Evolutionary game dynamics of multi-agent systems using local information considering hide right

The rapid development of generative artificial intelligence (GenAI) has generated significant economic and social value, alongside risks to user privacy. For this purpose, this study investigates privacy protection in human-AI interaction by employing a combined approach of evolutionary game and system dynamics. A three-party game model was developed to analyze the interactive effects and evolution of privacy protection strategies among the government, GenAI company, and users. Sensitivity analysis through system dynamics simulations was conducted on four kinds of factors—government, company, users, and incentive mechanisms, to reveal how these factors influence the strategy choices of the three parties. The results suggest that the government’s reputation, subsidies, free-riding benefits, fines, rewards from GenAI company to users, and the cost–benefit considerations of all three parties are key factors affecting strategic decisions. Moderate fine and subsidy policies can effectively promote privacy protection, with subsidy policies proving to be more effective than penalty policies. This paper provides theoretical support and decision-making guidance for balancing technological development and privacy protection in human–AI interaction, contributing to the regulated and orderly development of Generative Artificial Intelligence.

Evolutionary game dynamics with non-uniform interaction rates

So far, most studies on evolutionary game dynamics in finite populations have concentrated on a single update rule. However, given the impacts of the environment and individual cognition, individuals may use different update rules to change their current strategies. In light of this, the current paper reports on a study that constructed a mixed stochastic evolutionary game dynamic by combining the imitation and aspiration-driven update processes. The target was to clarify the influences of the aspiration-driven process on the evolution of the level of cooperation by considering the behavior of a population in which individuals have two strategies available: cooperation and defection. Through a numerical analysis of unstructured populations and simulation analyses of structured populations and of the random-matching model, the following results were found. First, the mean fraction of cooperators varied alongside the probability with which the individual adopted the aspiration-driven update rule. In the Prisoner's Dilemma and coexistence games, the aspiration-driven update process promoted cooperation in the well-mixed population but inhibited it in structured ones and the random-matching model; however, in the coordination game, the aspiration-driven update process was seen to exert the opposite effect on cooperation by inhibiting the latter in a homogeneously mixed population but promoting it in structured ones and in the random-matching model. Second, the mean fraction of cooperators changed with the aspiration level in the differently structured populations and random-matching model, and there appeared a phase transition point. Third, the evolutionary characteristics of the mean fraction of cooperators maintained robustness in the differently structured populations and random-matching model. These results extend evolutionary game theory.

Mobile edge computing (MEC) is an emerging paradigm that provides radio access networks with augmented resources to meet the requirements of Internet of Things (IoT) services. MEC allows IoT devices to offload delay sensitive and computation intensive tasks to edge clouds deployed at base stations (BSs). Offloading tasks to edge clouds can alleviate the computing and battery limitations of IoT devices. However, task offloading in MEC for IoT may face serious transmission latency and computation latency problems with massive number of IoT devices. Moreover, some edge clouds can be overloaded due to the spatially inhomogeneous distributions of IoT tasks. To solve these problems, we investigate the workload balancing problems to minimize the transmission latency and computation latency in task offloading process while considering the limited bandwidth resources of BSs and computation resources in edge clouds. We formulate the workload balancing problem as a population game in order to analyze the aggregate offloading decisions. We analyze the aggregate offloading decisions of mobile users through evolutionary game dynamics and show that the game always achieves a Nash equilibrium (NE). We further propose two workload balancing algorithms based on evolutionary dynamics and revision protocols. Simulation results show that our proposed workload balancing algorithms can achieve better performance than existing solutions.

Evolutionary game dynamics with impulsive effects

Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.

Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright-Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player's rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy (ESS) of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner's dilemma games (PDG) and the snowdrift games (SG). We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.

[This item is a preserved copy. To view the original, visit http://econtheory.org/] \n We prove that any regular ESS is asymptotically stable under any impartial pairwise comparison dynamic, including the Smith dynamic; under any separable excess payoff dynamic, including the BNN dynamic; and under the best response dynamic. Combined with existing results for imitative dynamics, our analysis validates the use of ESS as a blanket sufficient condition for local stability under evolutionary game dynamics.

Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Constrained evolutionary games by using a mixture of imitation dynamics

In this paper, the linear invariance of evolutionary game dynamical systems is exploited to systematically realize the spatial partitioning of payoff matrix parameters on a two-dimensional regular lattice with the Neumann neighborhood and the deterministic imitation rule. It is shown that 264 evolutionary game dynamical systems are identified. Meanwhile, a homeomorphism group is set up to establish 132 topological conjugacy equivalence classes. Particularly, for the snowdrift game model, 28 partition regions of the payoff matrix parameters are determined, and the corresponding bifurcation diagram is illustrated. Additionally, some subsystems of the evolutionary snowdrift game dynamical systems are constructed utilizing the glider structures, and the topological conjugacy relationships between these subsystems and infinite product systems of finite-type subshifts are analyzed. Subsequently, their chaotic dynamics is investigated in detail, including properties such as topological mixing and topological entropy, which reflect the complexity and unpredictability of the underlying evolutionary behaviors. It is undeniable that the proposed analytical method can be used to characterize the evolutionary game dynamics on regular grids with symmetric neighborhood structures and deterministic updates, offering a systematic and coherent theoretical framework for analyzing evolutionary dynamics.

This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in which such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest.

IntroductionAddressing the issue of land abandonment in rural areas is a critical strategy for ensuring national food security and promoting high-quality agricultural and rural development.MethodsBased on the assumption of bounded rationality, this paper constructs an evolutionary game model involving three key stakeholders: farmers, village collectives, and local governments. By integrating system dynamics, we simulate and analyze the behavioral strategies of participants, examining the mechanisms of government regulation. Additionally, we explore the moderating role of agricultural social services and further investigate the impact of incentive and penalty measures.Results(1) under specific constraints, the system evolves toward the optimal equilibrium (1,1,1); (2) government policies influence the strategic choices of farmers and village collectives, with excessively high or low incentive and penalty measures proving ineffective in mitigating land abandonment; (3) compared to incentives, penalty measures exhibit a more substantial impact on addressing land abandonment; (4) enhancing agricultural social services can strengthen the effectiveness of incentive and penalty policies.DiscussionBased on these results, the paper offers policy recommendations from four perspectives: regulatory reform, the integration of incentives and penalties, flexible subsidies, and enhanced collaboration among key stakeholders, thereby providing both theoretical insights and practical guidance for addressing land abandonment.

Development strategies for green methanol in the shipping industry with government subsidies: An analysis based on evolutionary game and system dynamics

The evolutionary language game: An orthogonal approach