  We define and study a rather complex market model, inspired from the Santa Fe
artificial market and the Minority Game. Agents have different strategies among
which they can choose, according to their relative profitability, with the
possibility of not participating to the market. The price is updated according
to the excess demand, and the wealth of the agents is properly accounted for.
Only two parameters play a significant role: one describes the impact of
trading on the price, and the other describes the propensity of agents to be
trend following or contrarian. We observe three different regimes, depending on
the value of these two parameters: an oscillating phase with bubbles and
crashes, an intermittent phase and a stable `rational' market phase. The
statistics of price changes in the intermittent phase resembles that of real
price changes, with small linear correlations, fat tails and long range
volatility clustering. We discuss how the time dependence of these two
parameters spontaneously drives the system in the intermittent region. We
analyze quantitatively the temporal correlation of activity in the intermittent
phase, and show that the `random time strategy shift' mechanism that we
proposed earlier allows one to understand the observed long ranged
correlations. Other mechanisms leading to long ranged correlations are also
reviewed. We discuss several other issues, such as the formation of bubbles and
crashes, the influence of transaction costs and the distribution of agents
wealth.
