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 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.
 Physics , 2005, Abstract: In this paper, we introduce a framework to study local interactions due to the presence of herding behavior in a minority game. The idea behind this approach is to consider that some of the agents who play the game believe that some of their neighbors are more informed than themselves. Thus, in this way, these agents imitate their most informed neighbors. The notion of neighborhood here is given by a regular network, a random network or a small world network. We show that under herding behavior the cooperation between the agents is less efficient than that one which arises in the standard minority game. On the other hand, depending on the topology of the network, we show that that the well known curve volatility versus memory, which caracterizes the minority game, is a monotone decreasing curve.
 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.
 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.
 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.
 Physics , 2004, DOI: 10.1103/PhysRevE.69.067106 Abstract: We show that a simple evolutionary scheme, when applied to the minority game (MG), changes the phase structure of the game. In this scheme each agent evolves individually whenever his wealth reaches the specified bankruptcy level, in contrast to the evolutionary schemes used in the previous works. We show that evolution greatly suppresses herding behavior, and it leads to better overall performance of the agents. Similar to the standard non-evolutionary MG, the dependence of the standard deviation $\sigma$ on the number of agents $N$ and the memory length $m$ can be characterized by a universal curve. We suggest a Crowd-Anticrowd theory for understanding the effect of evolution in the MG.
 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.
 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.
 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.
 Physics , 2003, DOI: 10.1016/j.physa.2004.06.083 Abstract: We analyze the minority game for patients, and the results known from the minority game are applied to the patient problem consulted at the department of pediatric cardiology. We find numerically the standard deviation and the global efficiency, similar to the El Farol bar problem. After the score equation and the scaled utility are introduced, the dynamical behavior of our model is discussed for particular strategies. Our result presented will be compared with the well-known minority games.
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