Dynamical Solution of the On-Line Minority Game

Details Dynamical Solution of the On-Line Minority Game Dynamical Solution of the On-Line Minority Game

2001-07-30

arxiv.org/abs/cond-mat/0107600v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

25 pages LaTeX, no figures

Scientific paper

10.1088/0305-4470/34/49/304

We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functions defined via an effective continuous-time single-trader process, which are exact in both the ergodic and in the non-ergodic regime of the minority game. Our solution also explains why, although one cannot formally truncate the Kramers-Moyal expansion of the process after the Fokker-Planck term, upon doing so one still finds the correct solution, that the previously proposed diffusion matrices for the Fokker-Planck term are incomplete, and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions.

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