Evolutionary Games: An Algorithmic View

Chapter 28 Game theory and evolutionary biology

We analyze the main dynamical properties of the evolutionarily stable strategy (ℰ𝒮𝒮) for asymmetric two-population games of finite size and its corresponding replicator dynamics. We introduce a definition of ℰ𝒮𝒮 for two-population asymmetric games and a method of symmetrizing such an asymmetric game. We show that every strategy profile of the asymmetric game corresponds to a strategy in the symmetric game, and that every Nash equilibrium (𝒩ℰ) of the asymmetric game corresponds to a (symmetric) 𝒩ℰ of the symmetric version game. We study the (standard) replicator dynamics for the asymmetric game and we define the corresponding (non-standard) dynamics of the symmetric game. We claim that the relationship between 𝒩ℰ, ℰ𝒮𝒮 and the stationary states (𝒮𝒮) of the dynamical system for the asymmetric game can be studied by analyzing the dynamics of the symmetric game.KeywordsNash EquilibriumMixed StrategyPure StrategyEvolutionary GameStable StrategyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The classification and recycling of construction waste is important for reducing waste emissions, preventing marine pollution, and protecting the natural environment, which can promote carbon trading and carbon sink cycles. Based on the evolutionary game theory, this paper investigated the evolutionary decision-making process and stable strategies of three stakeholders in the construction waste recycling system, namely, the Department of Environment Regulation (DER), the Construction Waste Recycler (CWR), and the Construction Project Contractor (CPC), and analyzed the main factors affecting the stakeholders’ strategies, the evolutionary stable strategies and stable conditions from the perspective of public participation and carbon trading. Then, a DER-CWR-CPC benefit matrix and a replicator dynamics equation representing strategy selection were constructed, in which parameters represent the interest relationship of the three parties, and evolutionary stable strategy (ESS) points were obtained by solving the Jacobian matrix. Finally, the validity of the model was verified by taking the actual values into the simulation. The results showed that DER needs to actively participate in the early stage of the development of the construction waste classification and recycling system, but with the increase of enterprises choosing to recycle construction waste, DER can gradually reduce its intervention in these enterprises. Setting reasonable incentives and penalties, mobilizing public participation, and developing cleaner construction waste sorting equipment to obtain more carbon emission trading targets can facilitate the development of construction waste recycling systems.

With the increasing popularization and application of the smart grid, the harm of the data silo issue in the smart grid is more and more prominent. Therefore, it is especially critical to promote data interoperability and sharing in the smart grid. Existing data-sharing schemes generally lack effective incentive mechanisms, and data holders are reluctant to share data due to privacy and security issues. Because of the above issues, a dynamic incentive mechanism for smart grid data sharing based on evolutionary game theory is proposed. Firstly, several basic assumptions about the evolutionary game model are given, and the evolutionary game payoff matrix is established. Then, we analyze the stabilization strategy of the evolutionary game based on the payoff matrix, and propose a dynamic incentive mechanism for smart grid data sharing based on evolutionary game theory according to the analysis results, aiming to encourage user participation in data sharing. We further write the above evolutionary game model into a smart contract that can be invoked by the two parties involved in data sharing. Finally, several factors affecting the sharing of data between two users are simulated, and the impact of different factors on the evolutionary stabilization strategy is discussed. The simulation results verify the positive or negative incentives of these parameters in the data-sharing game process, and several factors influencing the users’ data sharing are specifically analyzed. This dynamic incentive mechanism scheme for smart grid data sharing based on evolutionary game theory provides new insights into effective incentives for current smart grid data sharing.

The key technology concerning the dispatch and control of the cyber-physical-social systems (CPSS) integration and group machine learning (ML) based Web-of-Cells (WoC) is systematically investigated, aiming to develop an intelligent dispatching system that has a high penetration of distributed generations (DG). Based on practical engineering demands and the weakly-centralized WoC, which is characterized by self-organized co-evolution, high independence, high-efficiency synergy, and autonomous learning, a variety of advanced theoretical tools such as complex network theory, group ML, evolutionary game theory, and CPSS-based parallel system theory have been adopted to address the following key issue: How can we achieve overall optimal dispatching and control decision-making in a class of complex systems relying on a large number of group cells with characteristics of limited information, weak controllability, small capacity, and wide distribution? Starting from this, four basic scientific issues are discussed: 1) a modeling method for a self-organized coupled network of the CPSS integration-based WoC; 2) a stability analysis and stability control system of the self-organized evolution of the WoC; 3) a highly autonomous group intelligent decision (GID) method of an independent cell; 4) multi-cell synergetic evolutionary game and GID theory. Hence, an innovative breakthrough on the intersection of complex network game theory and group ML is expected to be obtained, contributing to the emergence of group knowledge in complex circumstances and a significant improvement in the level of GID. Lastly, based on the theoretical investigation in this paper, explorations on the development of the CPSS platform for the WoC as well as its engineering practice in application are conducted. Furthermore, the in-depth development of the WoC, as well as its anticipated technical challenges, are prospected and analyzed with the hope of applying it on practical smart distribution grid demonstration projects in the future.

Implementation of a multi-agent environmental regulation strategy under Chinese fiscal decentralization: An evolutionary game theoretical approach

Juglone is a 1,4-naphthoquinone (1,4-NQ) and the allelochemical responsible for the well-known toxic effects of black walnut (Juglans nigra) and other members of the Juglandaceae. Juglone affects a variety of weed species via a mode of action unlike any commercially available herbicides, and thus has the potential to be used as a new natural product-based herbicide. However, lack of knowledge about its metabolism precludes introducing juglone biosynthesis traits into resistant crops through biotechnology. Herein, we established that juglone is derived from the phylloquinone pathway at the level of the intermediate 1,4-dihydroxy-2-naphthoic acid (DHNA). Phylloquinone is a primary 1,4-NQ made by all plants for photosynthetic electron transport. Despite the fundamental importance of phylloquinone, there are still unanswered questions about the subcellular architecture of the phylloquinone pathway. In chapter 3, we show that o-succinylbenzoate CoA-ligase is localized to both chloroplasts and peroxisomes and that its activity is vital in both organelles. The required dual localization of CoA ligase activity is a theme common to other plant pathways with CoA metabolic steps occurring in peroxisomes and thus leads us to propose a revised model of the phylloquinone pathway. Lastly, given the potential of introducing juglone biosynthesis as part of novel weed management strategies, we investigated the circumstances, costs, and benefits of producing allelochemicals in crops using an evolutionary game theory model. Together, this work (i) shows that the phylloquinone pathway provides crops with the biosynthetic framework to produce juglone, (ii) sheds new light on the phylloquinone pathway architecture, and (iii) reveals the circumstances in which producing an allelochemical will be an evolutionarily stable strategy. We envision these results will assist biotechnological efforts to utilize juglone as a novel, natural product-based herbicide.

In the accelerating digital economy, small and medium-sized enterprises (SMEs) encounter a dual challenge in pursuing ambidextrous digital innovation (exploratory and exploitative), constrained by limited resources and path dependence. Industrial internet platforms, functioning as central hubs for resources, technologies, and data, play a pivotal role in addressing these challenges. Existing research has not sufficiently examined how the strategic interactions among governments, platforms, and SMEs influence SMEs’ ambidextrous digital innovation decisions within platform ecosystems. This study investigates these coupled strategies by constructing a group dynamic decision-making model grounded in evolutionary game theory. By employing replicator dynamics and evolutionary stability analysis, it reveals the patterns of strategic selection, and simulation experiments are conducted with reference to case studies. The results reveal significant coupling effects among the three parties’ strategies: the system may converge to a “conservative equilibrium” or shift toward a “high-level innovation equilibrium.” Critical factors, including ecosystem synergy value, technological spillover, government subsidy intensity, and the cost of platform empowerment, jointly determine the trajectory and pace of system evolution. Breaking away from suboptimal equilibria requires the establishment of risk-sharing and reward-sharing mechanisms, which foster evolutionary stability of the digital innovation ecosystem through tripartite collaboration. This research broadens the application of ambidextrous innovation theory in platform ecosystems and offers theoretical and practical insights for SME decision-making, platform empowerment, and policy design.

Energy efficiency construction in rural areas is of great significance to society. There will be a lot of social benefits and economic positive externalities. Because of positive externalities, the energy-saving products’ cost is higher than the traditional products’ cost. The famers have a very low income, and they are price-sensitive. There is always a market failure. According to the consumer features of the farmers summarized, the asymmetric 2 × 2 noncooperative repeated game between the government and the farmers is analyzed through the method of evolutionary game theory. The game model is used to research the government regulatory role for promoting the energy-efficient construction after the implementation of incentives. Then, the game equilibrium is obtained which is evolutionary stable strategy (ESS) and is uncertain and dependent on the initial states of the game. According to the game conclusion, the game equilibrium and parameters of the game were given. The government that is dominant in the game and with higher level of rationality should guide the farmers with a lower level of rationality to reach the Pareto optimal Nash equilibrium.

IntroductionPromoting the digital transformation of rural industry is a necessary path for the modernization and development of agriculture and rural areas.MethodsBased on the evolutionary game theory, this study constructs a tripartite evolutionary game model of the government, digital technology suppliers, and rural industry subjects. It analyzes the evolutionary stability strategies and influencing factors of each subject and carries out numerical simulation analysis using MATLAB.ResultsThe study found that: (1) The strategy choices of each game subject affect each other. The probability of the government's “encourage” strategy decreases with the increase of the probability of the digital technology supplier's active “supply” or the probability of the rural industry subject's active “adopt.” Similarly, a higher “encourage” probability by the government and a higher “adopt” probability by the rural industrial entities showed a higher “supply” probability by the digital technology providers. (2) The size of the initial probability and the change of each parameter have an important impact on the choice of behavioral strategy in the main body of the game. The evolutionary stability strategy eventually converges to the government choosing “encourage,” digital technology suppliers choosing “supply,” and rural industry subjects choosing “adopt.”DiscussionThis study biggest difference from previous research is that found that the evolutionary stability strategy ultimately converges to encourage the government, supply digital technology suppliers, and adopt rural industry entities. However, there are also shortcomings in the article, such as neglecting other stakeholders. this study finally proposes relevant suggestions from the government, digital technology suppliers, and rural industrial subjects.

Although biological invasions pose serious threats to biodiversity, they also provide the opportunity to better understand interactions between the ecological and evolutionary processes structuring populations and communities. However, ecoevolutionary frameworks for studying species invasions are lacking. We propose using game theory and the concept of an evolutionarily stable strategy (ESS) as a conceptual framework for integrating the ecological and evolutionary dynamics of invasions. We suggest that the pathways by which a recipient community may have no ESS provide mechanistic hypotheses for how such communities may be vulnerable to invasion and how invaders can exploit these vulnerabilities. We distinguish among these pathways by formalizing the evolutionary contexts of the invader relative to the recipient community. We model both the ecological and the adaptive dynamics of the interacting species. We show how the ESS concept provides new mechanistic hypotheses for when invasions result in long- or short-term increases in biodiversity, species replacement, and subsequent evolutionary changes.

Modeling Evolution

Violation problem in coal transportation has puzzled coal enterprises for a long time. Taking use of the evolutionary game theory, the paper builds the game model of coal transportation analyzing the dynamic evolution process of both sides' strategy. The results show that the transportation game is a dynamic process and the coal enterprises' can take measures to promote the transportation game evolving to the ideal running state (no supervision, no violation) and the measures are as follow: reducing the regulatory costs by improving the regulatory efficiency, improving of the transportation assessment mechanism by establishing the performance bonus, increasing the punishment strength and deepening the understanding of the importance of the coal transportation.

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

Evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behavior, but also widely used in economics and social sciences. Recently, in order to reveal the stochastic dynamical properties of evolutionary games in randomly fluctuating environments, the concept of stochastic evolutionary stability based on conditions for stochastic local stability for a fixation state was developed in the context of a symmetric matrix game with two phenotypes and random payoffs in pairwise interactions [Zheng et al., Phys. Rev. E 96, 032414 (2017)2470-004510.1103/PhysRevE.96.032414]. In this paper, we extend this study to more general situations, namely, multiphenotype symmetric as well as asymmetric matrix games with random payoffs. Conditions for stochastic local stability and stochastic evolutionary stability are established. Conditions for a fixation state to be stochastically unstable and almost everywhere stochastically unstable are distinguished in a multiphenotype setting according to the initial population state. Our results provide some alternative perspective and a more general theoretical framework for a better understanding of the evolution of animal behavior in a stochastic environment.