Minority Game

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.

In this paper, we study the self-coordination problem as demonstrated by the well-known El Farol problem (Arthur, 1994), which has later become what is known as the minority game in the econophysics community. While the El Farol problem or the minority game has been studied for almost two decades, existing studies are mostly only concerned with efficiency. The equality issue, however, has been largely neglected. In this paper, we build an agent-based model to study both efficiency and equality and ask whether a decentralized society can ever possibly self-coordinate a result with the highest efficiency while also maintaining the highest degree of equality. Our agent-based model shows the possibility of achieving this social optimum. The two key determinants to make this happen are social preferences and social networks. Hence, not only doe institutions (networks) matter, but individual characteristics (preferences) also matter. The latter are open to human-subject experiments for fu...

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words “Economics” and “Physics”, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes. We give a brief introduction in the first part and begin with discussing interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics in the second part. Then the third part is dedicated to empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged “stylized facts ” describing the distribution of the returns of financial assets: fat-tails, volatility clustering, etc. Then we show that some of these properties are directly linked to the way “time ”...

We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation introduces statistical arbitrages that traders exploit by adapting their trading strategies. The market impact depends on the nature of the stationary state: We find that the permanent impact is zero in the unpredictable (information efficient) phase, while in the predictable phase it is non-zero and grows linearly with the size of the meta-order. This establishes a quantitative link between information efficiency and trading efficiency (i.e. market impact). By using statistical mechanics methods for disordered systems, we are able to fully characterize the response in the predictable phase, to relate execution cost to response functions and obtain exact results for the permanent impact.

We show that the Minority Game, a model of interacting heterogeneous agents, can be described as a spin systems and it displays a phase transition between a symmetric phase and a symmetry broken phase where the games outcome is predicable. As a result a ``spontaneous magnetization'' arises in the spin formalism.

Abstract. Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum systems, quantum game theory has emerged as a framework for understanding the competitive flow of quantum information. Up till now, only two-and three-player quantum games have been demonstrated with restricted strategy sets. Here, we report the first experiment that implements a four-player ...

Generalization of the minority game to more than one market is considered. At each time step, every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of utility then market occupancies become inhomogeneous with preference given to this market where the fluctuation occurred first. There exists a critical size of agent population above which agents on bigger market behave collectively. In this regime, there always exists a history of decisions for which all agents on a bigger market react identically.

This work studies the properties of a coordination game in which agents repeatedly compete to be in the population minority. The game reflects some essential features of those economic situations in which positive rewards are assigned to individuals who behave in opposition to the modal behavior in a population. In this work we model a large group of agents who repeatedly interact in the game and we investigate the extent to which the system medium and long-run efficiency properties depend upon the specification of the agents’ microbehaviors in terms of their degree of rationality, the amount of information they use in making their choices, their learning patterns and the level of heterogeneity in the population. Our results show that, first, the system long-run properties strongly depend on the particular behavioral assumptions adopted, and, second, adding noise at the individual decision level and hence increasing heterogeneity in the population substantially improve aggregate welfare, although at the expense of a longer adjustment phase. In fact, the system achieves in that way a higher level of efficiency compared to that attainable by perfectly rational and completely informed agents.

We analyze grand-canonical minority games with infinite and finite score memory and different updating timescales (from `on-line' games to `batch' games) in detail with various complementary methods, both analytical and numerical. We focus on the emergence of `stylized facts' and on the production of exploitable information, as well as on the dynamic behaviour of the models. We find that with finite score memory no agent can be frozen, and that all the current analytical methods fail to provide satisfactory explanation of the observed behaviours.

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from

In this work several current complexity measures are studied. Further, the aplication of these measures to multi-agent based simulation results is examined, as an useful tool to multi-agent
simulation result interpretation. Multi-agent based modelling is briefly described following the
application of four of the described measures to the Minority Game model. This work confirms that complexity measures can validate minority game model theory findings. We conclude discussing that complexity measurement on multi-agent based simulation may prove to be useful on model conception and verification.

We show that, for a continuous set of entangled four-partite states, the task of max- imizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality with each observer choosing the same set of two dichotomic observables. We conclude the ex- istence of direct correspondences between (i) the payoff rule

Generalization of the minority game to more than one market is considered. At each time step every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of utility then market occupancies become inhomogeneous with preference given to this market where the fluctuation occured first. There exists a critical size of agent population above which agents on bigger market behave collectively. In this regime there always exists a history of decisions for which all agents on a bigger market react identically.

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 ...