Generalized minority games with adaptive trend-followers and contrarians

We introduce a simple extension of the minority game in which the market rewards contrarian (respectively, trend-following) strategies when it is far from (respectively, close to) efficiency. The model displays a smooth crossover from a regime where contrarians dominate to one where trend-followers dominate. In the intermediate phase, the stationary state is characterized by non-Gaussian features as well as by the formation of sustained trends and bubbles.