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Exact solution of a model for crowding and information transmission in financial markets
An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an exponential cut-off. As the size of these groups determines the supply and demand balance, this implies heavy tails in the distribution of price variation. The moments of the distribution are calculated, as well as the kurtosis. We find that the kurtosis is large for all model parameter values and that the model is not self-organizing
Democracy versus dictatorship in self-organized models of financial markets
Models to mimic the transmission of information in financial markets are introduced. As an attempt to generate the demand process, we distinguish between dictatorship associations, where groups of agents rely on one of them to make decision, and democratic associations, where each agent takes part in the group decision. In the dictatorship model, agents segregate into two distinct populations, while the democratic model is driven towards a critical state where groups of agents of all sizes exist. Hence, both models display a level of organization, but only the democratic model is self-organized. We show that the dictatorship model generates less-volatile markets than the democratic model
Transition from coherence to bistability in a model of financial markets
We present a model describing the competition between information transmission and decision
making in financial markets. The solution of this simple model is recalled, and possible variations discussed.
It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash. Two
extensions of this model are presented that allow to simulate the demand process. One of these extensions
has a coherent stable equilibrium and is self-organized, while the other has a bistable equilibrium, with a
spontaneous segregation of the population of agents. A new model is introduced to generate a transition
between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the
two extensions. We focuss our attention on the microscopic structure of the investment rate, which is the
main parameter of the original model. A constant investment rate seems to be a very good approximation
Efficiency and persistence in models of adaptation
A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We establish a link between these properties and determine two transitions for each property, a percolation transition and a depinning transition. If the adaptation process is iterated, the antipersistent state becomes an attractor of the dynamics. Extensions to higher dimensions are briefly discussed
Non-universal scaling and dynamical feedback in generalized models of financial markets
We study self-organized models for information transmission and herd behavior in financial markets. Existing models are generalized to take into account the effect of size-dependent fragmentation and coagulation probabilities of groups of agents and to include a demand process. Non-universal scaling with a tunable exponent for the group size distribution is found in the resulting system. We also show that the fragmentation and coagulation probabilities of groups of agents have a strong influence on the average investment rate of the system
Models for the size distribution of businesses in a price driven market
A microscopic model of aggregation and fragmentation is introduced to
investigate the size distribution of businesses. In the model, businesses are
constrained to comply with the market price, as expected by the customers,
while customers can only buy at the prices offered by the businesses. We show
numerically and analytically that the size distribution scales like a
power-law. A mean-field version of our model is also introduced and we
determine for which value of the parameters the mean-field model agrees with
the microscopic model. We discuss to what extent our simple model and its
results compare with empirical data on company sizes in the U.S. and debt sizes
in Japan. Finally, possible extensions of the mean-field model are discussed,
to cope with other empirical data.Comment: 12 pages, 2 figures, submitted for publicatio
Strategy Selection in the Minority Game
We investigate the dynamics of the choice of an active strategy in the
minority game. A history distribution is introduced as an analytical tool to
study the asymmetry between the two choices offered to the agents. Its
properties are studied numerically. It allows us to show that the departure
from uniformity in the initial attribution of strategies to the agents is
important even in the efficient market. Also, an approximate expression for the
variance of the number of agents at one side in the efficient phase is
proposed. All the analytical propositions are supported by numerical
simulations of the system.Comment: Latex file, 17 page, 4 figure
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