The demise of constant price impact functions and single-time step models of speculation

Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions are considered. The solution of the paradox lies in the non-constant nature of real-life price impact functions. A simple model that includes explicit position opening, holding, and closing is briefly introduced and its information ecology discussed, shedding new light on the relevance of the Minority Game to the study of financial markets.Comment: 10 pages, 2 figures. Proceedings of APFA5 conferenc

The Local Minority Game

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

Harms and benefits from social imitation

We study the role of imitation within a model of economics with adaptive agents. The basic ingredients are those of the Minority Game. We add the possibility of local information exchange and imitation of the neighbour's strategy. Imitators should pay a fee to the imitated. Connected groups are formed, which act as if they were single players. Coherent spatial areas of rich and poor agents result, leading to the decrease of local social tensions. Size and stability of these areas depends on the parameters of the model. Global performance measured by the attendance volatility is optimised at certain value of the imitation probability. The social tensions are suppressed for large imitation probability, but due to the price paid by the imitators the requirements of high global effectivity and low social tensions are in conflict, as well as the requirements of low global and low local wealth differences.Comment: 11 pages, elsart style, to appear in the proceedings of NATO ARW on Application of Physics in Economic Modelling, Prague, 8-10 February 200

Self-organization, resources and strategies in a minority game

We find that the existence of self-organization of the members of a recently proposed minority game, depends on the type of update rules used. The resulting resource distribution is studied in some detail, and a related strategy scheme is considered, as a tool to improve the understanding of the modelComment: 4 pages (barely), 3 figure

The Minority Game with interactions

We partially modify the rules of the Minority Game (MG) by introducing some degree of local information in the game, which is only available for some agents, called the interacting agents. Our work shows that, for small values of the new parameter of the model (the fraction of interacting agents), there is an improvement of the use of the resources with respect to the MG, while as this number grows the response of the system changes, and ends up behaving worst than the usual MG.Comment: 9 pages, 4 figures; typoos corrected; references upadted; Physica A -like LaTe

Dynamics of the Time Horizon Minority Game

We present exact analytic results for a new version of the Minority Game (MG) in which strategy performance is recorded over a finite time horizon. The dynamics of this Time Horizon Minority Game (THMG) exhibit many distinct features from the MG and depend strongly on whether the participants are fed real, or random, history strings. The THMG equations are equivalent to a Markov Chain, and yield exact analytic results for the volatility given a specific realization for the quenched strategy disorder.Comment: Latex file, 11 pages, 6 figure

The Full Strategy Minority Game

The Full Strategy Minority Game (FSMG) is an instance of the Minority Game (MG) which includes a single copy of every potential agent. In this work, we explicitly solve the FSMG thanks to certain symmetries of this game. Furthermore, by considering the MG as a statistical sample of the FSMG, we compute approximated values of the key variable {\sigma}2/N in the symmetric phase for different versions of the MG. As another application we prove that our results can be easily modified in order to handle certain kind of initial biased strategies scores, in particular when the bias is introduced at the agents' level. We also show that the FSMG verifies a strict period two dynamics (i.e., period two dynamics satisfied with probability 1) giving, to the best of our knowledge, the first example of an instance of the MG for which this feature can be analytically proved. Thanks to this property, it is possible to compute in a simple way the probability that a general instance of the MG breaks the period two dynamics for the first time in a given simulation.Comment: To appear in Physica

Evolutionary minority game with heterogeneous strategy distribution

We present detailed numerical results for a modified form of the so-called Minority Game, which provides a simplified model of a competitive market. Each agent has a limited set of strategies, and competes to be in a minority. An evolutionary rule for strategy modification is included to mimic simple learning. The results can be understood by considering crowd formation within the population.Comment: Revtex file + 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

Evolutionary freezing in a competitive population

We show that evolution in a population of adaptive agents, repeatedly competing for a limited resource, can come to an abrupt halt. This transition from evolutionary to non-evolutionary behavior arises as the global resource level is changed, and is reminiscent of a phase transition to a frozen state. Its origin lies in the inductive decision-making of the agents, the limited global information that they possess and the dynamical feedback inherent in the system.Comment: LaTeX file + 4 separate (pdf) figures. Revised version has minor change in Fig. 3 axis labe