Narrow Results

In this paper, we introduce a history-fitness-based updating rule into the evolutionary prisoner's dilemma game (PDG) on square lattices, and study how it works on the evolution of cooperation level. Under this updating rule, the player i will firstly select player j from its direct neighbors at random and then compare their fitness which is determined by the current payoff and history fitness. If player i's fitness is larger than that of j, player i will be more likely to keep its own strategy. Numerical results show that the cooperation level is remarkably promoted by the history-fitness-based updating rule. Moreover, there exists a moderate mixing proportion of current payoff and history fitness that can induce the optimal fitness, where the highest cooperation level is obtained. Our work may shed some new light on the ubiquitous cooperative behaviors in nature and society induced by the history factor.

In this paper, we propose a growing spatial network (GSN) model and investigate its topology properties and dynamical behaviors. The model is generated by adding one node i with m links into a square lattice at each time step and the new node i is connected to the existing nodes with probabilities proportional to: , where k_j is the degree of node j, α is the tunable parameter and d_ij is the Euclidean distance between i and j. It is found that both the degree heterogeneity and the clustering coefficient monotonously increase with the increment of α, while the average shortest path length monotonously decreases. Moreover, the evolutionary game dynamics and network traffic dynamics are investigated. Simulation results show that the value of α can also greatly influence the dynamic behaviors.

We present and numerically investigate a quadruple co-evolutionary model for 2 × 2 Prisoner's Dilemma games which allows not only for agents to adopt strategy (Cooperation C or Defection D) and for network topology, but also for the probability of link rewiring that controls the speed of network evolution and the updating rule itself. The results of a series of simulations reveal that C agents in a coexisting phase increase their rewiring probability to avoid neighboring D agents' exploitation through the Game Exit Option. This evolutionary process leads most agents to adopt pairwise updating even though Imitation Max update adopted by all agents brings a higher payoff.

In the light of the prospect theory (PT), we study the prisoner's dilemma game (PDG) on square lattice by integrating the deterministic and Data envelopment analysis (DEA) efficient rule into adaptive rules: the individual will change evolutionary rule and migrate if its payoff is lower than their aspiration levels. Whether the individual choose to change the evolutionary rule and migrate is determined by the relation between its payoff and aspiration level. The results show that the cooperation frequency can hold unchange with the increasing of temptation to defect. The individual chooses to adopt DEA efficient rule and to migrate that can induce the emergence of cooperation as the payoff is lower than its aspiration.

We propose and study the competitiveness of a class of adaptive zero-determinant strategies (ZDSs) in a population with spatial structure against four classic strategies in iterated prisoner’s dilemma. Besides strategy updating via a probabilistic mechanism by imitating the strategy of a better performing opponent, players using the ZDSs can also adapt their strategies to take advantage of their local competing environment with another probability. The adapted ZDSs could be extortionate-like to avoid being continually cheated by defectors or to take advantage of unconditional cooperators. The adapted ZDSs could also be a compliance strategy so as to cooperate with the conditionally cooperative players. This flexibility makes adaptive ZDSs more competitive than nonadaptive ZDSs. Results show that adaptive ZDSs can either dominate over other strategies or at least coexist with them when the ZDSs are allowed to adapt more readily than to imitate other strategies. The effectiveness of the adaptive ZDSs relies on how fast they can adapt to the competing environment before they are replaced by other strategies. The adaptive ZDSs generally work well as they could adapt gradually and make use of other strategies for suppressing their enemies. When adaptation happens more readily than imitation for the ZDSs, they outperform other strategies over a wide range of cost-to-benefit ratios.

The extortion strategy can let its surplus exceed its opponents by a fixed percentage, hence the influence of extortion strategy in a population games has drawn wide attention. In this paper, we study the evolution of extortion strategy with unconditional cooperation and unconditional defection strategies in the Kagome lattice with abundant triangles. Our investigation shows that the extortion strategy can act as catalysts to promote the evolution of cooperation in the networked Prisoner’s Dilemma game. Moreover, proper strength of extortion slope can improve the living environment of the cooperators, thus they enhance cooperation level in the network. Moreover, proper strength of extortion can not only enhance the cooperation level, but also delay the extinction of cooperation. The underlying overlapping triangles help individuals form cooperation cliques that play crucial roles for the evolution of cooperation in those lattices.

Cooperation has attracted considerable attention in recent years. In order to explain altruistic cooperation behaviors that emerged in social dilemmas, a large number of mechanisms have been proposed under the framework of traditional evolutionary game (EG) theory, especially network reciprocity, which has achieved great success. On the other hand, the design of AI algorithm provides a new idea for agents’ decision-making behaviors. The influence of multi-agent reinforcement learning (RL) on cooperation has also received a lot of attention. However, the study of EG with AI algorithm in a population located on spatial structures has not been thoroughly considered. In this paper, we incorporate RL into EGs conducted on spatial structures. By numerical simulations, we find that, in comparison to the well-mixed case, cooperation might be impeded in the population located on spatial structures when the agents update their strategies by adopting Q-learning algorithm instead of pairwise imitation that widely used in traditional EGs. We further reveal the mechanism for the evolution of cooperation in the EGs with Q-learning algorithm, by investigating the distributions of the Q-tables held by agents in the population. Our findings may help understand the different outcomes on spatial structures in EGs with Q-learning algorithm when compared with that in traditional EGs.

The implications and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how decision makers’ (DMs) emotion type and intensity affect rumor spreading. Based on the rank-dependent expected utility (RDEU) and evolutionary game theory (EGT), we construct an evolutionary game model between rumormongers (RMs) and managers (Ms) by considering emotions. We use MATLAB to simulate and reveal the influencing mechanism of DMs’ emotion type and intensity on rumor spreading. The results indicate that the DMs’ strategy choice is not only affected by their own emotion preference and intensity, but also by the other players in rumor spreading. Moreover, pessimism has a more significant influence than optimism on the stability of the evolutionary game, Ms’ emotion is more sensitive to the game results than RMs’ emotion and the emotion intensity is proportional to the evolution speed. More significantly, some earthshaking emotional thresholds are found, which can be used to predict RMs’ behavior, help Ms gain critical time to deal with rumors, and avoid the Tacitus Trap crisis. Furthermore, the evolution results fall into five categories: risk, opportunity, ideal, security and hostility. The results of this work can benefit Ms’ public governance.

This study explored whether a policy with maximum velocity limitation prior to each jam point in a traffic flow system can mitigate jam situations in a highway. To quantify this question, a new cellular automata traffic model based on the Revised S-NFS model was established. We perused two specific scenarios: a jam naturally brought by a high traffic density, and one brought by a lane-closed section placed as an explicit bottleneck. The result of multi-agent simulation (MAS) reveals that such maximum velocity limitation policy can certainly mitigate jam situations when each jam is naturally bought up not by a bottleneck, as proved by several statistics, and cannot improve the traffic flux.

Online peer-to-peer (P2P) lending is an emerging financial mode that combines the Internet with private lending to provide unsecured lending among individuals. The interest rate and risk depend on online lenders and borrowers’ behavior choices and game in the context of P2P lending. In this paper, we propose an evolutionary behavior forecasting model for online participants based on the risk preference behavior of lenders and the credit choice of borrowers. We highlight four evolutionary equilibrium states of online lenders and borrowers’ behavior and their effects on the risk of online P2P lending platforms. We run a numeric experiment using the Paipaidai platform in China as a case and find that the evolutionary behavior of online lenders and borrowers is determined by the mutual effect of the interest rate, information gathering cost, borrowing cost, and yield rate. This paper uses evolutionary game methodology to analyze online P2P lending behavior in China and explores P2P fund success from the dual perspective of lenders and borrowers.

This paper describes the interaction between major and auxiliary container transport carriers (MCs and ACs) by using evolutionary game theory models, enabling them to cooperate and share information under sufficient penalties and incentives. The MCs are generally logistics service integrators, mega shipping companies, and port authorities, which affect the regulations and technology innovation much, while the ACs are rest carriers and logistics service providers. Evolutionary games are used to study the cooperative behavior between MCs and ACs in the shipping industry. As indicated by analytical studies, the cooperation between MCs and ACs will be invalid without introducing blockchain technology for adequate supervision. In peak season, an evolutionary equilibrium incurs between MCs and ACs under cooperation or non-cooperation behavior strategies. However, in off-seasons, the evolutionary equilibrium is unique in which both parties choose not to cooperate. When introducing blockchain technology for supervision, the carriers will cooperate in peak and off-seasons. Besides, through a simulation analysis of the established models, the results show that the introduction of blockchain technology can enable carriers to form cooperative alliances, resolve inefficient operations, and achieve a long-term stable equilibrium strategy. We can also apply the results for reference to the regional shipping industry.

Cloud/ fog computing resource pricing is a new paradigm in the blockchain mining scheme, as the participants would like to purchase the cloud/ fog computing resource to speed up their mining processes. In this paper, we propose a novel two-stage game to study the optimal price-based cloud/ fog computing resource management, in which the cloud/fog computing resource provider (CFP) is the leader, setting the resource price in Stage I, and the mining pools act as the followers to decide their demands of the resource in Stage II. Since mining pools are bounded rational in practice, we model the dynamic interactions among them by an evolutionary game in Stage II, in which each pool pursues its evolutionary stable demand based on the observed price, through continuous learning and adjustments. Backward induction method is applied to analyze the sub-game equilibrium in each stage. Specifically in Stage II, we first build a general study framework for the evolutionary game model, and then provide a detailed theoretical analysis for a two-pool case to characterize the conditions for the existence of different evolutionary stable solutions. Referring to the real world, we conduct a series of numerical experiments, whose results validate our theoretical findings for the case of two mining pools. Additionally, the impacts from the size of mining block, the unit transaction fee and the price of token on the decision makings of participants are also discussed.

With the implementation of new environmental policies such as “carbon peak” and “carbon neutrality”, reducing carbon emissions through the development of clean technology in the automobile industry has become a key priority. However, the high cost of researching and developing green technology has led to high vehicle prices, which poses a major barrier to expanding the market share of such vehicles. The decision of whether to invest in research and development (R&D) has become a challenging one for automobile manufacturers. In this paper, we propose a game theory analysis scheme to study the R&D investment decisions of two original equipment manufacturers (OEMs) — an electric vehicle manufacturer (EM) and a fuel vehicle manufacturer (FM) — who, respectively, produce electric vehicles (EVs) and fuel vehicles (FVs). Since the manufacturers exhibit bounded rationality and their R&D investment decision-making involves a long-term, continuously learning and adjusting process, we model this dynamic R&D investment decision-making process as an evolutionary game to study manufacturers’ stable evolutionary behaviors in optimal R&D investment strategies. Different from previous literatures, where the prices for vehicles with high or low R&D investment were predetermined, we optimize the price of each vehicle, market shares, and optimal utilities of OEMs using a two-stage Stackelberg game for each investment strategy profile. Additionally, we use the Personal Carbon Trading (PCT) mechanism to help reduce carbon emissions. The main contribution of this paper is exploring the conditions for the evolutionary stable strategies (ESSs) of the evolutionary game based on the optimal utilities of the OEMs under different strategy profiles. The impact of preference parameters and green R&D coefficients on the OEMs’ decisions, as well as consumers’ purchase choices are also discussed. Finally, numerical simulations using real-world data are conducted to verify the theoretical results on ESSs.

The meteoric rise of live streaming e-commerce, an emergent form of electronic commerce, is accompanied by frequent occurrences of “live streaming mishaps”. Live streaming’s visual nature offers a more varied and intuitive method for showcasing traceable products, thereby enhancing customer engagement and contracting customers. However, due to the diverging interests, conflicts and contradictions among the stakeholders in traceable products persist, introducing challenges and complexities to its management. We develop an evolutionary game-theoretical model involving three key entities: the platform, anchors (live stream hosts), and consumers. Through the establishment of a payment matrix, we analyze their interactive behaviors and equilibrium states. Additionally, we examine the impacts of key factors on the system and find that platforms and anchors play a pivotal “dual-core” role in traceable product management within the live streaming e-commerce landscape. Moreover, factors such as market attention, anchor characteristics, and consumer dissatisfaction emerge as critical determinants for effective traceable product management. This research contributes valuable insights into enhancing coordination of traceable products in live streaming e-commerce. It offers perspectives on the evolutionary dynamics and strategies for selecting traceable products by platforms, broadcasters, and consumers.

Extortion strategies can unilaterally transcend any opponent’s expected payoffs and promote cooperative behaviors in an iterated prisoner’s dilemma game. However, extortion strategies have the evolutionary instability if the players game with uniform structure. In this paper, we study the influence of extortion on the evolution of cooperation in the scale-free network with the player’s game payoffs calculated by average payoffs and the strategy update rule according to the replicator dynamics rule. Firstly, we study the stability of evolutionary game results after introducing the extortion strategy and the influence of evolution extortion on cooperation. In addition, we compare the results of our model with the donation games of the accumulated payoff in the BA networks. Moreover, we study the influence of the model parameters on game results. The results show that extortion can form long-term stable relationships with neighbors and the average payoffs’ inhibiting effect of cooperative behaviors disappear after introducing the extortion strategies in the scale-free network. The smaller value of the extortion actor and the benefit factor have a greater effect on the stability density of the strategies but the initial strategy density does not.

Understanding the appearance and maintenance of cooperation behavior is one of the most interesting challenges in natural and social sciences. Evolutionary game is a useful tool to study this issue. Here, we consider a basic strategy updating rule: the probability of a player updating its strategy is affected by the learning ability, which is determined by payoffs and an aspiration parameter $w$. For positive $w$, learning ability is directly proportional to player’s own payoff. When $w$ equals 0, it returns to traditional situation. It is found that increasing the value of $w$ can promote the cooperation. With the increase of $w$, the player’s learning ability is continuously enhanced, and the probability of changing strategies is also increased. This paper verifies the influence of the introduced selection parameter $w$ on the cooperation rate from different aspects. We tested this hypothesis through the Monte Carlo simulation, and demonstrated that introducing $w$ changed the network of interaction effectively, therefore changing the effect of the adoption of the strategy on the uncertainty of cooperation evolution. This paper analyzed the results of the payoff-dependence learning ability of different players when they imitate the strategies of their opponents, which can effectively promote the evolution of cooperation.

The evolutionary game on graphs provides a natural framework to investigate the cooperation behavior existing in natural and social society. In this paper, degree-based pinning control and random pinning control are introduced into the evolutionary prisoner's dilemma game on scale-free networks, and the effects of control mechanism and control cost on the evolution are studied. Numerical simulation shows that forcing some nodes to cooperate (defect) will increase (decrease) the frequency of cooperators. Compared with random pinning control, degree-based pinning control is more efficient, and degree-based pinning control costs less than random pinning control to achieve the same goal. Numerical results also reveal that the evolutionary time series is more stable under pinning control mechanisms, especially under the degree-based pinning control.

The competitive relationships among ports become complicated as the consequence of the prosperity of international trade. Typical oligopoly competition models cannot be competent for the analysis of ports competition in real scenario. In this paper, the scale-free network is adopted to characterize the interactions among ports with various number of neighbors. For each port node, not only direct competition but also indirect influences exerted by its neighbor are taken into account. Following the hypothesis in evolutionary game theory, social learning behavior among competitors occurs generally in our model. Conforming to reality, strategies considering both price collusion and price competition are proposed to investigate evolutionary dynamics of competition among ports in the self-organization process of imitation. It shows that neighbors have the same goal but play different roles in affecting strategy transition during the evolution with two competitive means. We explore how evolutionary dynamics are influenced by different imitation means. Then this paper verifies that price collusion is more conducive to port development when abundant resources is provided. Our results obtained in this evolutionary framework with different imitation means may enhance port-operation efficiency.

Data-driven smart investment decisions are important for financial development, which has not received much attention from academia. As a result, this paper resorts to the evolutionary game theory, and proposes a novel multi-agent financial investment decision method. Specifically, an evolutionary game theory-based decision-making approach is formulated as the main model for the research purpose. By considering the strategic choices and adaptability among various entities, a comprehensive analysis of the behavior and decision-making process of entities in the financial market is achieved. This paper combines stock exchanges and financial data providers (Bloomberg and Thomson Reuters) to conduct case studies on this method, verifying its effectiveness and feasibility in practical applications. By comparing traditional financial investment decision-making methods, it can be seen that the proposal has significant advantages in improving investment efficiency, reducing risks, and responding to market volatility. This paper delves into the multi-agent financial investment decision-making method based on the evolutionary game, providing new ideas and methods for academic research and practical applications in the financial field.

The emergence and evolution of cooperation in complex natural, social and economical systems is an interdisciplinary topic of recent interest. This paper focuses on the cooperation on complex networks using the approach of evolutionary games. In particular, the phenomenon of diversity-optimized cooperation is briefly reviewed and the effect of network clustering on cooperation is treated in detail. For the latter, a general type of public goods games is used with the result that, for fixed average degree and degree distributions in the underlying network, a high clustering coefficient can promote cooperation. Basic quantities such as the cooperator and defector clusters, mean payoffs of cooperators and defectors along their respective boundaries, the fraction of cooperators for different classes as well as the mean payoffs of hubs in scale-free networks are also investigated. Since strong clustering is typical in many social networks, these results provide insights into the emergence of cooperation in such networks.