Market mechanism and expectations in minority and majority games

We present a derivation of the minority game from a market mechanism. This shows that the minority nature of the interaction crucially depends on the expectation model of agents. The same market mechanism with different expectations leads indeed to the majority game. We study in detail the minority game without information and clarify the role of initial conditions on the dynamics. The stronger and the more heterogeneous the prior beliefs which agents hold on the best choice, the more efficient is the final stationary state. We also review the effect of market impact. Finally we discuss mixed minority–majority games in order to address the issue of whether the dynamics of the market satisfies the expectations of agents. We find that in both a minority and a majority game expectations are self-fulfilled.