Quenching and Annealing in the Minority Game

We report the occurrence of quenching and annealing in a version of the Minority Game (MG) in which the winning option is to join a given fraction of the population that is a free, external parameter. We compare this to the different dynamics of the Bar Attendance Model (BAM) where the updating of the attendance strategy makes use of all available information about the system and quenching does not occur. We provide an annealing schedule by which the quenched configuration of the MG reaches equilibrium and coincides with the one obtained with the BAMComment: 8 pages, 4 figure

Adaptive Boolean Networks and Minority Games with Time--Dependent Capacities

In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a system for different values of the mean connectivity $K$ of the network, and show that the system with K=2 shows a high degree of coordination for relatively large variations of the capacity level.Comment: 4 pages, 4 figure

Crowd-anticrowd theory of the Minority Game

The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Despite its importance, a quantitative explanation of the game's fluctuations which applies over the entire parameter range of interest has so far been lacking. We provide such a quantitative description based on the interplay between crowds of like-minded agents and their anti-correlated partners (anticrowds).Comment: Shortened version of cond-mat/0003486. Submitted for publicatio

Alsophis rufiventris

Number of Pages: 4Integrative BiologyEarth and Planetary Science

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable -- which plays a role similar to price -- whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the ``thermodynamic'' limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even ``infinitesimally'' for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a ``price taker'' behavior if agents account for their market impact.Comment: 38 pages + 5 figures (needs elsart.sty). New results adde

Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''

We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper [Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that the effects of the temperature in the Thermal Minority Game ``can be eliminated by time rescaling'' and consequently the behaviour is ``independent of T'' has no general validity.Comment: 1 page, 1 figur

Shedding light on El Farol

We mathematize El Farol bar problem and transform it into a workable model. In general, the average convergence to optimality at the collective level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.Comment: 8 pages, 5 figure