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The game of go as a complex network  [PDF]
Bertrand Georgeot,Olivier Giraud
Computer Science , 2011, DOI: 10.1209/0295-5075/97/68002
Abstract: We study the game of go from a complex network perspective. We construct a directed network using a suitable definition of tactical moves including local patterns, and study this network for different datasets of professional tournaments and amateur games. The move distribution follows Zipf's law and the network is scale free, with statistical peculiarities different from other real directed networks, such as e. g. the World Wide Web. These specificities reflect in the outcome of ranking algorithms applied to it. The fine study of the eigenvalues and eigenvectors of matrices used by the ranking algorithms singles out certain strategic situations. Our results should pave the way to a better modelization of board games and other types of human strategic scheming.
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.
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.
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.
Algorithmic Complexity in Minority Game  [PDF]
Ricardo Mansilla Corona
Physics , 1999,
Abstract: In this paper we introduce a new approach for the study of the complex behavior of Minority Game using the tools of algorithmic complexity, physical entropy and information theory. We show that physical complexity and mutual information function strongly depend on memory size of the agents and yields more information about the complex features of the stream of binary outcomes of the game than volatility itself.
The Interactive Minority Game: Instructions for Experts  [PDF]
Peter Ruch,Joseph Wakeling,Yi-Cheng Zhang
Quantitative Finance , 2002,
Abstract: The Interactive Minority Game (IMG) is an online version of the traditional Minority Game in which human players can enter into competition with the traditional computer-controlled agents. Through the rich (and, importantly, analytically understood) behaviour of the MG, we can explore humans' behaviour in different kinds of market--crowded, efficient, critical--with a high degree of control. To make the game easily understandable even to those who are encountering it for the first time, we have presented the game with a rather simplified interface; in this working paper we explain the underlying technical aspects for those who have experience with the traditional MG.
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.
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.
Emergence of grouping in multi-resource minority game dynamics  [PDF]
Zi-Gang Huang,Ji-Qiang Zhang,Jia-Qi Dong,Liang Huang,Ying-Cheng Lai
Physics , 2012,
Abstract: TheMinority Game (MG) has become a paradigm to probe complex social and economical phenomena where adaptive agents compete for a limited resource, and it finds applications in statistical and nonlinear physics as well. In the traditional MG model, agents are assumed to have access to global information about the past history of the underlying system, and they react by choosing one of the two available options associated with a single resource. Complex systems arising in a modern society, however, can possess many resources so that the number of available strategies/resources can be multiple. We propose a class of models to investigate MG dynamics with multiple strategies. In particular, in such a system, at any time an agent can either choose a minority strategy (say with probability p) based on available local information or simply choose a strategy randomly (with probability 1 - p). The parameter p thus defines the minority-preference probability, which is key to the dynamics of the underlying system. A striking finding is the emergence of strategy-grouping states where a particular number of agents choose a particular subset of strategies. We develop an analytic theory based on the mean-field framework to understand the "bifurcation" to the grouping states and their evolution. The grouping phenomenon has also been revealed in a real-world example of the subsystem of 27 stocks in the Shanghai Stock Market's Steel Plate. Our work demonstrates that complex systems following the MG rules can spontaneously self-organize themselves into certain divided states, and our model represents a basic mathematical framework to address this kind of phenomena in social, economical, and even political systems.
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