Replica symmetry breaking in the minority game

Citation
A. De Martino et M. Marsili, Replica symmetry breaking in the minority game, J PHYS A, 34(12), 2001, pp. 2525-2537
Citations number
15
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
12
Year of publication
2001
Pages
2525 - 2537
Database
ISI
SICI code
0305-4470(20010330)34:12<2525:RSBITM>2.0.ZU;2-5
Abstract
We extend and complete recent work concerning the analytic solution of the minority game. Nash equilibria (NE) of the game have been found to be relat ed to the ground states of a disordered Hamiltonian with replica symmetry b reaking (RSB), signalling the presence of a large number of NE. Here we stu dy the number of NE both analytically and numerically. We then analyse the stability of the recently obtained replica-symmetric solution and, in the r egion where it becomes unstable, derive the solution within one-step RSB ap proximation. We are finally able to draw a detailed phase diagram of the mo del.