2001/07/30 by A C C Coolen, J A F Heimel · 4 citations
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Digital Platforms and Economics #Game Theory and Applications #cond-mat.dis-nn #q-fin.TR
paper · pdf · doi:10.1088/0305-4470/34/49/304
25 pages LaTeX, no figures
arxiv created 2001/07/30 · openalex publication_date 2001/12/05 · arxiv updated 2009/11/30 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/30
We solve the dynamics of the on-line minority game (MG), 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 MG. 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.