Non-consensus Opinion Models on Complex Networks

Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. (Phys. Rev. Lett. 103:01870, 2009). The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also revisit another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model (Li et al. in Phys. Rev. E 84:066101, 2011), which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. To place the inflexible contrarians in the ICO model we use two different strategies, random placement and one in which high-degree nodes are targeted. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster in both strategies, but the effect is more pronounced under the targeted method. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. Because opinions propagate not only within single networks but also between networks, and because the rules of opinion formation within a network may differ from those between networks, we study here the opinion dynamics in coupled networks. Each network represents a social group or community and the interdependent links joining individuals from different networks may be social ties that are unusually strong, e.g., married couples. We apply the non-consensus opinion (NCO) rule on each individual network and the global majority rule on interdependent pairs such that two interdependent agents with different opinions will, due to the influence of mass media, follow the majority opinion of the entire population. The opinion interactions within each network and the interdependent links across networks interlace periodically until a steady state is reached. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. We also find that the effect of interdependent links is more pronounced in interdependent scale free networks than in interdependent Erd?s Rényi networks.     

Modeling and analyzing of botnet interactions

The dynamics of interacting botnets and the effects of the strategies selected by interacting botnet owners on the spread of botnets remain unclear. As a result, in this paper, we present a botnet interaction model, obtained by coupling a fast evolutionary game dynamics to a slow population dynamics model, in which two botnet types are considered. We analyze the fast evolutionary game model and obtain two stable equilibria. Additionally, we substitute them into the complete model and get two reduced models. Such models allow us to study the effects of strategies selected by botnet owners. Analysis of the models shows that when all owners adopt the cooperative strategy both types of botnets can survive with much lower contact rates. However, while they choose the competitive strategy one type of botnet will become extinct and the other will persist with a lower infection rate. The equilibrium conditions of the evolutionary game model, which can guide us in designing effective counter-botnet methods, are also obtained.     

基于博弈论的认知无线电网络跨层资源分配

针对多跳认知无线电网络的多层资源分配问题,提出了协作去耦合方法和跨层联合方法,协作去耦合方法首先单独完成路径选择任务,随后进行信道与功率的博弈分配;跨层联合方法则通过博弈直接对路径、信道、功率三层资源进行同时分配,两种方法都综合考虑网络层、介质访问控制层、物理层的启发原则,引入了节点被干扰度信息和节点主动干扰度信息来辅助路径选择,设计了基于功率允许宽度信息的Boltzmann探索来完成信道与功率选择,设计了长链路和瓶颈链路替换消除机制以进一步提高网络性能,从促进收敛角度,选择序贯博弈并设计了具体的博弈过程,此外还分析了博弈的纳什均衡,讨论了两种算法的复杂度,仿真结果表明,协作去耦合方法和跨层联合方法在成功流数量、流可达速率、发射功耗性能指标上均优于简单去耦合的链路博弈、流博弈方法。     

Voter model on adaptive networks

Voter model is an important basic model in statistical physics. In recent years, it has been more and more used to describe the process of opinion formation in sociophysics. In real complex systems, the interactive network of individuals is dynamically adjusted, and the evolving network topology and individual behaviors affect each other. Therefore, we propose a linking dynamics to describe the coevolution of network topology and individual behaviors in this paper, and study the voter model on the adaptive network. We theoretically analyze the properties of the voter model, including consensus probability and time. The evolution of opinions on dynamic networks is further analyzed from the perspective of evolutionary game. Finally, a case study of real data is shown to verify the effectiveness of the theory.     

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model.     

基于体感技术的游戏重构框架的应用研究

为满足体感游戏市场需求,降低3D游戏前期投入风险,文章提出通过开发中间件模块对游戏开发过程进行简单改造,实现3D游戏向体感游戏平滑过渡的过程。先是简单介绍了体感技术的原理和工作过程,接着结合Kinect硬件系统提出了3D游戏到体感游戏重构框架（3D-MS重构框架）,然后设计和实现了中间件模块,并对现有3D游戏的提出具体改进策略和方法。最后以《神龙》游戏为案例进行了重构和实验测试,实验表明3D-MS重构框架是可行的,采用中间件技术可平滑、快速实现从3D游戏到体感游戏,比直接改造游戏的效率高2.2倍,同时能提高游戏的人机互动效果。     

Reputation-based network selection mechanism using game theory

Current and future wireless environments are based on the coexistence of multiple networks supported by various access technologies deployed by different operators. As wireless network deployments increase, their usage is also experiencing a significant growth. In this heterogeneous multi-technology multi-application multi-terminal multi-user environment users will be able to freely connect to any of the available access technologies. Network selection mechanisms will be required in order to keep mobile users “always best connected” anywhere and anytime. In such a heterogeneous environment, game theory techniques can be adopted in order to understand and model competitive or cooperative scenarios between rational decision makers. In this work we propose a theoretical framework for combining reputation-based systems, game theory and network selection mechanism. We define a network reputation factor which reflects the network’s previous behaviour in assuring service guarantees to the user. Using the repeated Prisoner’s Dilemma game, we model the user–network interaction as a cooperative game and we show that by defining incentives for cooperation and disincentives against defecting on service guarantees, repeated interaction sustains cooperation.     

Coevolving agent strategies and network topology for the public goods games

Much of human cooperation remains an evolutionary riddle. Coevolutionary public goods games in structured populations are studied where players can change from an unproductive public goods game to a productive one, by evaluating the productivity of the public goods games. In our model, each individual participates in games organized by its neighborhood plus by itself. Coevolution here refers to an evolutionary process entailing both deletion of existing links and addition of new links between agents that accompanies the evolution of their strategies. Furthermore, we investigate the effects of time scale separation of strategy and structure on cooperation level. This study presents the following: Foremost, we observe that high cooperation levels in public goods interactions are attained by the entangled coevolution of strategy and structure. Presented results also confirm that the resulting networks show many features of real systems, such as cooperative behavior and hierarchical clustering. The heterogeneity of the interaction network is held responsible for the observed promotion of cooperation. We hope our work may offer an explanation for the origin of large-scale cooperative behavior among unrelated individuals.     

Non-Classical Rules in Quantum Games

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players’ strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.     

On evolutionary spatial heterogeneous games

How cooperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one-parameter payoff matrix. Here, the effects of spatial heterogeneities of the environment and/or asymmetries in the interactions among the individuals are analysed through different extensions of this model. Instead of using the same universal payoff matrix, bimatrix games in which each cell at site (i, j) has its own different ‘temptation to defect’ parameter T(i,j) are considered. First, the case in which these individual payoffs are constant in time is studied. Second, an evolving evolutionary spatial game such that T=T(i,j;t), i.e. besides depending on the position evolves (by natural selection), is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices.     

Some Analytical Properties of the Model for Stochastic Evolutionary Games in Finite Populations with Non-uniform Interaction Rate

Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, "The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations." In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.     

Zero-determinant strategy:An underway revolution in game theory

Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions according to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant(ZD) strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two players, indicating that a smart player can control her unwitting co-player’s payoff in a unilateral way [Proc. Acad. Natl. Sci.USA 109, 10409(2012)]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players,and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis,cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.     

A competitive game whose maximal Nash-equilibrium payoff requires quantum resources for its achievement

While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting. We construct a competitive game between four players based on the minority game where the maximal Nash-equilibrium payoff when played with the appropriate quantum resource is greater than that obtainable by classical means, assuming a local hidden variable model.     

Memory-based evolutionary game on small-world network with tunable heterogeneity

Most papers about evolutionary games on graph assume agents have no memory. Yet, in the real world, interaction history can also affect an agent’s decision. So we introduce a memory-based agent model and investigate the Prisoner’s Dilemma game on a Heterogeneous Newman-Watts small-world network based on a Genetic Algorithm, focusing on heterogeneity’s role in the emergence of cooperative behaviors. In contrast with previous results, we find that a different heterogeneity parameter domain range imposes an entirely different impact on the cooperation fraction. In the parameter range corresponding to networks with extremely high heterogeneity, the decrease in heterogeneity greatly promotes the proportion of cooperation strategy, while in the remaining parameter range, which relates to relatively homogeneous networks, the variation of heterogeneity barely affects the cooperation fraction. Also our study provides a detailed insight into the microscopic factors that contribute to the performance of cooperation frequency.     

Tripartite Dynamic Zero-Sum Quantum Games

The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.     

Cooperative behavior in evolutionary snowdrift game with bounded rationality

An evolutionary snowdrift game (SG) that incorporates bounded rationality and limited information in the evolutionary process is proposed and studied. Based on SG in a well-mixed population and defining the winning action at a turn to be the one that gets a higher payoff, the most recent m winning actions can be used as a public information based on which the competing agents decide their next actions. This defines a strategy pool from which each agent picks a number of strategies as their tool in adapting to the competing environment. The payoff parameter r in SG serves to set the maximum number of winners per turn. Due to the bounded rationality and limited information, the cooperative frequency shows steps and plateaux as a function of r and these features tend to be smoothed out as m increases. These features are results of an interplay between a restricted subset of m-bit histories that the system can visit at a value of r and the limited capacity that agents can adapt. The standard deviation in the number of agents taking the cooperative action is also studied. For general values of r, our model generates a realization of the binary-agent-resource model. The idea of introducing bounded rationality into a two-person game to realize the minority game or binary-agent-resource model could be a useful tool for future research.     

Evacuation of pedestrians from a hall by game strategy update

In this paper, a cellular automaton model considering game strategy update is proposed to study the pedestrian evacuation in a hall. Pedestrians are classified into two categories, i.e., cooperators and defectors, and they walk to an exit according to their own strategy change. The conflicts that two or three pedestrians try to occupy the same site at the same time are investigated in the Game theory model. Based on it, the relationship between the pedestrian flow rate and the evacuation time as well as the variation of cooperative proportion against evacuation time is investigated from the different initial cooperative proportions under the influence of noise. The critical value of the noise is found when there is a small number of defectors in the initial time. Moreover, the influences of the initial cooperative proportion and strength of noise on evacuation are discussed. The results show that the lower the initial cooperative proportion as well as the bigger the strength of noise, the longer the time it takes for evacuation.     

Behavior of Collective Cooperation Yielded by Two Update Rules in Social Dilemmas:Combining Fermi and Moran Rules

We combine the Fermi and Moran update rules in the spatial prisoner's dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice.Large-scale simulations indicate that,compared to the model with only one update rule,the cooperation behavior exhibits the richer phenomena,and the role of update dynamics should be paid more attention in the evolutionary game theory.Meanwhile,we also observe that the introduction of Moran rule,which needs to consider all neighbor's information,can markedly promote the aggregate cooperation level,that is,randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents.Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological,economic and social systems.     

Behavior of Collective Cooperation Yielded by Two Update Rules in Social Dilemmas: Combining Fermi and Moran Rules

We combine the Fermi and Moran update rules in the spatial prisoner's dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the cooperation behavior exhibits the richer phenomena, and the role of update dynamics should be paid more attention in the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor's information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.     

Hybrid Basketball Game Outcome Prediction Model by Integrating Data Mining Methods for the National Basketball Association

The sports market has grown rapidly over the last several decades. Sports outcomes prediction is an attractive sports analytic challenge as it provides useful information for operations in the sports market. In this study, a hybrid basketball game outcomes prediction scheme is developed for predicting the final score of the National Basketball Association (NBA) games by integrating five data mining techniques, including extreme learning machine, multivariate adaptive regression splines, k-nearest neighbors, eXtreme gradient boosting (XGBoost), and stochastic gradient boosting. Designed features are generated by merging different game-lags information from fundamental basketball statistics and used in the proposed scheme. This study collected data from all the games of the NBA 2018–2019 seasons. There are 30 teams in the NBA and each team play 82 games per season. A total of 2460 NBA game data points were collected. Empirical results illustrated that the proposed hybrid basketball game prediction scheme achieves high prediction performance and identifies suitable game-lag information and relevant game features (statistics). Our findings suggested that a two-stage XGBoost model using four pieces of game-lags information achieves the best prediction performance among all competing models. The six designed features, including averaged defensive rebounds, averaged two-point field goal percentage, averaged free throw percentage, averaged offensive rebounds, averaged assists, and averaged three-point field goal attempts, from four game-lags have a greater effect on the prediction of final scores of NBA games than other game-lags. The findings of this study provide relevant insights and guidance for other team or individual sports outcomes prediction research.