Networked Evolutionary Game Research Articles

Analysis and control of demand response in smart grids: An evolutionary game method

As an effective strategy for load management in smart grids, demand response establishes a bidirectional connection between the electricity supplier and users. Based on the networked evolutionary game theory, this paper studies the demand-response issue for a class of smart grids by using the semi-tensor product of matrices. The paper proceeds as follows. (i) Considering the dynamic interactions between the supplier and users, the demand response is modeled as a heterogeneous networked evolutionary game and is expressed as dynamical form by semi-tensor product. (ii) A sufficient and necessary condition is provided to verify the convergence to a fixed point of the considered system. (iii) A feedback controller is designed to ensure the system electricity consumption and price to maintain at a desired level. Finally, an example is presented to illustrate the feasibility of the proposed method.

Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies

AbstractIn the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper.

Networked Evolutionary Game-Based Demand Response via Feedback Controls

In this paper, the demand response considering interactive decision making between residential users and utility companies is modelled and controlled using networked evolutionary game (NEG) theory. The NEG is achieved via a widely used mathematical tool, namely the semi-tensor product (STP) of matrices, through which, feedback controls can be implemented to dynamically regulate the game-based networks. Firstly, the dynamic interactions between utility companies who provide various energy consumption packs and residential users who can intelligently choose preferable packs are modelled in the state-space form, in which both sides are consistently pursuing their maximum payoffs. Then, a quantitive analysis of such system’s equilibria is conducted using rigorous mathematical derivations, followed by the design of a profile feedback controller when the existing equilibria are not satisfactory towards the required energy consumption. Finally, an illustrative example is demonstrated, where the dynamic gaming between utility companies and users is illustrated and the effectiveness of the proposed feedback control is validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper addresses a very practical engineering problem, which is the demand response in the modern smart grid. Different from general optimization approaches in the existing works, the method proposed by this paper improves the demand response via feedback control of networked systems, which is based on the rigorous matrix approaches via state space equations. In addition, the work in this paper considers very practical factors in actual engineering (i.e., users with different action choices and decision logics being all together), which also provides much value to practitioners than the relevant works with similar theoretical approaches. The method proposed in this paper provides an effective regulation of the demand response in practice and can be flexibly adjusted according to actual situations.

Minimum cost control of weighted networked evolutionary games with switched topologies and threshold

Networked evolutionary games (NEGs) are a class of models that capture the interactions and evolution of strategies among rational agents in a network. In this paper, we study the problem of minimum cost control of NEGs with switched topologies and threshold, where the network structure can change over time and the agents have a minimum payoff requirement to survive. Using the semi-tensor product (STP) of matrices, we express the weighted networked evolutionary game in an algebraic form. Then, we propose an efficient algorithm to design the minimum cost control that ensures the survival of the agents. Finally, we demonstrate the validity of our theoretical results with an example and simulations.

A dynamic incentive mechanism for data sharing in manufacturing industry

Data sharing is a critical component in a blockchain traceability platform. Therefore, creating a reasonable incentive mechanism to ensure that all enterprises participate in data sharing is vital for blockchain platforms. Currently, many researchers employ evolutionary game theory to analyze problems related to data sharing. However, evolutionary game theory typically assumes that the population composed of enterprises is mixed uniformly. Enterprises in the manufacturing industry are not uniformly mixed, as they tend to have specific connections with each other due to the size of enterprises and volume of business. Therefore, a networked evolutionary game is introduced to solve this problem. Firstly, an incentive model for enterprises sharing data is established. Then, a scale-free network is employed to simulate the connections between enterprises. To comprehensively consider the individual and group benefits of enterprises in the game, this study designs a strategy update rule for networked evolutionary game based on Discrete Particle Swarm Optimization and Variable Neighborhood Descent algorithm. To tackle the challenge of determining reasonable incentive values in networked evolutionary games, this study proposes a dynamic incentive mechanism based on the Q-Learning algorithm. Finally, the experiments indicate that this method can successfully facilitate the stable involvement of enterprises in data sharing.

Fear of missing out and market stability: A networked minority game approach

This study examines the influence of the fear of missing out (FOMO), which spreads through social networks, on financial market stability. We extend the networked evolutionary minority game model, a widely used methodology in econophysics, by incorporating the asymmetric reward structure and investors’ FOMO. The agent-based simulation results reveal that the asymmetric reward structure significantly improves the stability of the system. In contrast, the FOMO significantly reduces market stability. FOMO-induced irrational behavior disrupts the market’s normal functioning, leading to decreased stability. However, as agents become more interconnected and actively adapt their strategies, the adverse effects of FOMO on the system diminish.

Weighted Nash equilibrium of incomplete‐profile networked evolutionary games with multiple payoffs

AbstractThis paper investigates the existence and convergence of weighted Nash equilibrium for incomplete‐profile networked evolutionary games with multiple payoffs. First, the incomplete‐profile networked evolutionary game under probabilistic myopic best response adjustment rule is transformed into an algebraic form based on the semi‐tensor product of matrices. Second, a method for calculating weighted Nash equilibrium is presented, and the relationship between weighted Nash equilibrium and positive‐probability fixed point is derived. Furthermore, a criterion is provided to verify whether the profiles in the feasible profile set can converge to the set of weighted Nash equilibriums with probability one. Finally, an illustrative example is given to support the new results obtained in this paper.

Research on low-carbon technology diffusion among enterprises in networked evolutionary game

The diffusion of low-carbon technologies (LCTs) is one of the important measures to mitigate carbon emissions. Local governments, enterprises, and consumers are crucial participants in the complex adaptive LCT diffusion system. In this context, this study builds an evolutionary game model based on a complex network comprised of three sub-networks, which respectively represent the connections of local governments, enterprises and consumers. Using this model, this research explores the impacts of homogeneous subsidies, heterogeneous subsidies, homogeneous carbon taxes, heterogeneous carbon taxes, targeted penalties, market demand, and policy mixes combined with these instruments on LCT diffusion. The results show that carbon taxes, subsidies, and penalties can all promote the diffusion of LCTs. The comprehensive effect of LCT diffusion brought by heterogeneous subsidies or carbon taxes is slightly better than those achieved by the fixed subsidy or the carbon tax equal to their respective mean values. Compared with pure carbon tax and subsidy policies, the mixed policy of introducing targeted fines brings a more obvious LCT diffusion effect. However, none of these policy interventions can achieve the complete spread of LCTs. Meanwhile, increasing the potential market demand for low-carbon products can achieve a very significant diffusion of LCTs. And when the proportion of white consumers reaches 0.9, the full proliferation of LCTs can be realized. This research develops a valuable framework that enriches the modeling practice of the diffusion of LCTs and provides insights for implementing well-designed policy packages.

Impact of Decision Feedback on Networked Evolutionary Game with Delays in Control Channel

Impact of Decision Feedback on Networked Evolutionary Game with Delays in Control Channel

Impact of social reward on the evolution of cooperation in voluntary prisoner’s dilemma

The existence and sustainability of cooperation is a critical issue in nature and social systems. Reward is an essential mechanism to enhance cooperation. Meanwhile, some individuals loathe competition and then choose to escape and become a loner in competition. In this scenario, we propose a four-strategy networked evolutionary game model involving rewarders, loners, cooperators, and defectors. The classical square lattice and the Erdös–Rényi random network are adopted to describe the interaction between individuals. The four-strategy model is an extension of the classic prisoner’s dilemma game model. The simulation results show that the introduction of new strategic choices can significantly improve cooperation in the population. The promotion level of cooperation is directly correlated with reward intensity and negatively correlated with reward cost. With regard to the evolution of altruistic behaviors, the fixed income from interactions with loners has an impact that is connected to the temptation to defect. Furthermore, by analyzing characteristic snapshots of four strategies, we further dissect the essence of the evolution of cooperation. As the temptation value increases, cooperators and rewarders first form compact clusters, then more and more loners join to resist the intrusion of defectors. Eventually, the three strategies coexist stably in a spatially structured population. Our research may shed some light on exploring the nature of cooperation and solving social dilemmas in the future.

A Matrix Approach to the Modeling and Analysis of Network Evolutionary Games with Mixed Strategy Updating Rules

So far, most studies on networked evolutionary game have focused on a single update rule. This paper investigated the seeking of the Nash Equilibrium and strategy consensus of the evolutionary networked game with mixed updating rules. First, we construct the algebraic formulation for the dynamics of the evolutionary networked game by using the semi-tensor product method. Second, based on the algebraic form, the dynamic behavior of networked evolutionary games is discussed, and an algorithm to seek the Nash equilibrium is proposed. Third, we investigate the strategy consensus problem for a special networked evolutionary game. Finally, some illustrative examples are given to verify our conclusions.

How dynamic renewable portfolio standards impact the diffusion of renewable energy in China? A networked evolutionary game analysis

Renewable portfolio standard is an effective administrative tool to guide the behavior of electricity producers and impact the renewable energy diffusion. However, currently the renewable energy quota is generally set to be static and the efficiency is limited. In this paper, we proposed a dynamic renewable portfolio standard policy and we aimed to analyze how it will impact the renewable energy diffusion in China. The connections between electricity producers were simulated under both the perfectly competitive market and monopoly market. And a networked evolutionary game approach is applied considering dynamic linking between the electricity producers. The results show that dynamic quota policy is effective in promoting the proportion of wind power generation from 20% to 59.17% and promoting the proportion of solar power generation from 20% to 79.25%. With the sensitivity analysis, we found that renewable energy quota and the on-grid price are the most influential parameters. The proportion will reach 76.47% if quota is 0.7 and 68.1% if on-grid price is 630 Yuan/MWh. And the influence of tradable green certificate prices and generation cost is limited in promoting renewable energy diffusion. This paper offers the Chinese government a potential implementation for the perfection of national renewable energy diffusion.

Modeling and Dynamics of Networked Evolutionary Game With Switched Time Delay

Time delay is inevitable in information communication. Switched time delay, as a time-varying delay, plays an important role in information interaction between agents. In this article, networked evolutionary games (NEGs) with switched time delay are investigated, including modeling and dynamics analysis. First, the dynamic model of the delayed NEG is proposed, then the algebraic formulation is established by using the algebraic state-space approach. Second, dynamic behavior of the game is discussed, involving general convergence and evolutionarily stable profile analysis. Necessary and sufficient conditions are derived for convergence of the game and evolutionarily stable profile, respectively. Finally, two illustrative examples are employed to demonstrate the validity of the theoretical results.

Dynamics and convergence of hyper-networked evolutionary games with time delay in strategies☆

Networked evolutionary game theory is an important tool to study the emergence and maintenance of cooperation in natural, social, and economical systems. In this paper, we investigate the dynamics and convergence of a generalized networked evolutionary game, i.e., delayed hyper-networked evolutionary game (HNEG), which considers the multi-players in fundamental network game and time delay in strategies simultaneously. Based on the tool of semi-tensor product (STP) of matrices, the definition of delayed potential HNEG and representation of potential function are given. Moreover, we conclude the steps to analyze the dynamics and convergence of delayed potential HNEGs. Considering the efficiency in updating process, we define a new strategy updating rule based on the myopic best response adjustment rule (MBRAR), which is called delayed group-based sequential MBRAR. Furthermore, we prove that delayed potential HNEG converges to one of the pure Nash equilibrium trajectories under this rule. Finally, public good game is provided to illustrate the realistic application of our results.

Strategy optimisation for coupled evolutionary public good games with threshold

In actual economic activities, different economic systems usually interact with each other, and the coupled networked evolutionary game is an important theoretical tool to describe and analyse such economic activities. In this paper, we investigate a kind of coupled evolutionary public good games (PGGs) with threshold which have two enhancement factors. First, the algebraic formulation for the dynamics of the given coupled PGGs is constructed by using a semi-tensor product (STP) of matrices. Then, the strategy optimisation problem is considered based on the algebraic expression, and all valid state feedback controls are designed to make the investment of the coupled evolutionary game in each layer reach their own threshold. Finally, an illustrative example is studied to support our new results.

Intermittent control for demand‐side management of a class of networked smart grids

This work studies the demand-side management problem and intermittent control for a class of networked smart grids. Firstly, the networked smart grid is modelled into a special networked evolutionary game via the semi-tensor product of matrices. Secondly, to minimise the overall cost of all the communities and reduce the control execution time, intermittent control is designed for some communities, in which these players work as controllers at some special strategy profiles. By designing the intermittent open-loop control, a necessary and sufficient condition is provided to assure the stabilisation of the networked smart grid. Then, an intermittent state feedback control is designed, based on which, the smart grid can converge to the desired strategy profile globally. Algorithms that can compute the state feedback controllers are given. Finally, a numerical example is worked out to illustrate the effectiveness of the developed theoretical results.

Modeling, Analysis and Control of Networked Evolutionary Games

Consider a networked evolutionary game (NEG). According to its strategy updating rule, a fundamental evolutionary equation (FEE) for each node is proposed, which is based on local information. Using FEEs, the network strategy profile dynamics (SPD) is expressed as a $k$ -valued (deterministic or probabilistic) logical dynamic system. The SPD is then used to analyze the network dynamic behaviors, such as the fixed points, the cycles, and the basins of attractions, etc. Particularly, when the homogeneous networked games are considered, a necessary and sufficient condition is presented to verify when a stationary stable profile exists. Then the equivalence of two NEGs is investigated. Finally, after a rigorous definition of controlled NEGs, some control problems, including controllability, stabilization, and network consensus, are considered, and some verifiable conditions are presented. Examples with various games are presented to illustrate the theoretical results. The basic tool for this approach is the semi-tensor product (STP) of matrices, which is a generalization of the conventional matrix product.

Evolutionary games played by multi-agent system with different memory capacity

The evolution of cooperation is still an enigma. Resolution of cooperative dilemma is a hot topic as a perplexing interdisciplinary project, and has captured wide attention of researchers from many disciplines as a multidisciplinary field. Our main concern is the design of a networked evolutionary game model in which players show difference in memory capability. The idea of different memory capacities has its origin on the pervasive individual heterogeneity of real agents in nature. It is concluded that this proposed multiple memory capacity stimulates cooperation in lattice-structured populations. The networking effect is also investigated via a scale free network which is associated with the heterogeneous populations structure. Interestingly, results suggest that the effectiveness of a heterogeneous network at fostering cooperation is reduced in the presence of individual memory here. A thorough inquiry in the coevolutionary dynamics of individual memory and spatial structure in evolutionary games is planned for the immediate future.

On finite potential games

A linear system, called the potential equation (PE), is presented. It is proved that a finite game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential. Some interesting examples are presented to illustrate the theoretical results.

Effects of average degree on cooperation in networked evolutionary game

We study effects of average degree on cooperation in the networked prisoner's dilemma game. Typical structures are considered, including random networks, small-world networks and scale-free networks. Simulation results show that the average degree plays a universal role in cooperation occurring on all these networks, that is the density of cooperators peaks at some specific values of the average degree. Moreover, we investigated the average payoff of players through numerical simulations together with theoretical predictions and found that simulation results agree with the predictions. Our work may be helpful in understanding network effects on the evolutionary games.