Classical Game Theory Research Articles

Spontaneous Formation of Evolutionary Game Strategies for Long-Term Carbon Emission Reduction Based on Low-Carbon Trading Mechanism

In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices.

Measure-Theoretic Analysis of Stochastic Competence Sets and Dynamic Shapley Values in Banach Spaces

We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path continuity and moment estimates. The dynamic Shapley value is rigorously defined as a càdlàg stochastic process with an axiomatic characterization. We derive a martingale representation for this process and establish its asymptotic properties, including a strong law of large numbers and a functional central limit theorem under α-mixing conditions. This framework provides a rigorous basis for analyzing dynamic value attribution in abstract spaces, with potential applications to economic and game-theoretic models.

Open access publishing and quantum game theory under modified EWL scheme

Game theory deals with the strategies of rational players to obtain the best possible outcomes for a player in a game. Quantum game theory is an extension of classical game theory, where players can adopt quantum strategies to maximize their payoff advantage. In quantum game theory, we have two prominent quantization schemes, namely the Eisert Wilkens-Lewenstein (EWL) scheme and the Marinatto Weber (MW) scheme. Recently, modified EWL scheme is being used to study the game dynamics. In the era of digital information revolution, scientists have unrestricted access to most of the scientific information. Different scientific disciplines prefer different paths of publication either open access or traditional. Taking this as a framework, we model an open-access game played by scientists with open access and traditional publishing as their strategies. In this work, we study these publication patterns using the quantum game theory approach under the modified EWL quantization scheme. Specifically, we investigate the role of entangling operators and players’ strategies in maximizing the payoff (reputation) for the scientists playing in the open-access game.

Game Theoretic Approaches to Modelling Cooperative and Competitive Dynamics for Enhanced Routing and Resource Allocation

The goal of the field of game theory is to simulate scenarios in which decision-makers must choose between courses of action that may or may not conflict and in which the choices made by one element may affect the choices made by other elements. Techniques from game theory have been widely used to solve a variety of engineering design issues. Game theory may be applied to wireless networks to create cooperative strategies between nodes, terminals and network providers, among other organizations. The majority of the time, game theory has been used in networking to address routing and resource allocation issues in competitive settings. Because radio communication channels are typically shared in wireless networks, the actions of one wireless device may have an impact on the communication capabilities of a neighboring device. Game theory may be used to simulate situations such as these. A multi-layered viewpoint is presented in Applications of Game Theory in Wireless Networking, highlighting the domains in which game theory might find practical application. This explains how different wireless network interactions may be represented as games and how game-theoretical methods can accurately mimic or forecast genuine user behavior in cooperative or competitive settings. Because of these similarities, it is possible to grasp the intricate relationships between nodes in this highly dynamic and dispersed environment by using a strong mapping between classical game theory components and network parts

A Study of Quantum Game for Low-Carbon Transportation with Government Subsidies and Penalties

Traditional classical game theory struggles to effectively address the inefficiencies in subsidizing and penalizing the R&D and production of low-carbon transportation vehicles. To avoid the shortcomings of classic game theory, this research integrates quantum game theory with Nash games to explore the characteristics of automakers’ behavior for low-carbon transportation with government subsidies and penalties. We first constructed a low-carbon transportation game model between the government and automakers. Then, the optimal profit strategies for both parties in a quantum entangled state were analyzed. Finally, the impact of quantum superposition states and the initial entangled state on the profit strategies of both parties was simulated and analyzed using Monte Carlo simulations. We find that under the joint effects of government subsidies and penalties, quantum game states and the initial quantum entangled state have a crucial influence on the game’s outcomes. They can encourage the realization of Nash equilibrium and perfect coordination in the quantum game, significantly increasing the profits for both parties. This in turn effectively stimulates automakers to research and produce low-carbon transportation solutions, promoting the rapid development of low-carbon transportation technology. In theory, this research can enrich the Quantum game for improvements in the Nash equilibrium solution for the government to subsidize and penalize the low-carbon transportation problem. Meanwhile, in practice, it can provide guidance and reference in optimal strategy selection conditions for government policymakers and automakers for low-carbon transportation.

Stability, period and chaos of the evolutionary game strategy induced by time-delay and mutation feedback

In the classical evolutionary game theory, mutation is usually considered as a constant, however strategy mutation is affected by strategies in the real game process. Therefore, the main purpose of this paper is to study the effects of mutation feedback and time delays on strategy dynamics, where mutation is a linear feedback related to strategy. First, we construct a co-evolutionary game model with two time delays induced by mutation feedback and analyze the existence and stability of the equilibria of the non-time delay system. The conditions for the coexistence of the two strategies and the mutation rate are obtained. Second, Sotomayor’s theorem is used to explore the transcritical bifurcation of the system. Then, the existence of Hopf bifurcation is investigated by using feedback delay and payoff delay as bifurcation parameters in the time-delay system. Furthermore, we discuss the direction of the Hopf bifurcation, stability and periodic change of the periodic solution in detail. Finally, a series of numerical simulations are used to describe the theoretical analysis. The main results are as follows: (i) Mutation causes negative feedback to cooperative strategy. (ii) As the time delay increases, the stable equilibrium point becomes unstable, and which branches a stable limit cycle. When the time delay continues to increase sufficiently, the stable limit cycle becomes unstable and produces irregular oscillation and chaos. (iii) When the two time delays are large enough, the coexistence of the two strategies becomes that defective strategy is dominant, and the mutation rate also reaches the maximum.

Methodology for regional industrial complex management: Architecture of an agent-based model

Industry is the backbone of the economy of developed countries and individual regions. To optimize management processes in such a complex and multi-level sector, specific economic-mathematical models and practical tools have to be developed. The paper discusses the optimal architecture of the regional industrial complex management model on a modern theoretical-methodological and instrumental (program) basis. The classical management theory, optimization theory and game theory constitute the methodology of this study. Among the research methods applied are agent-based and minimax approaches. We substantiate the use of agent-based modelling to simulate administering the regional industrial complex. The paper presents a three-tiered management architecture consisting of federal, regional and company level authorities (united by type of activity). For each level, control agents are identified and a set of indicators formed, which cover the structure of the phase vector, including its attributes, key parameters, control actions used, risks, a model of the parameters’ dynamics, and a model of the data possessed by the object. We build a hierarchical structure of administration and information relationships in the model and, based on the minimax approach, create an algorithm of agents’ efforts to select optimal control actions. The proposed architecture will allow forming a flexible toolkit for assessing industrial development scenarios and producing the best step-by-step management pattern of the regional industrial complex.

Delay-aware optimized scheduling algorithm for high performance wireless sensor networks

Because of the phenomenal expansion of Internet of Things (IoT) devices around the world, Wireless Sensor Networks (WSN) have become increasingly important among the technical community, and research in this area has been growing exponentially. Researchers have used a variety of WSN technologies to address issues such as processing power constraints, bandwidth-limited connections, delays and energy consumption outlines that arise with sensor networks. However, in terms of delay optimization, affordability and effective energy consumption, WSN is the most suitable and alluring technology. This paper uses an Enhanced Scheduling Algorithm (ESA) with a probabilistic approach called Random Classical Game Theory (RCGT) to reduce the delay in WSN. Retransmissions are minimized when ESA and RCGT are used, which improve WSN delay. The idea is to improve the scheduling algorithm by using RCGT to lengthen the lifespan of the entire network. It has been demonstrated that the improved technique outperforms the existing algorithms in terms of throughput, energy consumption, hop count, delay and lifespan ratio.

A model based on the evolutionary game theory for implementing green mining principles in riverine sand and gravel resources

An evolutionary Game Theory (GT) model was presented to study the dynamics between the mine management and government for implementing Green Mining (GM) principles in riverine sand and gravel mines. In this regard, a game was planned in which the mine management is the executing agent, while the government acts as the supervisor. Investigating the performance of the proposed model, regulatory factors such as governmental incentives and penalties were introduced. In order to compare the results, the effects of regulatory measures on strategy changes by mine management were analyzed into two distinct scenarios: classical GT and evolutionary GT, which provide valuable insights into the complex interactions between mine management and government. The Shahed sand and gravel mine near the Kordan River in Alborz province, Iran, was selected as a case study to validate the developed GT models. The results obtained from the classical GT model showed that a fine of $ 0.2 per tonne and a 30% governmental incentive for the mining and equipment costs, may encourage the mine management to choose the GM strategy. Conversely, the results of the evolutionary GT model indicated that by increasing the government subsidy from 30% to 50%, the rate of encouraging the mine management to choose the GM strategy could be accelerated. This situation is similar to the government incentive for mine management in case of fines from $0.2 to $1 per tonne. According to the results of the evolutionary GT model, when the population ratio increases over time, the selected strategy is more compatible and powerful compared to other ones. Therefore, it is concluded that the mine management in Shahed mine may turn to the GM strategy by imposing a penalty more than $0.6 per tonne.

Impact of misinformation in the evolution of collective cooperation on networks.

Human societies are organized and developed through collective cooperative behaviours. Based on the information in their environment, individuals can form collective cooperation by strategically changing unfavourable surroundings and imitating superior behaviours. However, facing the rampant proliferation and spreading of misinformation, we still lack systematic investigations into the impact of misinformation on the evolution of collective cooperation. Here, we study this problem by classical evolutionary game theory. We find that the existence of misinformation generally impedes the emergence of collective cooperation on networks, although the level of cooperation is slightly higher for weak social cooperative dilemma below a proven threshold. We further show that this possible advantage diminishes as social connections become denser, suggesting that the detrimental effect of misinformation further increases when 'social viscosity' is low. Our results uncover the quantitative effect of misinformation on suppressing collective cooperation, and pave the way for designing possible mechanisms to improve collective cooperation.

Applications of evolutionary game theory in urban road transport network: A state of the art review

A sustainable transport infrastructure is one of the pillars of a sustainable city. However, the literature indicates that urbanization, population growth, changes in population density, and motorization make it difficult for the current road transport system to meet mobility needs for a sustainable city. Traffic crashes and congestion on roads are common as a result of increasing travel times, fuel consumption, and carbon emissions, thereby reducing efficiency and sustainability of mobility systems. Managing these issues involves the interaction of multiple decision-makers, such as vehicles, pedestrians, traffic system operators, and authorities. Accordingly, these are well-suited to being analyzed under the guise of game theory. While classical game theory possesses multiple limitations, it can be argued that evolutionary game theory (EGT) models are more effective for real-world scenarios. This manuscript presents a state-of-the-art review on EGT applied to the road transportation network. The manuscript has divided the application of EGT in advancing the transportation network into multiple categories, i.e., choice-based analysis, traffic management, behavioral interactions, routing operation, and transport safety. This manuscript provides an in-depth analysis and a comparative criticism of the various proposed evolutionary game models. Finally, the manuscript discusses the challenges and provides recommendations for future research on evolutionary game models in transportation networks. These insights aim to facilitate targeted activities based on current research needs.

The quantum foundations of utility and value.

This work presents a generalization of game theory and new perspectives on utility and value. Using quantum formalism, we prove that classical game theory is a special case of quantum game theory. We show that the von Neumann entropy and von Neumann-Morgenstern utility are equivalent and that the Hamiltonian operator represents value. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Half a century of evolutionary games: a synthesis of theory, application and future directions.

Half a century of evolutionary games: a synthesis of theory, application and future directions.

Stackelberg evolutionary game theory: how to manage evolving systems.

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

On the adoption of nonpharmaceutical interventions during the pandemic: An evolutionary game model.

The adoption of behavioral nonpharmaceutical interventions (NPIs) among the public is essential for tackling the COVID-19 pandemic, yet presents challenges due to the complexity of human behaviors. A large body of literature has utilized classic game theory to investigate the population's decisions regarding the adoption of interventions, where the static solution concept such as the Nash equilibrium is studied. However, individual adoption behavior is not static, instead it is a dynamic process that involves the strategic interactions with other counterparts over time. The study of quantitatively analyzing the dynamics on precautionary behavior during an outbreak is rather scarce. This article fills the research gap by developing an evolutionary game-theoretic framework to model the dynamics of population behavior on the adoption of NPI. We construct the two-group asymmetric game, where behavioral change for each group is characterized by replicator equations. Sensitivity analyses are performed to examine the long-term stability of equilibrium points with respect to perturbation of model parameters. We found that the limiting behavior of intervention adoption in the population consists of only pure strategies in a game setting, indicating that the evolutionary outcome is that everyone either takes up the preventive measure or not. We also applied the framework to examine the mask-wearing behavior, and validated with actual data. Overall, this article provides insights into population dynamics on the adoption of intervention strategy during the outbreak, which can be beneficial for policy makers to better understand the evolutionary trajectory of populationbehavior.

Joint optimization of delay and energy in partial offloading using Dual-population replicator dynamics

Due to the growing demand for delay-sensitive applications, partial offloading is very important in fog/cloud computing. In partial offloading, different parts of each task are run in parallel on the end device, fog device, and remote cloud. Generally, a fog/cloud environment consists of independent, selfish agents who want to get more resources. Game theory is a well-known mathematical tool for modeling the interactions of these selfish agents. In traditional game-theoretical models, the mobile user is considered a player. A significant problem with such modeling is scalability. When the number of players is very large, the algorithm may require a long time to converge. The reason is that with the increase in the number of users, the search space for strategies becomes larger. The player must have complete knowledge about competitors to make the best decision. Moreover, the dynamic changes in the fog environment have been ignored in almost all previous studies. This paper presents dual-population modeling using replicator dynamics considering the interaction between the user and the fog environment. Unlike classical game theory, here, the offloading decision (strategy) is viewed as the player. The proposed method can very efficiently model the growing/shrinking behavior of two populations of CPU cycles on both the user and the network sides. It is scalable and converges to a stable equilibrium point regardless of the number of mobile users. We derive conditions under which agents can update their decisions according to the dynamics of the environment. The simulation results reveal the superiority of the proposed method over the full local execution, full offloading, evolutionary algorithms, and the Stackelberg methods. It saves 180% and 380% of the time and energy compared to the best state-of-the-art and baseline methods.

Behavioral Strategies between Government and Real Estate Developers on Prefabricated Buildings Based on Triangular Fuzzy Matrix Game

The subsidies provided by the local government to real estate developers are an important and common practice to promote the development of prefabricated buildings worldwide. However, there is a lack of current research on how government subsidies affect the decision-making of real estate developers with respect to adopting prefabricated construction methods. This study developed a fuzzy game model integrating classical game theory with the triangular fuzzy number approach between the local government and a real estate developer, with different behavioral strategies regarding whether or not to develop prefabricated buildings. It analyzed the Nash equilibriums under the circumstances of pure and mixed strategies and probed the influencing factors of the game equilibrium results via numerical simulation. The research conclusions are as follows: (1) the government should encourage real estate developers to actively participate in prefabricated building by using financial subsidies, fund rewards, process supervision and economic penalties comprehensively; (2) the pure strategy (no manufacturing process supervision, active development) between the government and real estate developers is feasible when the benefit of “active development” for real estate developers is larger than that of “passive development”; (3) positive incentives, such as offering financial subsidies, reducing the cost of prefabricated building development and improving the popularity of prefabricated construction in the building market, should be taken to motivate real estate developers; and (4) negative incentives, such as increasing economic punishment and enhancing manufacturing process supervision, can also facilitate real estate developers to actively participate in the development of prefabricated buildings. Incentives are more effective when the economic penalties are greater than the incremental costs of developing prefabricated buildings. Some policy implications are given to guide prefabricated building market development. Finally, the main problems that need further study in the future are highlighted.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

Rationality Now!

Rationality Now!

A Study on College Students’ Cognitive Intention and Path Choice of Entrepreneurship from the Perspective of Individual and Group Cooperation

In order to study the overall low entrepreneurial enthusiasm of college students, a method was proposed based on the cognitive intention and path choice of college students’ entrepreneurship from the perspective of individual and group cooperation. The method briefly introduces the achievement motivation theory, entrepreneurial intention theory, entrepreneurial cognition theory, classical game theory, computer simulation, and experimental methods. Then, the research hypothesis and model construction method are elaborated, and a questionnaire is designed to study the cognitive intention and path of entrepreneurship of college students. Finally, data analysis and hypothesis testing are described to provide a guarantee for college students’ entrepreneurship. The results show that the fundamental driving force for the great progress of entrepreneurship education in colleges and universities is to meet the needs of both the collective and the individual in the top-level design and to realize the mechanism through which entrepreneurship education can achieve common development.