We briefly review data analysis of the Island order book, part of NASDAQ, which suggests a framework to which all limit order markets should comply. Using a simple exclusion particle model, we argue that short-time over-diffusion in limit order markets is due to the non-equilibrium of order...

A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the order book are essential to ensure consistency at the...

The minority game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extent this is a reasonable statement, and present minimal modifications that make this model reproduce stylized facts. The resulting model shows...

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...

We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of σ2/N in the N⪡2M region. The ability of the players to learn a given payoff is also analyzed, and we show that the...

We present and study a Minority Game based model of a financial market where adaptive agents—the speculators—interact with deterministic agents—called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active...

Using the minority game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow: producers feed in the information whereas speculators make it...

Starting from the Minority Game and building more and more sophisticated models of adaptive agents, we show that minority mechanisms underly any model where agents learn collectively a resource level that can be either obvious and constant in time, obvious and time-varying, or hidden.

A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical...

We report on a statistical analysis of the Island ECN (NASDAQ) order book. We determine the static and dynamic properties of this system, and then analyze them from a physicist's viewpoint using an equivalent particle system obtained by treating orders as massive particles and price as position....