Local Minority Game with Evolutionary Strategies

We study a model of local minority game in the random Kauffman network with evolutionary strategies and propose three methods to update the strategy of poor agents, with lower points in a given generation： namely to update either the Boolean function of their strategies randomly, or their local information of randomly adjacent m agents, or the number m of randomly chosen adjacent agents. The results of extended numerical simulations show that the behaviour of strategies in the three methods may enhance significantly the entire coordination of agents in the system. It is also found that a poor agent tends to use both small m strategies and correlated strategies, and the strategies of agents will finally self-organize into a steady-state distribution for a long time playing of the game.     

Intelligent minority game with genetic crossover strategies

We have developed a novel game theoretical model of N interacting agents playing a minority game such that they change their strategies intelligently or adaptively depending on their temporal performances. The strategy changes are done by generating new strategies through one-point genetic crossover mechanism. The performances of agents are found to change dramatically (from losing to winning or otherwise) and the game moves rapidly to an efficient state, in which fluctuations in the number of agents performing a particular action, characterized by the variance , reaches a low value.Received: 2 June 2003, Published online: 11 August 2003PACS: 87.23.Ge Dynamics of social systems - 02.50.Le Decision theory and game theory - 87.23.Kg Dynamics of evolution     

Network evolution based on minority game with herding behavior

The minority game (MG) is used as a source of information to design complex networks where the nodes represent the playing agents. Differently from classical MG consisting of independent agents, the current model rules that connections between nodes are dynamically inserted or removed from the network according to the most recent game outputs. This way, preferential attachment based on the concept of social distance is controlled by the agents wealth. The time evolution of the network topology, quantitatively measured by usual parameters, is characterized by a transient phase followed by a steady state, where the network properties remain constant. Changes in the local landscapes around individual nodes depend on the parameters used to control network links. If agents are allowed to access the strategies of their network neighbors, a feedback effect on the network structure and game outputs is observed. Such effect, known as herding behavior, considerably changes the dependence of volatility σ on memory size: it is shown that the absolute value of σ as well as the corresponding value of memory size depend both on the network topology and on the way along which the agents make their playing decisions in each game round.     

经纪人模仿在演化少数者博弈模型中引入的自组织分离效应

引入真实金融市场中普遍存在的模仿机理,提出并研究了一种新的演化少数者博弈模型.在该模型中,所有的经纪人排列成满足一维周期性条件的链并有一个共同的策略.每个经纪人有一个概率p值,作决定时以概率p选择策略预测的取胜方,以概率1-p作出相反的决定,同时经纪人可以模仿财富高于自己的最近邻邻居的p值.数值模拟结果显示,通过演化使得经纪人组成的系统自组织分离成由极端行为表征的相反人群.模仿引起的演化可以明显提高系统的协作. 关键词： 科学与社会 自组织系统     

System dynamics of behaviour-evolutionary mix-game models

In real financial markets there are two kinds of traders:one is fundamentalist,and the other is a trend-follower.The mix-game model is proposed to mimic such phenomena.In a mix-game model there are two groups of agents:Group 1 plays the majority game and Group 2 plays the minority game.In this paper,we investigate such a case that some traders in real financial markets could change their investment behaviours by assigning the evolutionary abilities to agents:if the winning rates of agents are smaller than a threshold,they will join the other group;and agents will repeat such an evolution at certain time intervals.Through the simulations,we obtain the following findings:(i) the volatilities of systems increase with the increase of the number of agents in Group 1 and the times of behavioural changes of all agents;(ii) the performances of agents in both groups and the stabilities of systems become better if all agents take more time to observe their new investment behaviours;(iii) there are two-phase zones of market and non-market and two-phase zones of evolution and non-evolution;(iv) parameter configurations located within the cross areas between the zones of markets and the zones of evolution are suited for simulating the financial markets.     

Study on system dynamics of evolutionary mix-game models

Mix-game model is ameliorated from an agent-based MG model, which is used to simulate the real financial market. Different from MG, there are two groups of agents in Mix-game: Group 1 plays a majority game and Group 2 plays a minority game. These two groups of agents have different bounded abilities to deal with historical information and to count their own performance. In this paper, we modify Mix-game model by assigning the evolution abilities to agents: if the winning rates of agents are smaller than a threshold, they will copy the best strategies the other agent has; and agents will repeat such evolution at certain time intervals. Through simulations this paper finds: (1) the average winning rates of agents in Group 1 and the mean volatilities increase with the increases of the thresholds of Group 1; (2) the average winning rates of both groups decrease but the mean volatilities of system increase with the increase of the thresholds of Group 2; (3) the thresholds of Group 2 have greater impact on system dynamics than the thresholds of Group 1; (4) the characteristics of system dynamics under different time intervals of strategy change are similar to each other qualitatively, but they are different quantitatively; (5) As the time interval of strategy change increases from 1 to 20, the system behaves more and more stable and the performances of agents in both groups become better also.     

Global optimization of minority game by intelligent agents

We propose a new model of minority game with intelligent agents who use trail and error method to make a choice such that the standard deviation σ² and the total loss in this model reach the theoretical minimum values in the long time limit and the global optimization of the system is reached. This suggests that the economic systems can self-organize into a highly optimized state by agents who make decisions based on inductive thinking, limited knowledge, and capabilities. When other kinds of agents are also present, the simulation results and analytic calculations show that the intelligent agent can gain profits from producers and are much more competent than the noise traders and conventional agents in original minority games proposed by Challet and Zhang.     

A game theoretic algorithm to detect overlapping community structure in networks

Community detection can be used as an important technique for product and personalized service recommendation. A game theory based approach to detect overlapping community structure is introduced in this paper. The process of the community formation is converted into a game, when all agents (nodes) cannot improve their own utility, the game process will be terminated. The utility function is composed of a gain and a loss function and we present a new gain function in this paper. In addition, different from choosing action randomly among join, quit and switch for each agent to get new label, two new strategies for each agent to update its label are designed during the game, and the strategies are also evaluated and compared for each agent in order to find its best result. The overlapping community structure is naturally presented when the stop criterion is satisfied. The experimental results demonstrate that the proposed algorithm outperforms other similar algorithms for detecting overlapping communities in networks.     

Evolutionary ultimatum game on complex networks under incomplete information

This paper studies the evolutionary ultimatum game on networks when agents have incomplete information about the strategies of their neighborhood agents. Our model assumes that agents may initially display low fairness behavior, and therefore, may have to learn and develop their own strategies in this unknown environment. The Genetic Algorithm Learning Classifier System (GALCS) is used in the model as the agent strategy learning rule. Aside from the Watts-Strogatz (WS) small-world network and its variations, the present paper also extends the spatial ultimatum game to the Barabási-Albert (BA) scale-free network. Simulation results show that the fairness level achieved is lower than in situations where agents have complete information about other agents’ strategies. The research results display that fairness behavior will always emerge regardless of the distribution of the initial strategies. If the strategies are randomly distributed on the network, then the long-term agent fairness levels achieved are very close given unchanged learning parameters. Neighborhood size also has little effect on the fairness level attained. The simulation results also imply that WS small-world and BA scale-free networks have different effects on the spatial ultimatum game. In ultimatum game on networks with incomplete information, the WS small-world network and its variations favor the emergence of fairness behavior slightly more than the BA network where agents are heterogeneously structured.     

Social learning with bounded confidence and heterogeneous agents

This paper investigates an opinion formation model in social networks with bounded confidence and heterogeneous agents. The network topologies are shaped by the homophily of beliefs, which means any pair of agents are neighbors only if their belief difference is not larger than a positive constant called the bound of confidence. We consider a model with both informed agents and uninformed agents, the essential difference between which is the informed agents have access to outside signals which are function of the underlying true state of the social event concerned. More precisely, the informed agents update their beliefs by combining the Bayesian posterior beliefs based on their private observations and weighted averages of the beliefs of their neighbors. The uninformed agents update their beliefs simply by linearly combining the beliefs of their neighbors. We find that the whole group can learn the true state only if the bound of confidence is larger than a positive threshold which is related to the population density. Furthermore, simulations show that the proportion of informed agents required for collective learning decreases as the population density increases. By tuning the learning speed of informed agents, we find the following: the higher the speed, the shorter the time needed for the whole group to achieve a steady state, and on the other hand, the higher the speed, the lower the proportion of agents with successful learning — there is a trade-off.     

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.     

Evolutionary game dynamics of combining the Moran and imitation processes

One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.     

Mesoscopic approach to minority games in herd regime

We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of the state of the game. Using this approach, the game can be represented as a Markov process with substantially reduced number of states with explicitly computable probabilities. For any payoff, the finiteness of the number of states is proved. Interesting features of an extensive random variable, called aggregated demand, viz. its strong inhomogeneity and presence of patterns in time, can be easily interpreted. Using Markov theory and quenched disorder approach, we can explain important macroscopic characteristics of the game: behavior of variance per capita and predictability of the aggregated demand. We prove that in the case of linear payoff many attractors in the state space are possible.     

Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency

Using the minority game as a model for competition dynamics, we investigate the effects of interagent communications across a network on the global evolution of the game. Agent communication across this network leads to the formation of an influence network, which is dynamically coupled to the evolution of the game, and it is responsible for the information flow driving the agents' actions. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a scale-free robust leadership structure. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.     

Cooperation and charity in spatial public goods game under different strategy update rules

Human cooperation can be influenced by other human behaviors and recent years have witnessed the flourishing of studying the coevolution of cooperation and punishment, yet the common behavior of charity is seldom considered in game-theoretical models. In this article, we investigate the coevolution of altruistic cooperation and egalitarian charity in spatial public goods game, by considering charity as the behavior of reducing inter-individual payoff differences. Our model is that, in each generation of the evolution, individuals play games first and accumulate payoff benefits, and then each egalitarian makes a charity donation by payoff transfer in its neighborhood. To study the individual-level evolutionary dynamics, we adopt different strategy update rules and investigate their effects on charity and cooperation. These rules can be classified into two global rules: random selection rule in which individuals randomly update strategies, and threshold selection rule where only those with payoffs below a threshold update strategies. Simulation results show that random selection enhances the cooperation level, while threshold selection lowers the threshold of the multiplication factor to maintain cooperation. When charity is considered, it is incapable in promoting cooperation under random selection, whereas it promotes cooperation under threshold selection. Interestingly, the evolution of charity strongly depends on the dispersion of payoff acquisitions of the population, which agrees with previous results. Our work may shed light on understanding human egalitarianism.     

Emergence of trend trading and its effects in minority game

In this paper, we extended Minority Game (MG) by equipping agents with both value and trend strategies. In the new model, agents (we call them strong-adaptation agents) can autonomically select to act as trend trader or value trader when they game and learn in system. So the new model not only can reproduce stylized factors but also has the potential to investigate into the process of some problems of securities market. We investigated the dynamics of trend trading and its impacts on securities market based on the new model. Our research found that trend trading is inevitable when strong-adaptation agents make decisions by inductive reasoning. Trend trading (of strong-adaptation agents) is not irrational behavior but shows agent's strong-adaptation intelligence, because strong-adaptation agents can take advantage of the pure value agents when they game together in hybrid system. We also found that strong-adaptation agents do better in real environment. The results of our research are different with those of behavior finance researches.     

Dynamic behaviours of mix-game model and its application

In this paper a minority game (MG) is modified by adding into it some agents who play a majority game. Such a game is referred to as a mix-game. The highlight of this model is that the two groups of agents in the mix-game have different bounded abilities to deal with historical information and to count their own performance. Through simulations, it is found that the local volatilities change a lot by adding some agents who play the majority game into the MG, and the change of local volatilities greatly depends on different combinations of historical memories of the two groups. Furthermore, the analyses of the underlying mechanisms for this finding are made. The applications of mix-game mode are also given as an example.     

通过博弈的室内行人疏散动力学研究

在室内行人疏散过程中,行人博弈对疏散效率有着重要的影响.本文把抵制博弈策略更新的强度定义为抵制强度. 为了研究抵制强度对疏散效率的影响, 通过在行人博弈策略更新的概率中引入抵制强度,基于元胞自动机模型数值计算在不同的行人密度, 出口宽度下疏散总时间随抵制强度变化的关系.结果表明: 室内行人疏散过程中, 抵制强度小会使得争抢行为极其容易蔓延. 当行人密度小且出口宽大时, 输入以急速疏散为主的规范信息,鼓励行人模仿优胜者更新博弈策略, 当行人密度大且出口狭小时, 输入以避让为主的规范信息抑制行人争抢,都能提高疏散效率. 最后找出不同条件下与最短疏散总时间相对应的优化抵制强度, 为提高室内行人疏散效率提供一个新的视角.     

金融市场中经纪人相互竞争和适应性行为的物理模型

金融物理中的争当少数者博奕模型,是一个用来模拟金融市场动力学行为的最简单的模型,可以尝试利用它来对实际金融市场中许多现象提供物理的理解.文章介绍了关于金融物理的争当少数者博奕模型的一些主要研究结果和若干最新的发展方向.     

Dynamics of networking agents competing for high centrality and low degree

We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution, the success of the agents is related only to their position in the network. The agents use strategies based on local information to improve their chance of success. Both the evolution of strategies and network structure are investigated. We find a dramatic time evolution with cascades of strategy change accompanied by a change in network structure. On average the network self-organizes to a state close to the transition between a fragmented state and a state with a giant component. Furthermore, with increasing system size both the average degree and the level of fragmentation decreases.