arXiv subjects

Xiaojie Chen

Publications and source records attributed to Xiaojie Chen.

At least 19 recordsLinked to original sources

arXiv2026

Efficiency of cooperation incentives in evolutionary population games under payoff-observation errors

Traditional studies on evolutionary dynamics of cooperation have concentrated on an idealized game setup free of payoff-observation errors. However, in real-world scenarios, individuals frequently encounter errors when observing the payoffs of their opponents during game interactions, resulting from unintentional mistakes, such as data misrecording, overlooking critical details, and miscalculations. This gap between idealized error-free game models and the error-prone real-world game interactions leads to the lack of insight into the impact of payoff-observation errors on the evolutionary dynamics of population games, in particular the efficiency of cooperation incentives. In this paper, we construct a research framework for population games with payoff-observation errors, which enables us to investigate the effects of errors on the evolutionary dynamics of cooperation in the evolutionary Prisoner's Dilemma game with combined incentives. To quantify the implementation costs of incentives in the presence of errors, we devise an index function and employ optimal control theory to derive the optimal incentive protocols. Our theoretical and numerical results reveal that payoff-observation errors can lower the costs compared to error-free cases, and we also derive the theoretical conditions for these results. Finally, we formulate an optimization problem to explore the cost difference between the optimal incentive protocols with and without errors, and further design an algorithm to obtain the numerical solution that minimizes this difference.

math.OC↗

arXiv2026

Evolutionary dynamics of collective decision-making with local social influence on static and dynamic networks

Collective decision-making is ubiquitous across the living world and artificial societies. Individuals often choose an option based on intrinsic values of options. However, individual decision-making is also swayed by neighbors' choices, generating local social influence. Hence, an important question arises naturally, yet remains unanswered: when such social influence is integrated into the individual evaluation process for option choices, how does it affect collective decision-making outcomes in structured populations modeled by graphs. To address this, we consider a baseline model of binary options with social influence and assume that individuals not only evaluate the intrinsic values of options, but are also influenced by their neighbors' choices. We propose a perceived utility function integrating these two aspects for individual decision-making. By means of theoretical analysis, we first derive the average frequency of an option on static weighted connected graphs and present the mathematical condition under which this option prevails in the population. We find that the introduction of social influence can amplify the advantage of a superior option or compensate for the deficiency of an inferior one. We also reveal that the average degree of network exerts a dual effect on collective decision outcomes. Furthermore, we consider our evolutionary model on dynamic networks switching among distinct graph configurations. Our theoretical analysis shows that the evolutionary outcomes depend not only on the average degree of each network configuration, but also on its expected duration. We perform computer simulations to verify our theoretical predictions on static and dynamic networks.

physics.soc-ph↗

arXiv2026

Evolutionary dynamics in public goods games with general frequency-dependent returns

The public goods game serves as a significant paradigm for investigating the emergence and maintenance of cooperation in conflicting situations. In the traditional public goods game, the multiplication factor characterizing the synergy effect of common efforts is typically assumed to be constant. In real-world scenarios, however, investment returns are often dynamic and vary with the strategic composition of the interaction group. To date, the evolutionary dynamics of the public goods game with such frequency-dependent returns have remained not fully understood. In this work, we introduce a general frequency-dependent multiplication factor that depends on the strategy composition within the game group. Through theoretical analysis, we derive the mathematical conditions under which cooperation is favored. Our results show that whether cooperation has an evolutionary advantage over defection depends on the investment return rate in the full-contribution state of the game group, irrespective of the return rates in other states. An increase in this rate leads to a higher abundance of cooperators. Furthermore, we introduce a general frequency-dependent multiplication factor into the public goods game with peer punishment, and systematically explore its effects on the cooperation dilemma and the second-order free-rider problem. Our results highlight that the abundance of cooperators or punishers is governed solely by the investment return values in the full-cooperation and full-punishment compositions of the group. A higher return rate in the full-cooperation state facilitates the promotion of cooperation, whereas a higher return rate in the full-punishment state favors the emergence of punishment. Our theoretical findings are verified by individual-based simulations.

q-bio.PE↗

arXiv2026

Optimal network structure for collective performance with strategic information sharing

Information sharing between individuals is crucial to improve performance in collective tasks. However, in a competitive world, individuals may be reluctant to share information with the others, and it is still unclear how the presence of strategic behaviors affects the collective performance of a group. In this study, we introduce an evolutionary game modeling the dynamics of individual behaviors in a collective estimation task. The individuals are organized in a network and have to guess the distribution of ball colors in a box. Each of them samples a given number of balls and can strategically decide whether to share or not this information with its neighbors. We develop a framework that allows to investigate analytically how the collective performance depends on the network structure. We find that the optimal network results from a trade-off between the sharing rate and the way the information is integrated in the network. We further reveal that there exists an intermediate average degree for each type of network maximizing the collective performance. In addition to the uniform case, we consider the case of non-homogeneous allocations of the number of individual samples, showing that the largest collective performance is obtained when the number of ball extracted by an individual is inversely proportional to its degree.

physics.soc-ph↗

arXiv2026

Evolutionary Dynamics of Variable Games in Structured Populations

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic properties in structured populations, derive theoretical conditions for cooperation, and identify the optimal game distribution for promoting cooperation. To address these issues, we propose the variable game framework in a structured population, where the game interactions between different individuals change over time. By means of the Markov chain and the pair approximation method, we derive theoretical conditions under which cooperation is favored by natural selection and when it is favored over defection under weak selection. Furthermore, we respectively formulate and solve two optimization problems to determine the optimal game distribution that most effectively fosters the evolution of cooperation by maximizing the gradient of cooperation selection and minimizing the fitness difference between defectors and cooperators. The theoretical predictions regarding both the conditions for cooperation and optimal game distribution are further validated by numerical calculations and extensive Monte Carlo simulations. Our findings offer novel insights into the mechanisms driving cooperative behavior in complex systems and provide theoretical guidance for designing optimal game environments that facilitate the evolution of cooperation.

cs.GT↗

arXiv2025

Modeling and Experiments of an Injection-Locked Magnetron With Various Load Reflection Levels

In this article, we investigate the performance of an injection-locked 5.8-GHz continuous-wave magnetron with various load reflection levels. The load reflection is introduced to an equivalent magnetron model to theoretically evaluate the system performance. The effects of different load reflection levels on the magnetron's output are numerically analyzed. Experiments are performed while the load reflection is varied using an E-H tuner between a magnetron and a circulator. A narrower locking bandwidth is observed under constant injection power with increasing load reflection. The proper-mismatched system suppresses its sideband energy, thereby reducing phase noise. The experimental features qualitatively validate the theoretical analyses results. The investigation results also provide guidance for advanced applications in communication and high-energy physics based on injection-locked magnetrons.

physics.app-ph↗

arXiv2025

High-Efficiency Isolator-Free Magnetron Power Combining Method Based on H-Plane Tee Coupling and Peer-to-Peer Locking

Magnetrons are widely used as high-performance microwave sources in microwave heating, microwave chemistry, and microwave power transmission due to their high efficiency, low cost, and compact size advantages. However, the output power of a single magnetron is limited by its resonant cavities, posing a physical constraint. High-efficiency coherent power combining based on the injection-locking technique effectively overcomes this limitation and meets the demand for higher output power. Nevertheless, using isolators, such as circulators, introduces significant insertion loss, and the injection signal sources and phase shifters increase the system size, cost, and complexity in a conventional magnetron power combining (MPC) system. A novel method is proposed to utilize the coupling between two ports of an H-plane tee to achieve peer-to-peer injection locking magnetrons. Meanwhile, an asymmetric phase compensation is realized using a section of waveguide to adjust the magnetron output characteristics. Theoretical and numerical analyses provided qualitative insight into the system output behavior. Subsequently, an experimental system was developed for verification. In the experiments, the system achieved maximum microwave power combining efficiencies 90.2%, 93.6%, and 93.6% at electrical waveguide lengths corresponding to 90, 135, and 225, with output powers of 1650, 1260, and 1610 W, respectively, without the use of any isolators or external injection sources. The experimental results show good agreement with numerical calculations. This method offers the advantages of low cost, compact size, and low loss, providing a new approach for developing high-performance MPC systems in the future.

physics.app-ph↗

arXiv2025

A High-Efficiency Microwave Power Combining System Based on Frequency-Tuning Injection-Locked Magnetrons

To increase the power level and energy utilization rate of injection-locked magnetron sources, a dual way 1-kW S-band magnetron microwave power combining system with high combining efficiency was proposed and validated. A waveguide magic-Tee was used to achieve power combining and to provide a pathway for the reference signal. This system utilizes the power-dividing characteristic of a magic-Tee to lock two magnetrons. Frequency tuning is applied to adjust the phase difference between the two magnetrons' signals so as to achieve a high combining efficiency. Experimental results indicate that the microwave power combining efficiency of the proposed system reaches 94.5%. The attenuation of microwave power is caused only by the waveguides and magic-Tee. Our investigation provides a guideline for future high-power microwave combining systems with low losses.

physics.app-ph↗

arXiv2025

Evolutionary dynamics in state-feedback public goods games with peer punishment

Public goods game serves as a valuable paradigm for studying the challenges of collective cooperation in human and natural societies. Peer punishment is often considered as an effective incentive for promoting cooperation in such contexts. However, previous related studies have mostly ignored the positive feedback effect of collective contributions on individual payoffs. In this work, we explore global and local state-feedback, where the multiplication factor is positively correlated with the frequency of contributors in the entire population or within the game group, respectively. By using replicator dynamics in an infinite well-mixed population we reveal that state-based feedback plays a crucial role in alleviating the cooperative dilemma by enhancing and sustaining cooperation compared to the feedback-free case. Moreover, when the feedback strength is sufficiently strong or the baseline multiplication factor is sufficiently high, the system with local state-feedback provides full cooperation, hence supporting the ``think globally, act locally'' principle. Besides, we show that the second-order free-rider problem can be partially mitigated under certain conditions when the state-feedback is employed. Importantly, these results remain robust with respect to variations in punishment cost and fine.

physics.soc-ph↗

arXiv2025

Evolutionary dynamics of continuous public goods games in structured populations

Over the past few decades, many works have studied the evolutionary dynamics of continuous games. However, previous works have primarily focused on two-player games with pairwise interactions. Indeed, group interactions rather than pairwise interactions are usually found in real situations. The public goods game serves as a paradigm of multi-player interactions. Notably, various types of benefit functions are typically considered in public goods games, including linear, saturating, and sigmoid functions. Thus far, the evolutionary dynamics of cooperation in continuous public goods games with these benefit functions remain unknown in structured populations. In this paper, we consider the continuous public goods game in structured populations. By employing the pair approximation approach, we derive the analytical expressions for invasion fitness. Furthermore, we explore the adaptive dynamics of cooperative investments in the game with various benefit functions. First, for the linear public goods game, we find that there is no singular strategy, and the cooperative investments evolve to either the maximum or minimum depending on the benefit-to-cost ratio. Subsequently, we examine the game with saturating benefit functions and demonstrate the potential existence of an evolutionarily stable strategy (ESS). Additionally, for the game with the sigmoid benefit function, we observe that the evolutionary outcomes are closely related to the threshold value. When the threshold is small, a unique ESS emerges. For intermediate threshold values, both the ESS and repellor singular strategies can coexist. When the threshold value is large, a unique repellor displays. Finally, we perform individual-based simulations to validate our theoretical results.

physics.soc-ph↗

arXiv2025

Targeted incentives for social tipping in heterogeneous networked populations

Many societal challenges, such as climate change or disease outbreaks, require coordinated behavioral changes. For many behaviors, the tendency of individuals to adhere to social norms can reinforce the status quo. However, these same social processes can also result in rapid, self-reinforcing change. Interventions may be strategically targeted to initiate endogenous social change processes, often referred to as social tipping. While recent research has considered how the size and targeting of such interventions impact their effectiveness at bringing about change, they tend to overlook constraints faced by policymakers, including the cost, speed, and distributional consequences of interventions. To address this complexity, we introduce a game-theoretic framework that includes heterogeneous agents and networks of local influence. We implement various targeting heuristics based on information about individual preferences and commonly used local network properties to identify individuals to incentivize. Analytical and simulation results suggest that there is a trade-off between preventing backsliding among targeted individuals and promoting change among non-targeted individuals. Thus, where the change is initiated in the population and the direction in which it propagates is essential to the effectiveness of interventions. We identify cost-optimal strategies under different scenarios, such as varying levels of resistance to change, preference heterogeneity, and homophily. These results provide insights that can be experimentally tested and help policymakers to better direct incentives.

physics.soc-ph↗

arXiv2025

Coevolutionary dynamics of feedback-evolving games in structured populations

The interdependence between an individual strategy decision and the resulting change of environmental state is often a subtle process. Feedback-evolving games have been a prevalent framework for studying such feedback in well-mixed populations, yielding important insights into the coevolutionary dynamics. However, since real populations are usually structured, it is essential to explore how population structure affects such coevolutionary dynamics. Our work proposes a coevolution model of strategies and environmental state in a structured population depicted by a regular graph. We investigate the system dynamics, and theoretically demonstrate that there exist different evolutionary outcomes including oscillation, bistability, the coexistence of oscillation and dominance, as well as the coexistence of cooperation and defection. Our theoretical predictions are validated through numerical calculations. By using Monte Carlo simulations we examine how the number of neighbors influences the coevolutionary dynamics, particularly the size of the attractive domain of the replete environmental state in the cases of bistability or cooperation-defection coexistence. Specifically, in the case of bistability, a larger neighborhood size may be beneficial to save the environment when the environmental enhancement rate by cooperation / degradation rate by defection is high. Conversely, if this ratio is low, a smaller neighborhood size is more beneficial. In the case of cooperator-defector coexistence, environmental maintenance is basically influenced by individual payoffs. When the ratio of temptation minus reward versus punishment minus sucker's payoff is high, a larger neighborhood size is more favorable. In contrast, when the mentioned ratio is low, a smaller neighborhood size is more advantageous.

q-bio.PE↗

arXiv2024

When faster rotation is harmful: the competition of alliances with inner blocking mechanism

Competitors in an intransitive loop of dominance can form a defensive alliance against an external species. The vitality of this super-structure, however, is jeopardized if we modify the original rock-scissors-paper-like rule and allow that the vicinity of a predator blocks stochastically the invasion success of its neighboring prey towards a third actor. To explore the potential consequences of this multi-point interaction we introduce a minimal model where two three-member alliances are fighting but one of them suffers from this inner blocking mechanism. We demonstrate that this weakness can be compensated by a faster inner rotation which is in agreement with previous findings. This broadly valid principle, however, is not always true here because the increase of rotation speed could be harmful and results in series of reentrant phase transitions on the parameter plane. This unexpected behavior can be explained by the relation of the blocked triplet and a neutral pair formed by a triplet member with an external species. Our results provide novel aspects to the fundamental laws which determine the evolutionary process in multi-strategy ecological systems.

q-bio.PE↗

arXiv2024

When selection pays: structured public goods game with a generalized interaction mode

The public goods game is a broadly used paradigm for studying the evolution of cooperation in structured populations. According to the basic assumption, the interaction graph determines the connections of a player where the focal actor forms a common venture with the nearest neighbors. In reality, however, not all of our partners are involved in every games. To elaborate this observation, we propose a model where individuals choose just some selected neighbors from the complete set to form a group for public goods. We explore the potential consequences by using a pair-approximation approach in a weak-selection limit. We theoretically analyze how the number of total neighbors and the actual size of the restricted group influence the critical enhancement factor where cooperation becomes dominant over defection. Furthermore, we systematically compare our model with the traditional setup and show that the critical enhancement factor is lower than in the case when all players are present in the social dilemma. Hence the suggested restricted interaction mode offers a better condition for the evolution of cooperation. Our theoretical findings are supported by numerical calculations.

physics.soc-ph↗

arXiv2024

RecWizard: A Toolkit for Conversational Recommendation with Modular, Portable Models and Interactive User Interface

We present a new Python toolkit called RecWizard for Conversational Recommender Systems (CRS). RecWizard offers support for development of models and interactive user interface, drawing from the best practices of the Huggingface ecosystems. CRS with RecWizard are modular, portable, interactive and Large Language Models (LLMs)-friendly, to streamline the learning process and reduce the additional effort for CRS research. For more comprehensive information about RecWizard, please check our GitHub https://github.com/McAuley-Lab/RecWizard.

cs.IR↗

arXiv2023

Emergence of Fairness Behavior Driven by Reputation-Based Voluntary Participation in Evolutionary Dictator Games

Recently, reputation-based indirect reciprocity has been widely applied to the study on fairness behavior. Previous works mainly investigate indirect reciprocity by considering compulsory participation. While in reality, individuals may choose voluntary participation according to the opponent's reputation. It is still unclear how such reputation-based voluntary participation influences the evolution of fairness. To address this question, we introduce indirect reciprocity with voluntary participation into the dictator game (DG). We respectively consider good dictators or recipients can voluntarily participate in games when the opponents are assessed as bad. We theoretically calculate the fairness level under all social norms of third-order information. Our findings reveal that several social norms induce the high fairness level in both scenarios. However, more social norms lead to a high fairness level for voluntary participation of recipients, compared with the one of good dictators. The results also hold when the probability of voluntary participation is not low. Our results demonstrate that recipients' voluntary participation is more effective in promoting the emergence of fairness behavior.

cs.GT↗

arXiv2023

Optimally combined incentive for cooperation among interacting agents in population games

Combined prosocial incentives, integrating reward for cooperators and punishment for defectors, are effective tools to promote cooperation among competing agents in population games. Existing research concentrated on how to adjust reward or punishment, as two mutually exclusive tools, during the evolutionary process to achieve the desired proportion of cooperators in the population, and less attention has been given to exploring a combined incentive-based control policy that can steer the system to the full cooperation state at the lowest cost. In this work we propose a combined incentive scheme in a population of agents whose conflicting interactions are described by the prisoner's dilemma game on complete graphs and regular networks, respectively. By devising an index function for quantifying the implementation cost of the combined incentives, we analytically construct the optimally combined incentive protocol by using optimal control theory. By means of theoretical analysis, we identify the mathematical conditions, under which the optimally combined incentive scheme requires the minimal amount of cost. In addition to numerical calculations, we further perform computer simulations to verify our theoretical results and explore their robustness on different types of network structures.

math.OC↗

arXiv2023

Game-theoretical approach for task allocation problems with constraints

The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population of individuals, where there are no constraints for affording task amounts. The latter condition, however, cannot always be hold. In this paper, we study the task allocation problem with constraints of task allocation in a game-theoretical framework. We assume that each individual can afford different amounts of task and the cost function is convex. To investigate the problem in the framework of population games, we construct a potential game and calculate the fitness function for each individual. We prove that when the Nash equilibrium point in the potential game is in the feasible solutions for the limited task allocation problem, the Nash equilibrium point is the unique globally optimal solution. Otherwise, we also derive analytically the unique globally optimal solution. In addition, in order to confirm our theoretical results, we consider the exponential and quadratic forms of cost function for each agent. Two algorithms with the mentioned representative cost functions are proposed to numerically seek the optimal solution to the limited task problems. We further perform Monte Carlo simulations which provide agreeing results with our analytical calculations.

cs.GT↗