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The Minority Game: an introductory guide  [PDF]
Esteban Moro
Physics , 2004,
Abstract: The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to clear up and understand the behavior of this model. Our emphasis is on trying to derive the underlying effective equations which govern the dynamics of the original Minority Game, and on making an interpretation of the results from the point of view of the statistical mechanics of disordered systems.
Minority game with arbitrary cutoffs  [PDF]
N. F. Johnson,P. M. Hui,Dafang Zheng,C. W. Tai
Physics , 1999, DOI: 10.1016/S0378-4371(99)00117-X
Abstract: We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the actual attendance is above or below L. For L-> N/2, the game reproduces the main features of Challet and Zhang's minority game. As L is lowered, however, the mean attendances in different runs tend to divide into two groups. The corresponding standard deviations for these two groups are very different. This grouping effect results from the dynamical feedback governing the game's time-evolution, and is not reproduced if the agents are fed a random history.
Controlling collective dynamics in complex, minority-game resource-allocation systems  [PDF]
Ji-Qiang Zhang,Zi-Gang Huang,Zi-Gang Huang,Liang Huang,Tie-Qiao Huang,Ying-Cheng Lai
Physics , 2013, DOI: 10.1103/87.052808
Abstract: Resource allocation takes place in various kinds of real-world complex systems, such as the traffic systems, social services institutions or organizations, or even the ecosystems. The fundamental principle underlying complex resource-allocation dynamics is Boolean interactions associated with minority games, as resources are generally limited and agents tend to choose the least used resource based on available information. A common but harmful dynamical behavior in resource-allocation systems is herding, where there are time intervals during which a large majority of the agents compete for a few resources, leaving many other resources unused. Ac- companying the herd behavior is thus strong fluctuations with time in the number of resources being used. In this paper, we articulate and establish that an intuitive control strategy, namely pinning control, is effective at harnessing the herding dynamics. In particular, by fixing the choices of resources for a few agents while leaving majority of the agents free, herding can be eliminated completely. Our investigation is systematic in that we consider random and targeted pinning and a variety of network topologies, and we carry out a comprehensive analysis in the framework of mean-field theory to understand the working of control. The basic philosophy is then that, when a few agents waive their freedom to choose resources by receiving sufficient incentives, majority of the agents benefit in that they will make fair, efficient, and effective use of the available resources. Our work represents a basic and general framework to address the fundamental issue of fluctuations in complex dynamical systems with significant applications to social, economical and political systems.
Effects of Contrarians in the Minority Game  [PDF]
Li-Xin Zhong,Da-Fang Zheng,Bo Zheng,P. M. Hui
Physics , 2004, DOI: 10.1103/PhysRevE.72.026134
Abstract: We study the effects of the presence of contrarians in an agent-based model of competing populations. Contrarians are common in societies. These contrarians are agents who deliberately prefer to hold an opinion that is contrary to the prevailing idea of the commons or normal agents. Contrarians are introduced within the context of the Minority Game (MG), which is a binary model for an evolving and adaptive population of agents competing for a limited resource. Results of numerical simulations reveal that the average success rate among the agents depends non-monotonically on the fraction $a_{c}$ of contrarians. For small $a_{c}$, the contrarians systematically outperform the normal agents by avoiding the crowd effect and enhance the overall success rate. For high $a_{c}$, the anti-persistent nature of the MG is disturbed and the few normal agents outperform the contrarians. Qualitative discussion and analytic results for the small $a_{c}$ and high $a_{c}$ regimes are also presented, and the crossover behavior between the two regimes is discussed.
The Minority Game with Variable Payoffs  [PDF]
Yi Li,Adrian VanDeemen,Robert Savit
Physics , 2000, DOI: 10.1016/S0378-4371(00)00095-9
Abstract: In the standard minority game, each agent in the minority group receives the same payoff regardless of the size of the minority group. Of great interest for real social and biological systems are cases in which the payoffs to members of the minority group depend on the size of the minority group. This latter includes the fixed sum game. We find, remarkably, that the phase structure and general scaling behavior of the standard minority game persists when the payoff function depends on the size of the minority group. there is still a phase transition at the same value of z, the ratio of the dimension of the strategy space to the number of agents playing the game. We explain the persistence of the phase structure and argue that it is due to the absence of temporal cooperation in the dynamics of the minority game. We also discuss the behavior of average agent wealth and the wealth distribution in these variable payoff games.
Statistical and Multifractal Properties of the Time Series Generated by a Modified Minority Game  [PDF]
Yu. A. Kuperin,M. M. Morozova
Quantitative Finance , 2010,
Abstract: In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigated with the aim of reproducing the basic properties of real financial time series. It was proved that such properties as the clustering of volatility, the Levy distribution and multifractality are inherent for generated by this version of the Minority Game time series of prices.
Multiple Choice Minority Game  [PDF]
F. K. Chow,H. F. Chau
Physics , 2001,
Abstract: Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game by allowing players to choose one out of many alternatives. Nevertheless, such an extension is not straight-forward due to the difficulties in finding a set of reasonable, unbiased and computationally feasible strategies. Here, we propose a variation of the minority game where every player has more than two options. Results of numerical simulations agree with the expectation that our multiple choices minority game exhibits similar behavior as the original two-choice minority game.
The minority game: An economics perspective  [PDF]
Willemien Kets
Quantitative Finance , 2007,
Abstract: This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning models commonly used in economics. We relate the learning model from the minority game literature to standard game-theoretic learning models, and show that in fact it shares many features with these models. However, the predictions of the learning model differ considerably from the predictions of most other learning models. We discuss the main predictions of the learning model proposed in the minority game literature, and compare these to experimental findings on congestion games.
The Local Minority Game  [PDF]
Susanne Moelbert,Paolo De Los Rios
Physics , 2001, DOI: 10.1016/S0378-4371(01)00480-0
Abstract: Ecologists and economists try to explain collective behavior in terms of competitive systems of selfish individuals with the ability to learn from the past. Statistical physicists have been investigating models which might contribute to the understanding of the underlying mechanisms of these systems. During the last three years one intuitive model, commonly referred to as the Minority Game, has attracted broad attention. Powerful yet simple, the minority game has produced encouraging results which can explain the temporal behaviour of competitive systems. Here we switch the interest to phenomena due to a distribution of the individuals in space. For analyzing these effects we modify the Minority Game and the Local Minority Game is introduced. We study the system both numerically and analytically, using the customary techniques already developped for the ordinary Minority Game.
Minority Game With Peer Pressure  [PDF]
H. F. Chau,F. K. Chow,K. H. Ho
Physics , 2003, DOI: 10.1016/j.physa.2003.10.009
Abstract: To study the interplay between global market choice and local peer pressure, we construct a minority-game-like econophysical model. In this so-called networked minority game model, every selfish player uses both the historical minority choice of the population and the historical choice of one's neighbors in an unbiased manner to make decision. Results of numerical simulation show that the level of cooperation in the networked minority game differs remarkably from the original minority game as well as the prediction of the crowd-anticrowd theory. We argue that the deviation from the crowd-anticrowd theory is due to the negligence of the effect of a four point correlation function in the effective Hamiltonian of the system.
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