2007/12/02 by A C C Coolen, A. C. C. Coolen, N. Shayeghi +1
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Covariance matrix #Digital Platforms and Economics #Eigenvalues and eigenvectors #Game Theory and Applications #Game theory #Inner product space #Phenomenology (philosophy) #Product (mathematics) #Table (database) #physics.soc-ph
paper · pdf · doi:10.1088/1751-8113/41/32/324005
30 pages, 12 figures (some lower resolution to enable submission, originals available upon request), submitted to Journal of Physics A
arxiv created 2007/12/02 · openalex publication_date 2008/07/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use generating functional methods to solve the so-called inner product versions of the minority game (MG), with fake and/or real market histories, by generalizing the theory developed recently for look-up table MGs with real histories. The phase diagrams of the look-up table and inner product MG versions are generally found to be identical, with the exception of inner product MGs where histories are sampled linearly, which are found to be structurally critical. However, we encounter interesting differences both in the theory (where the role of the history frequency distribution in look-up table MGs is taken over by the eigenvalue spectrum of a history covariance matrix in inner product MGs) and in the static and dynamic phenomenology of the models. Our theoretical predictions are supported by numerical simulations.