Search Results (21)

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations. Full article

Individuals can learn about others from sources far from them, and conformity can operate not only on a local scale but also on a global scale. This study aimed to investigate the influence of conformity and global learning on social systems of cooperation using agent-based models of the spatial prisoner’s dilemma game. Three agent-based models incorporating differing types of global conformity were built and analyzed. The results suggested that global learning was generally unfavorable for cooperation. However, in some cases, it enabled resistance to the dominance of defection. Moreover, referring to more diverse sources was less harmful to cooperation than referring to a larger number of similar sources. Evolutionary dynamics were generated according to how competing forces of cooperative and defective agents were balanced. Random drifts toward either the cooperation- or defection-dominant state occurred under some parameter conditions. Whether the drifts were equally or unequally probable toward either state differed according to the parameter conditions. This study highlights the importance of individuals’ psychological biases in the evolution of cooperation. It also shows that differing practices of those biases can generate different dynamics, resulting in the system having different states. Full article

Team dynamics significantly influence the outcomes of modern football matches. This study employs an information-theoretical approach, specifically causal emergence, combined with graph theory to explore how team-level dynamics arise from complex interactions among players, utilizing tracking data from 34 J-League matches. We focused on how collective behaviors arise from the interdependence of individual actions, examining team coordination and dynamics through player positions and movements to identify emergent properties. Specifically, we selected relative distance to the field’s center, center of mass (CoM) and clustering coefficients based on velocity similarity and inverse distance as macroscopic features to capture the key aspects of team structure, coordination, and spatial relationships. Relative distance and CoM represent the collective positioning of the team, while clustering coefficients provide insights into localized cooperation and movement similarity among the players. The results indicate that average causal emergence with relative distance and CoM as a macroscopic feature across entire games shows a strong correlation with differences in ball possession rate between home and away teams. In contrast, clustering coefficients based on inverse distance and velocity similarity showed moderate to weak correlations with ball possession rate, indicating that these metrics may capture localized interactions that are less directly tied to team-level emergent behavior compared to CoM. Additionally, relative distance and CoM as macroscopic features yield higher causal emergence in attacking phases than in defending phases before shooting, suggesting that the collective positioning of players may play a more significant role in facilitating successful attacks than in defensive stability. This study offers a novel perspective on team coordination in football, suggesting that effective team coordination may be characterized by emergent patterns arising from collective positioning. These findings have practical implications for understanding coordinated team behaviors and inform coaching and performance analysis focused on enhancing team dynamics. Full article

In spatial public goods games, groups consisting solely of defectors do not benefit. Consequently, intelligent defectors are inclined to incur the cost of punishing other defectors to enable cooperators to flourish within the group, thereby safeguarding their own advantages. Drawing from real-world observations where early preparation often dictates future success, we integrated probabilistic punishment into the public goods game and analyzed two scenarios. In the first scenario, a probabilistic punishment mechanism was established, wherein the higher the cost was of monitoring and enforcement, the greater was the probability of punishment. In the second scenario, a compensation and fine distribution mechanism was introduced alongside probabilistic punishment, where the outcome of the punishment determined whether the smart defector recovered part of the fine or rewarded cooperators with additional benefits. This incentivized smart defectors to judiciously assess the punishment cost required to effectively protect their interests. The study demonstrated that both mechanisms significantly enhanced cooperation, with the probabilistic punishment model involving fine distribution and compensation proving more effective than simple probabilistic punishment alone. These results offer novel insights into the dynamics of probabilistic punishment and the role of fine distribution in fostering cooperation. Full article

This paper introduces a comprehensive cooperative game theory framework to measure the significance of location and neighborhood relations in conjunction with the magnitude of players/parties. The significances of these relations are measured over the EU geography. In this case, there are (i) the test of availability of a core solution that satisfies all associated parties/players; (ii) the measurement of players’/parties’ rational minimal and maximal return expectations from the grand coalition regarding their all individual and sub-group strategies and associated return rationalities; (iii) the determination of the critical players/parties in the grand coalition. The study’s main contributions are the provision of a methodology that identifies spatially/geographically critical players/parties and the design of an algorithm for handling exponentially growing strategies alongside increasing numbers of players/parties. In sum, a comprehensive cooperative game theory framework is introduced to measure the significance of location and neighborhood relations in conjunction with the magnitude of the players/parties. The case of the EU has revealed the union’s geographically critical countries, with Germany being found to be the most influential. Full article

Little is known about landbird group dynamics in response to predation. Here, we describe the interactions between the Helmeted Guineafowl (Numida meleagris) and its predators regarding the survival advantages grouping behaviour may provide. Livestream webcam observations were conducted in Madikwe Game Reserve (South Africa) from August 2020 to August 2021. Emphasis was placed on predator–prey interaction and its effect on group size and structure in a spatial framework. We hypothesise that while grouping is crucial for a number of daily activities in this highly social species, it might turn into a higher predatory pressure. We found, indeed, that the probability of attacks by black-backed jackals (Lupulella mesomelas) significantly increased with guineafowl group size, unlike what happened with raptors. Moreover, when attacked by jackals, the birds responded by standing close to each other. These results suggest, in line with the proposed hypothesis, that a trade-off occurs between the defensive function of grouping in this galliform and the probability of jackal attack that increases as a function of prey group size. Nevertheless, we argue that Helmeted Guineafowl cooperative social groups also play a role as a defensive strategy against predators, with the many-eyes and dilution effects likely compensating for the higher predatory pressure. Full article

Using the differential game model, this study examines the impact of the digital economy and regional cooperative innovation on green innovation efficiency. Additionally, based on the two-stage Super-NSBM model, this study evaluates the effects of the digital economy on green innovation efficiency, its spatial spillover effects, and the moderating role of regional cooperative innovation. The findings of the study indicate that (1) the digital economy significantly enhances green innovation efficiency but has negative spatial spillover effects on surrounding regions. (2) Regional cooperative innovation positively moderates the promotional effect of the digital economy on green innovation efficiency. Moreover, the moderating effect exhibits a single-threshold effect. (3) The influence of the digital economy on green innovation efficiency is more significant in regions with advanced industrialization, robust transportation infrastructure, and high R&D intensity. The coordinated development of digital industrialization and governance is crucial for effectively promoting the development of green innovation. Full article

Domestic regional synergistic emission reduction is important in achieving national climate goals. This study constructed a game theory-based model for regional synergistic emission reduction, modified the Basic Climate Game using the exact-hat algebra method, and expanded the game model using a general spatial equilibrium model to incorporate cross-regional economic impacts generated by emission reduction actions through factors and product flows. The formation of regional comparative advantages in emission reductions and their impact on synergistic emission reductions were revealed through regional characteristics such as emission elasticity, sectoral structure, regional trade shares, and green total factor productivity. A form of synergy was then proposed that utilizes the comparative advantages of different regions, allowing for synergistic emission reductions across different income regions and engagement with regions that are still at the carbon-peaking stage in cooperation. Moreover, the model was created to be as close to the economic reality as possible to provide a trade, industry, and economic growth policy that complements emission-reduction policies. Full article

The spatial political logic of the construction of Chinese metropolitan areas (CMAs) is unique and complex, involving the interaction of power, spatial production, and the construction of political rationality between multiple scales. Taking the representative Nanjing metropolitan area as an example, we use the “material–organizational–discursive” analytical framework of politics of scale theory to analyze the construction logic of CMAs. This study finds the following: (1) In general, the CMA is a high-quality spatial construction resulting from multi-city negotiation, inter-provincial collaboration, and central–territory linkage, and has generally undergone a process of increasing the power of subjects, nested power relations, frequent scale interactions, and complex interest games; among them, planning is not only a scale tool for competing for power, but also an important representation of the results of multiple power games. (2) In terms of the construction of material space, both the delineation of boundaries and the cross-border connection of infrastructure represent rational thinking and stand as two-way choices of the two power subjects in the MA based on the maintenance and expansion of their own spatial development rights. (3) In terms of organizational space construction, CMAs mainly adopt flexible means, with bilateral and multilateral cooperation at the horizontal level, while there is a certain power inequality at the vertical level. (4) In the construction of discursive space, CMAs have experienced increasing construction significance, escalating scale subjects, and overlapping discourse narratives, and the contrast of power relations has also changed. The contribution of this paper is an expansion of the analytical framework of politics of scale based on the division of spatial dimensions, which provides a new perspective for understanding the construction of CMAs, and also helps us to picture Chinese city–regionalism. Full article

In biological evolution, organisms that are more adapted to the environment tend to survive better, which can be explained in part by evolutionary game theory. In this paper, we propose an improved spatial prisoner’s dilemma game model, which allows the focal player to access the strategy of other agents beyond their nearest neighbors with a specified probability. During the strategy update, a focal player usually picks up a randomly chosen neighbor according to a Fermi-like rule. However, in our model, unlike the traditional strategy imitation, a focal agent will decide to update their strategy through the modified rule with a specific probability q. In this case, the focal agent accesses n other individuals who have the same strategy as the imitated neighbor, where the information accessing cost needs to be paid, and then compares their discounted payoff with the average payoff of those $n+1$ agents to make the decision of strategy adoption; otherwise, they only refer to their own payoff and their neighbor’s payoff to decide whether the strategy spread happens. Numerical simulations indicate that a moderate value of n can foster the evolution of cooperation very well, and increase in q will also improve the dilemma of cooperators. In addition, there exists an optimal product of $n\times c$ to cause the emergence of cooperation under the specific simulation setup. Taken together, the current results are conducive to understanding the evolution of cooperation within a structured population. Full article

Influence, as an inherently special attribute, is bound to profoundly affect a player’s behavior. Meanwhile, a growing body of studies suggests that interactions among networks may be more important than isolated ones. Thus, we try our best to research whether such a setup can stimulate the sense of cooperation in spatial prisoner’s dilemma games through the co-evolution of strategy imitation and interdependence networks structures. To be specific, once a player’s influence exceeds the critical threshold $\tau$, they will be permitted to build a connection with the corresponding partner on another network in a self-organized way, thus gaining additional payoff. However, a player’s influence changes dynamically with the spread of strategy, resulting in time-varying connections between networks. Our results show that influence-based self-organization can facilitate cooperation, even under quite poor conditions, where cooperation cannot flourish in a single network. Furthermore, there is an optimal threshold $\tau$ to optimize the evolution of cooperation. Through microcosmic statistical analysis, we are surprised to find that the spontaneous emergence of connections between interdependence networks, especially those between cooperators, plays a key role in alleviating social dilemmas. Finally, we uncover that if the corresponding links between interdependence networks are adjusted to random ones, the evolution of cooperation will be blocked, but it is still better than relying on simple spatial reciprocity on an isolated lattice. Full article

Recently, the social dilemma problem is no longer limited to unrealistic stateless matrix games but has been extended to temporally and spatially extended Markov games by multi-agent reinforcement learning. Many multi-agent reinforcement-learning algorithms have been proposed to solve sequential social dilemmas. However, most current algorithms focus on cooperation to improve the overall reward while ignoring the equality among agents, which could be improved in terms of practicality. Here, we propose a novel admission-based hierarchical multi-agent reinforcement-learning algorithm to promote cooperation and equality among agents. We extend the give-or-take-some model to Markov games, decompose the fairness of each agent, and propose an Admission reward. For better learning, we design a hierarchy consisting of a high-level policy and multiple low-level policies, where the high-level policy maximizes the Admission reward by choosing different low-level policies to interact with environments. In addition, the learning and execution of policies are realized through a decentralized method. We conduct experiments in multiple sequential social dilemmas environments and show that the Admission algorithm significantly outperforms the baselines, demonstrating that our algorithm can learn cooperation and equality well. Full article

Given that the two institutional arrangements of government regulation and market allocation cannot effectively solve the conflict between individual and collective interests in the process of water pollution control, this work presents a useful attempt on the third institutional arrangement of environmental governance—social governance—to overcome the dilemma. Based on common pool resource theory and multi-person prisoner game analysis framework, it incorporates environmental damage function, spatial network structure, and strategy update based on a learning mechanism into the analysis framework. In addition, it constructs a set of spatial cooperative evolution game models of basin water pollution social governance, so as to test the guarantee effect of the spontaneous collective action conditions of basin polluters on the long-term survival of the new system. This work adopts the Monte Carlo numerical simulation method to conduct the simulation experiment research. The experimental results show it is possible to successfully form collective actions entirely dependent on emitters, which yet requires a large initial scale of cooperation, that is, a majority of the emitter group autonomously abides by credible commitments. In this process, transparent full information and active organizational mobilization have a positive effect on the collective action development. The organic combination can better guide emitters to abide by credible commitments to achieve the optimal collective interests. The study results can provide a theoretical and practical reference for the social governance mechanism at a large-scale basin. Full article

The COVID-19 pandemic makes home-based telework commonplace and promotes a discussion about addressing mobility problems. Many studies focus on the relationship between the urban form at the place of residence and mode of transport or travel distance. Less attention has been paid to the spatial location of the workplace and its implications for mobility. In this article, we investigate these shifting patterns of work (places) from a socio-spatial mobility perspective. Companies in suburban areas are often characterised by limited access to public transport, cause accordingly high commuting volumes of car traffic and have a strong impact on mobility systems throughout whole regions. Anchored in a case study in Burgwedel, in the suburban area of Hannover, Germany, we analyse the impact and the potential of telework concerning workplaces and sustainable mobility. The data analysis is based on qualitative interviews with local employers (n = 10) and a survey of employees in Burgwedel (n = 367) during October–December 2021. We identify three groups of employees according to their abilities to implement telework defined by the nature of their job and their company’s culture. We show that teleworking can be a game-changer for sustainable mobility in cooperation with local companies. Full article

In order to ensure stable cooperation among the government, enterprise and university/institute in the green technology innovation process and guide an increasing number of innovation agents in the region to adopt cooperation, this paper studies the mechanism of green technology innovation. A tripartite evolutionary game model is established and the strategy choices of the government, industry and university/institute are analyzed through mathematical derivation. On this basis, the cellular automata theory is used to explore strategy choices of all innovation agents in the region from the perspective of a spatial game. From the numerical tests, the following results are obtained: increasing the cooperative innovation revenue, fairness of this revenue distribution or penalties for breach of contract can consolidate the cooperative relationship among the government, enterprise and university/institute, achieving the goal of guiding all innovation agents in the region to accept the collaborative innovation mode; regulating the government subsidy or government penalty can consolidate the cooperative relationship among participants in the pilot project, but cannot guide all innovation agents in the region accept the collaboration innovation mode. This paper’s results not only enrich the theory of government–industry–university–institute collaborative innovation in green technology, but provide ideas for stable cooperation mechanisms and comprehensive promotion of this collaborative innovation mode as well. Full article