the biological model of intra-species competition, the dynamics remain convergent for any parameter value; (ii) the dynamics of pairwise proportional imitation exhibit an entire range of behaviors for larger time steps and different equilibrium configurations (stability, instability, and even Li–Yorke chaos); while (iii) in the exponential/multiplicative weights algorithm, increasing the time step (almost) inevitably leads to chaos (again, in the formal, Li–Yorke sense). This divergence of behaviors comes in stark contrast to the globally convergent behavior of the replicator dynamics, and serves to delineate the extent to which the replicator dynamics provide a useful predictor for the long-run behavior of their discrete-time origins. [ABSTRACT FROM AUTHOR]

Rewarding cooperators and punishing defectors are effective measures for promoting cooperation in evolutionary game theory. Given that previous models treated rewards as constants, this does not reflect real-world dynamics changes. Therefore, this paper focused on the classical payoff matrix and examined the dynamic variable rewards affected by cooperation and defection strategies, as well as the impact of time delays. First, for the system without a time delay, we analyzed the existence and stability of numerous equilibrium points and explored transcritical bifurcations under various conditions. Second, for the time-delay system, we discussed a series of delayed dynamical behaviors including Hopf bifurcation, period, and the stability and direction of bifurcation. Finally, the changes of cooperation strategy were observed by numerical simulation, and some interesting results were obtained: (ⅰ) Under certain circumstances, even if the reward given to the cooperators reaches the maximum, the proportion of cooperators is still zero, which means that increasing rewards does not always promote cooperation. (ⅱ) The initial state can affect the choice of cooperation strategy and defection strategy. (ⅲ) The increase of the time delay makes the stable equilibrium point disappear and forms a stable limit cycle.

Socio-ecological models combine ecological systems with human social dynamics in order to better understand human interactions with the environment. To model human behavior, replicator dynamics can be used to model how societal influence and financial costs can change opinions about resource extraction. Previous research on replicator dynamics has shown how evolving opinions on conservation can change how humans interact with their environment and therefore change population dynamics of the harvested species. However, social-ecological models often assume that human societies are homogeneous with no social structure. Building on previous work on social-ecological models, we develop a two-patch socio-ecological model with social hierarchy in order to study the interactions between spatial dynamics and social inequity. We found that fish movement between patches is a major driver of model dynamics, especially when the two patches exhibit different social equality and fishing practices. Further, we found that the societal influence between groups of harvesters was essential to ensuring stable fishery dynamics. Next, we developed a case study of two independently managed fisheries that were connected by fish movement where one human group fishes sustainably while another was over-harvests, resulting in a fishery collapse of both patches. We also found that because in this model, the influence of one human patch on another only communicates the amount of each catch and no fishing strategies were employed, increased social influence decreased the sustainability of the fishery. The findings of this study indicate the importance of including spatial components to socio-ecological models and highlights the importance of understanding species' movements when making conservation decisions. Further, we demonstrate how incorporating fishing methods from outside sources can result in higher stability of the harvested population, demonstrating the need for effective communication across management regimes. [ABSTRACT FROM AUTHOR]

We study a class of asymmetric games with compact Polish strategy sets and provide sufficient conditions for the stability and convergence of profiles under the infinite-dimensional replicator dynamics on such games. We apply these results to analyze the dynamic behavior of the Cournot duopoly with different pricing mechanisms, the rope-pulling game, and a game with a Nash equilibrium profile consisting of uniform distributions. Further, we prove that the set of all Gaussian profiles remains invariant under the replicator dynamics on a large class of quadratic games. Moreover, we study the dynamics restricted to the set of Gaussian profiles, both analytically and numerically. [ABSTRACT FROM AUTHOR]

Rewarding cooperators and punishing defectors are effective measures for promoting cooperation in evolutionary game theory. Given that previous models treated rewards as constants, this does not reflect real-world dynamics changes. Therefore, this paper focused on the classical payoff matrix and examined the dynamic variable rewards affected by cooperation and defection strategies, as well as the impact of time delays. First, for the system without a time delay, we analyzed the existence and stability of numerous equilibrium points and explored transcritical bifurcations under various conditions. Second, for the time-delay system, we discussed a series of delayed dynamical behaviors including Hopf bifurcation, period, and the stability and direction of bifurcation. Finally, the changes of cooperation strategy were observed by numerical simulation, and some interesting results were obtained: (ⅰ) Under certain circumstances, even if the reward given to the cooperators reaches the maximum, the proportion of cooperators is still zero, which means that increasing rewards does not always promote cooperation. (ⅱ) The initial state can affect the choice of cooperation strategy and defection strategy. (ⅲ) The increase of the time delay makes the stable equilibrium point disappear and forms a stable limit cycle. [ABSTRACT FROM AUTHOR]

Featured Application: This article mainly utilizes the advantages and characteristics of evolutionary game theory and, based on the ideas and methods of evolutionary game theory, describes the relationship between the renewable energy generation enterprise group and the power grid enterprise group as a "learning" progressive evolution system, focusing on the evolution process of the relationship between various stakeholders and the influencing factors of evolutionary stability. It provides a reasonable explanation for the spontaneous formation of interest equilibrium between power generation enterprises and power grid companies and provides theoretical reference and policy recommendations for government regulation of the electricity bidding market. The insights derived from the simulations offer a framework that can inform practical applications, particularly in improving grid stability and promoting renewable energy adoption through effective peak shaving mechanisms and electricity pricing strategies. This paper presents a novel approach to optimizing the coordination between renewable energy generation enterprises and power grid companies using evolutionary game theory. The research focuses on resolving conflicts and distributing benefits between these key stakeholders in the context of large-scale renewable energy integration. A theoretical model based on replicator dynamics is developed to simulate and analyze the evolutionary stable strategies of power generation enterprises and grid companies with particular emphasis on peak shaving services and electricity bidding. These simulations are based on theoretical models and do not incorporate real-world data directly, but they aim to replicate scenarios that reflect realistic behaviors within the electricity market. The model is validated through dynamic simulation under various scenarios, demonstrating that the final strategic choices of both thermal power and renewable energy enterprises tend to evolve towards either high-price or low-price bidding strategies, significantly influenced by initial system parameters. Additionally, this study explores how the introduction of peak shaving compensation affects the coordination process and stability of renewable energy integration, providing insights into improving grid efficiency and enhancing renewable energy adoption. Although the results are simulation-based, they are designed to offer practical recommendations for grid management and policy development, particularly for the integration of renewable energies such as wind power in competitive electricity markets. The findings suggest that effective government regulation, alongside well-designed compensation mechanisms, can help establish a balanced interest distribution between stakeholders. By offering a clear framework for analyzing the dynamics of renewable energy integration, this work provides valuable policy recommendations to promote cooperation and stability in electricity markets. This study contributes to the understanding of the complex interactions in the electricity market and offers practical solutions for enhancing the integration of renewable energy into the grid. [ABSTRACT FROM AUTHOR]

Abstract Measuring the dynamics of microbial communities results in high-dimensional measurements of taxa abundances over time and space, which is difficult to analyze due to complex changes in taxonomic compositions. This paper presents a new method to investigate and visualize the intrinsic hierarchical community structure implied by the measurements. The basic idea is to identify significant intersection sets, which can be seen as sub-communities making up the measured communities. Using the subset relationship, the intersection sets together with the measurements form a hierarchical structure visualized as a Hasse diagram. Chemical organization theory (COT) is used to relate the hierarchy of the sets of taxa to potential taxa interactions and to their potential dynamical persistence. The approach is demonstrated on a data set of community data obtained from bacterial 16S rRNA gene sequencing for samples collected monthly from four groundwater wells over a nearly 3-year period (n = 114) along a hillslope area. The significance of the hierarchies derived from the data is evaluated by showing that they significantly deviate from a random model. Furthermore, it is demonstrated how the hierarchy is related to temporal and spatial factors; and how the idea of a core microbiome can be extended to a set of interrelated core microbiomes. Together the results suggest that the approach can support developing models of taxa interactions in the future.

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. [ABSTRACT FROM AUTHOR]

Measuring the dynamics of microbial communities results in high-dimensional measurements of taxa abundances over time and space, which is difficult to analyze due to complex changes in taxonomic compositions. This paper presents a new method to investigate and visualize the intrinsic hierarchical community structure implied by the measurements. The basic idea is to identify significant intersection sets, which can be seen as sub-communities making up the measured communities. Using the subset relationship, the intersection sets together with the measurements form a hierarchical structure visualized as a Hasse diagram. Chemical organization theory (COT) is used to relate the hierarchy of the sets of taxa to potential taxa interactions and to their potential dynamical persistence. The approach is demonstrated on a data set of community data obtained from bacterial 16S rRNA gene sequencing for samples collected monthly from four groundwater wells over a nearly 3-year period (n = 114) along a hillslope area. The significance of the hierarchies derived from the data is evaluated by showing that they significantly deviate from a random model. Furthermore, it is demonstrated how the hierarchy is related to temporal and spatial factors; and how the idea of a core microbiome can be extended to a set of interrelated core microbiomes. Together the results suggest that the approach can support developing models of taxa interactions in the future. [ABSTRACT FROM AUTHOR]

We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock–paper–scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N ⩾ 5 strategies seem to require declining populations, as we show in our discussion. [ABSTRACT FROM AUTHOR]

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One of the most well-known ways for cloud service providers (CSPs) to satisfy customers and reduce SLA violations is to offer resources through an auction market. In previous research based on classical games, the CSP has been considered as a player. A drawback of this type of modeling is that it is not scalable as the number of CSPs increases. In this paper, we use the combination of barter and evolutionary game theory to model the exchange of VM instances among CSPs. First, each CSP estimates the free and used resources. Then, according to the estimated valuation, the CSP announces its bid as a strategy to the auctioneer. We use evolutionary game theory to update the strategy of CSPs and increase their winning probability. The proposed method does not require any monetary exchange or registration of separate contracts between CSPs. In case of an SLA violation, a CSP can reclaim its rented resources from the other party. Moreover, since the violation of the agreement is costly for the violating party, the motivation for cooperation between CSPs increases. The simulation results show that the proposed model can lead to a 5% improvement in social welfare compared to the state-of-the-art barter double auction methods. Moreover, in addition to increasing the payoff of CSPs, it reduces the number of contracts by 3%. [ABSTRACT FROM AUTHOR]

Sustainable pumping of water resource requires intervention by a public agency in order to avoid over-exploitation. We study the evolution of compliance and regulation of groundwater resource when farmers can decide whether to comply or not with pumping quotas in an imitation rule described by replicator dynamics. The public agency sets the optimal quotas and the farmers can choose between compliance or violation of them. We investigate the policy of the public agency which may impose sanctions to discourage withdrawals that deviate from the optimal quota. Using numerical simulations, we analyze the effects that parameters have on the equilibrium of the aquifer and on the farmers' behavior. [ABSTRACT FROM AUTHOR]

We develop a 2 × 2 evolutionary matrix game to model vegetation dynamics due to the effect of autotoxicity. The phenomenon of autotoxicity refers to the rise in soil of negative conditions for plant performance induced by the plants themselves. Relating the Nash Equilibrium Strategies of the game to the stability of the equilibrium points of the induced population dynamics, we investigate under which conditions coexistence of low and highly sensitive to autotoxicity plants occurs and under which a monospecific population dominates the competition. Based on this classification, we investigate the optimal distribution of the two distinct types of plants in order to maximize the cumulative total fitness and determine if this distribution is stable. The primary outcome of this study is to analyze the necessary conditions for achieving the highest total fitness in both mixed and monospecific populations of low-sensitivity plants. In contrast, we argue that a monospecific population of highly sensitive plants can never maximize overall fitness. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of institutional resilience based on a population game. Agents in an economy are randomly matched to play a coordination game with two strategies, cooperate and defect. A breach of contract can be adjudicated in court. Agents can update their strategy, which is modelled using the replicator dynamic. In this context, cooperation is defined as the informal institution, whereas the legal system (contract law) constitutes the formal institution. Institutional resilience is defined by how the formal institution of a functioning legal system complements the informal institution of cooperation in a dynamic way. In the wake of an adverse exogenous shock, the formal institution can prevent a total breakdown of cooperation in the population. [ABSTRACT FROM AUTHOR]

The interplay between the strategies and environments has been shown to affect the evolution of cooperative behavior. Typically, it is assumed that the strategy-related changeable game environment alters the payoffs of strategic interactions, while the reciprocity mechanisms among interactions are usually ignored. Here we respectively study the feedback-evolving games with the direct and indirect mechanisms. This extension is facilitated by assuming the essential properties of reciprocity interactions are incorporated into the linear state-dependent payoff matrix. By the replicator dynamic process, it is found that except for the heteroclinic cycle or internal equilibrium present in the previous model, full cooperation and the highest level of the environment state can be dominant. Furthermore, by exploring the evolutionary dynamics in the local reciprocity-embedded feedback subsystems, we further stress that the most expected system states will be realized so long as cooperation is favored through the reciprocity manner in the circumstance that defection dominates. Even in terms of the internal equilibrium, the higher environmental state level can be enabled without the loss of cooperation. The results may explain the effectiveness of the reciprocity mechanism in avoiding the traps of social dilemmas within the time-invariant game interaction. [ABSTRACT FROM AUTHOR]

This article, titled "Historic Behavior in Nonautonomous Rock-Paper-Scissors Dynamics," explores the concept of historic behavior in dynamical systems. The author challenges the widely held belief that replicator equations in evolutionary game theory satisfy the "Folk Theorem of Evolutionary Game Theory." The paper proposes a class of replicator equations that exhibit historic behavior, where the time averages of the orbit do not converge. The article also presents some auxiliary results and provides a proof for the main theorem. The research was supported by ongoing institutional funding, and the author declares no conflicts of interest. [Extracted from the article]

In finite populations, the stability of three-strategy cyclic dominance dynamics is investigated. A model for three-strategy cyclic dominance games is proposed. The stability of dynamical system corresponding to the model is compared with that of replicator dynamics, it verifies that the results of finite populations are quite different from that of replicator dynamics. [ABSTRACT FROM AUTHOR]

Copyright of Efil Journal of Economic Research / Efil Ekonomi Araştırmaları Dergisi is the property of Efil Journal of Economic Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Evolutionary game theory (EGT) is one of several major developments of game theory. EGT covers ecology and population genetics, among other fields in biology. Most studies in EGT were on a two-player game but non-linearities in biology often occur that need to be considered. Huntington's disease (HD), named after the person who wrote the first detailed description of the disease in 1872, is a neurodegenerative disease that is inherited. This is a case in population genetics, which follows the inheritance pattern called the dominant lethal. In this study, we presented this disease as a multiplayer game among the alleles of the HD gene. We utilized Gokhale and Traulsen's model, wherein a payoff matrix for a four-player game was reduced into a payoff matrix for a two-player game. Depending on the fitness values of each genotype, we have determined that populations consisting of both Huntington and normal alleles may converge to either a purely Huntington, a purely normal, or a mixed composition where both types of genes coexist. If the normal genotype produces more surviving offspring than the other genotypes, then even if a small frequency of normal alleles is injected into a purely Huntington population, the population will be replaced by the normal genotype over time. Such a result was obtained using replicator dynamics and analysis of the stability of equilibrium points. Similar analyses on other genotypes were provided in relation to the inheritance pattern of HD. [ABSTRACT FROM AUTHOR]

The emergence and growth of drug-resistant cancer cell subpopulations during anti-cancer treatment is a major challenge for cancer therapies. Combination therapies are usually applied for overcoming drug resistance. In the present paper, we explored the evolution outcome of tumor cell populations under different combination schedules of chemotherapy and p53 vaccine, by construction of replicator dynamical model for sensitive cells, chemotherapy-resistant cells and p53 vaccine-resistant cells. The local asymptotic stability analysis of the evolutionary stable points revealed that cancer population could evolve to the population with single subpopulation, or coexistence of sensitive cells and p53 vaccine-resistant cells, or coexistence of chemotherapy-resistant cells and p53 vaccine-resistant cells under different monotherapy or combination schedules. The design of adaptive therapy schedules that maintain the subpopulations under control is also demonstrated by sequential and periodic application of combination treatment strategies based on the evolutionary velocity and evolutionary absorbing regions. Applying a new replicator dynamical model, we further explored the supportive effects of sensitive cancer cells on targeted therapy-resistant cells revealed in mice experiments. It was shown that the supportive effects of sensitive cells could drive the evolution of cell population from sensitive cells to coexistence of sensitive cells and one type of targeted therapy-resistant cells.

We consider a financial network represented at any time instance by a random liability graph which evolves over time. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liability edges. These random edges are modified (locally) by the agents over time, as they learn from their experiences and (possibly imperfect) observations. The settlement of the liabilities of various agents at the end of the contract period (at any time instance) can be expressed as solutions of random fixed point equations. Our first step is to derive the solutions of these equations (asymptotically and one for each time instance), using a recent result on random fixed point equations. The agents, at any time instance, adapt one of the two available strategies, risky or less risky investments, with an aim to maximize their returns. We aim to study the emerging strategies of such replicator dynamics that drives the financial network. We theoretically reduce the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). Using the attractors of the resulting ODE we show that the replicator dynamics converges to one of the two pure evolutionary stable strategies (all risky or all less risky agents); one can have mixed limit only when the observations are imperfect. We verify our theoretical findings using exhaustive Monte Carlo simulations. The dynamics avoid the emergence of the systemic-risk regime (where majority default). However, if all the agents blindly adapt risky strategy it can lead to systemic risk regime. [ABSTRACT FROM AUTHOR]

The economic agglomeration of one large city surrounded by satellite cities is observed worldwide and is a topic of keen economic interest. We theoretically investigate where such satellite cities emerge in a two-dimensional economic space in which discrete locations are evenly distributed in a regular-hexagonal domain. To elucidate this emergence, we introduce two viewpoints: (1) the bifurcation mechanism of the full agglomeration at the geographical center in this domain (mono-center), which produces satellite cities around this center, and (2) the existence of invariant patterns, which are equilibria for any value of the transport cost parameter. Theoretically-predicted agglomeration patterns are ensured to exist as stable equilibria for a spatial economic model proposed by Forslid and Ottaviano (2003). We theoretically find one large central city surrounded by hexagonal satellite cities that is a two-dimensional counterpart of the core-periphery pattern (Krugman 1991). Moreover, we demonstrate that spatial patterns of twin cities, three cities, and racetrack cities are absorbed into the mono-center as the transport cost decreases. These transitions are ubiquitously observed in the two-dimensional spatial platform with the geographical center. [ABSTRACT FROM AUTHOR]

An environmental policy to foster virtuous behaviour does not automatically establish a social norm in a population; that is, the policy might not be socially acceptable or enforceable. Some agents feel compelled to abide by environmental social norms and embrace them, but others do not. Some might want to imitate their peers, while others might prefer not to conform and play the role of a maverick. In this model, we describe the heterogeneity of preferences by proposing a taxonomy of five possible agent types that enrich the traditional triplet presented in the literature. We then employ a random matching model to study how a social norm spreads within a population when its composition changes. Considering three relevant population compositions (scenarios), we show that what is most important for the successful diffusion of social norms is not whether, but why agents abide by it. [ABSTRACT FROM AUTHOR]

There are rising concerns that reinforcement algorithms might learn tacit collusion in oligopolistic pricing, and moreover that the resulting 'black box' strategies would be difficult to regulate. Here, I exploit a strong connection between evolutionary game theory and reinforcement learning to show when the latter's rest points are Bayes–Nash equilibria, but also to derive a system of Pigouvian taxes guaranteed to implement an (unknown) socially optimal outcome of an oligopoly pricing game. Finally, I illustrate reinforcement learning of equilibrium play via simulation, which provides evidence of the capacity of reinforcement algorithms to collude in a very simple setting, but the introduction of the optimal tax scheme induces a competitive outcome. [ABSTRACT FROM AUTHOR]

Common resources are often overexploited and appear subject to critical transitions from one stable state to another antagonistic state. Many times resulting in tragedy of the commons (TOC)—exploitation of shared resources for personal gain/payoffs, leading to worse outcomes or extinction. An adequate response would be strategic interaction, such as inspection and punishment by institutions to avoid TOC. This strategic interaction is often coupled with dynamically changing common resources. However, effect of strategic interaction in complex, coupled socio-ecological systems is less studied. Here, we develop replicator equations using evolving games in which strategy and common resources co-evolve. We consider the shared commons as fish dynamics governed by the intrinsic growth rate, predation and harvesting. The joint dynamics exhibit an oscillatory TOC, revealing that institutions need to pay special attention to intrinsic growth rate and nonlinear interaction. Our research shows that the co-evolving system exhibits a broader range of dynamics when predation is present compared to the disengaged fishery system. We conclude that the usefulness, chances and challenges of modelling co-evolutionary games to create sustainable systems merit further research.

In the digital era, smart-home users face growing threats from cyberattacks that threaten their privacy and security. Hence, it is essential for smart-home users to prioritize cybersecurity education and training to secure their homes. Despite this, the high cost of such training often presents a barrier to widespread adoption and accessibility. This study aims to analyze the costs and benefits associated with various cybersecurity investment strategies for smart-home users in the context of cyberattacks. The study utilizes evolutionary game theory to model a game comprised of three populations: smart-home users, stakeholders, and attackers. We derive and analyze the replicator dynamics of this game to determine the evolutionarily stable strategy (ESS). Furthermore, we investigate the impacts of the costs and benefits of cybersecurity investment and cyberattack costs on the ESS. The findings indicate that incurring costs for cybersecurity training is beneficial for smart-home users to protect their homes and families. However, the training costs must be low and affordable for smart-home users in order to ensure their participation and engagement. Additionally, providing rewards for commitment to cybersecurity is crucial in sustaining interest and investment over the long term. To promote cybersecurity awareness and training for smart-home users, governments can incorporate it as a priority in national cybersecurity plans, provide subsidies for training costs, and incentivize good cybersecurity practices. [ABSTRACT FROM AUTHOR]

The paper analyzes a dynamic evolutionary game between banks and firms whose interaction has always been characterized by conflictual relationships. Banks would like that the funding is spent to achieve the objectives of the projects submitted, whereas firms would allocate these loans to obtain private benefits. Following replicator dynamics, we show that banks and firms have predator-prey interactions of the Lotka–Volterra type. Misbehaving firms who seek private benefits are "predators" and banks are their "prey". We analyze the dynamics emerging from the model and we prove that the stability of equilibria depending on the fundamental parameters which describe the banks–firms interaction. In addition, we compare equilibria in terms of Pareto efficiency computing welfare through the average profits with some numerical applications. Finally, we propose a stochastic replicator dynamics approach in order to assume a perturbation in the population growth rate and we suppose as endogenous the monitoring intensity. [ABSTRACT FROM AUTHOR]

This paper investigates a three-strategy (cooperators, toxin producers, and cheaters) N-player division of labor game in bacterial populations. We construct the replicator equation to discuss the evolution of the frequency of the three strategies. Firstly, we prove that the interior equilibrium is always unstable, the three strategies cannot coexist. Secondly, according to Sotomayor's theorem, the system undergoes transcritical bifurcation. Furthermore, the sensitivity of the two-dimensional evolutionary state diagrams to the third parameter (toxin rate, absorption rate, toxin quantity, etc) is analyzed. In summary, high toxicity rates, high levels of toxins, and low levels of competition tend to promote cooperation. All players choose to perform the task, and the cheater disappears. When the absorption rate of cooperators is high enough, only cooperators exist in the population over time. When the absorption rate of the cooperator is low, and the absorption rate of the toxin producer is greater than the threshold, the cooperator and the toxin producer coexist. All players perform the task. Finally, the triangle diagrams and three-dimensional diagrams are presented, which show the initial conditions of the three strategies also affect the dynamic results. As the amount of toxin increases, the range of players who choose to perform tasks widens. [ABSTRACT FROM AUTHOR]

It is estimated that half of all the water extracted, both in developed and developing countries, is unauthorized. This phenomenon makes the management of a groundwater even more difficult to avoid over-exploitation. To study the interaction between farmers, that could be compliant and non-compliant, and a water agency, we built a leader-follower differential game. However, we assumed that the water agency does not know neither ex-ante nor ex-post the number of compliant farmers. After illustrating the results of the dynamic game through numerical simulation using the Western La Mancha (Spain) data, we endogenize the types’ choice in an evolutionary context. Finally, we perform comparative dynamics in the steady state to understand the role of the sanction to counter illegal behaviors. [ABSTRACT FROM AUTHOR]

Male territorial-sneaker polymorphisms are common in nature. To understand how these polymorphisms evolve, we developed a game theoretical model analogous to the classical Hawk-Dove model, but with two important differences. First, we allowed non-uniform interaction rates of strategies to account for the possibility that some interactions between male strategies are disproportionately more frequent than others. Second, we allowed females to exhibit a preference for one type of male and thereby choose mates adaptively. Selection dynamics were modeled using coupled replicator equations. The model confirms that there is a broad range of conditions under which a male polymorphism will arise. We applied the model to understand the genetic polymorphism in adult male Mnais damselflies (Zygoptera). Here, orange-winged adult males defend oviposition sites and mate with females when they arrive, while clear-winged 'sneaker' males are typically non-territorial and opportunistically mate with females. Intriguingly, in allopatry, the males of Mnais costalis and M. pruinosa both exhibit the same orange-clear winged polymorphism but where the species co-occur, males of M. costalis evolve orange wings while males of M. pruinosa tend to evolve clear wings. To understand this phenomenon and evaluate the importance of female choice in mediating it, we extended our game-theoretical model to two interacting species. While both competitive and reproductive interference can explain the male monomorphisms in sympatry, reproductive interference explains the phenomenon under a wider set of conditions. When females of the rarer species change their male preferences to facilitate species discrimination, it can generate runaway selection on male phenotypes., Competing Interests: The authors are not aware of any competing or financial interests., (© The Author(s) 2025. Published by Oxford University Press on behalf of the International Society for Behavioral Ecology.)

This paper proposes a decentralized control scheme that mitigates floods in urban drainage systems (UDSs). First, we develop a partitioning algorithm of the UDS relying on a graph model of the system. Once this is done, we design a local controller for each partition based on the replicator dynamics model (a set of differential equations that describes the evolution of a population of players involved in a strategic game). The decentralized nature of the proposed strategy makes it suitable for applying it in large-scale systems. Stability of the closed-loop system is proved by using Lyapunov theory. Furthermore, we simulate the performance of the decentralized control scheme in two case studies. One of them models part of the Bogotá (Colombia) stormwater UDS. Finally, we compare the proposed technique with two widely used methods for-real time control of UDSs, i.e., constrained linear quadratic regulator (LQR) and model predictive control (MPC).

The article analyzes how conventionalists, pioneers and criminals choose between a national currency (e.g. a central bank digital currency) and a global currency (e.g. a cryptocurrency such as Bitcoin) that both have specific characteristics in an economy. Conventionalists favor what is traditional and historically common. They tend to prefer the national currency. Pioneers (early adopters) tend to break away from tradition, and criminals prefer not to get caught. They both tend to prefer the global currency. Each player has a Cobb-Douglas utility with one output elasticity for each of the two currencies, comprised of backing, convenience, confidentiality, transaction efficiency, financial stability, and security. The replicator equation is used to illustrate the evolution of the fractions of the three kinds of players through time, and how they choose among the two currencies. Each player’s expected utility is inverse U-shaped in the volume fraction of transactions in each currency, skewed towards the national currency for conventionalists, and towards the global currency for pioneers and criminals. Conventionalists on the one hand typically compete against pioneers and criminals on the other hand. Fifteen parameter values are altered to illustrate sensitivity. For parameter values where conventionalists go extinct, pioneers and criminals compete directly with each other. Players choose volume fractions of each currency and which kind of player to be. Conventionalists go extinct when criminals gain more from criminal behavior, and when the parameter values in the conventionalists’ expected utility are unfavorable, causing competition between pioneers and criminals.

In this paper, we construct a nonlinear evolutionary game model to analyze the cooperation mechanisms of the population based on a nonlinear relationship among environment and strategies. In the model, replicator dynamics and aspiration dynamics are used to explore the evolutionary outcomes of collective decision, respectively. The results suggest that the environment tends to become progressively more affluent as the number of cooperators increases, if there is a smaller intensity of environmental destruction of defectors. Interestingly, the enriched environments may attract more defectors. Hence, the population requires a higher level of vigilance against plentiful environments in response to the emergence of defectors. As opposed to replicator dynamics, aspiration dynamics can avoid the persistent oscillatory loops due to the level of aspiration. Further, we investigate the effect of complexity between the population strategy and the environment on the evolutionary outcomes. It is found that higher level of complexity can drive the environment closer to a state of affluence, but the population's strategy structure will not be modified. These insights into the relationship between environment and strategies further our understanding of the evolutionary mechanism of population and society. • A non-linear evolutionary game model considering the feedback between environment and strategies is proposed. • Aspiration dynamics can avoid the persistent oscillatory loops due to the level of aspiration. • The higher level of complexity can drive the environment closer to a state of affluence. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of fractional-order replicator dynamics with government involvement. Firstly, we extend replicator dynamics incorporating government intervention into a fractional-order framework. Subsequently, we introduce a novel property for the vector Lyapunov function tailored to fractional-order replicator dynamics with government involvement. We then use this new property to elucidate the asymptotic stability of fractional-order replicator dynamics with government intervention. Additionally, we tackle the scenario of fractional-order replicator dynamics with time delay, analyzing the system's asymptotic stability in the presence of delay. Finally, we validate the correctness and practicality of these novel theoretical results through numerical simulations conducted under various conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a possible mechanism for obtaining sizeable behavioral structures by simulating a network–agent dynamic on an evolutionary public good game with available social.learning. The model considers a population with a fixed number of players. In each round, the chosen players may contribute part of their value to a common pool. Then, each player may imitate the strategy of another player based on relative payoffs (whoever has the lower payoff adopts the strategy of the other player) and change his or her strategy using different exploratory variables. Relative payoffs are subject to incentives, including participation costs, but may also be subject to mutation, whose rate is sensitized by the network characteristics (social ties). The process discussed in this report is interesting and relevant across a broad range of disciplines that use game theory, including cultural evolutionary dynamics. [ABSTRACT FROM AUTHOR]

In symmetric evolutionary games with continuous strategy spaces, Cressman [ 6 ] has proved an interesting stability result for the associated replicator dynamics relating the concepts of neighborhood superiority and neighborhood attracting for polymorphic states with respect to the weak topology. Similar stability results are also established for monomorphic profiles in 2-player asymmetric games [ 8 ]. In the present paper, we use the model of asymmetric evolutionary games introduced by Mendoza-Palacios and Hernández-Lerma [ 17 ] and obtain a stability result for polymorphic profiles in -player asymmetric evolutionary games with continuous action spaces using the concept of neighborhood strong superiority (Definition 2.3). In particular, we prove that neighborhood strong superior polymorphic profiles are neighborhood attracting. It is also shown that a polymorphic neighborhood strong superior profile is in fact a vector of Dirac measures. Moreover, we establish that the notion of neighborhood strong superiority does not imply strong uninvadability and vice-versa. [ABSTRACT FROM AUTHOR]