Trading behavior and excess volatility in toy markets

We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive reactivity of agents. These issues are dealt with in detail in the simple case without public information. We also derive, for the general case, the critical learning rate above which trading behavior leads to turbulent dynamics of the market.Comment: 14 pages, 4 figures, minor change

On the High-dimensional Bak-Sneppen model

We report on extensive numerical simulations on the Bak-Sneppen model in high dimensions. We uncover a very rich behavior as a function of dimensionality. For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process becomes transient. Finally the exponents reach their mean field values for d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.Comment: 4 pages, 3 eps figure

A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model

A recent renormalization group approach to a modified Bak-Sneppen model is discussed. We propose a self-consistency condition for the blocking scheme to be essential for a successful RG-method applied to self-organized criticality. A new method realizing the RG-approach to the Bak-Sneppen model is presented. It is based on the Monte-Carlo importance sampling idea. The new technique performs much faster than the original proposal. Using this technique we cross-check and improve previous results.Comment: 11 pages, REVTex, 2 Postscript figures include

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

Criticality and finite size effects in a simple realistic model of stock market

We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple argument, we show that, in Minority Games, the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets as critical systems.Comment: 4 pages, 4 figure