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 related to the ground states of a disordered Hamiltonian with replica symmetry breaking (RSB), signalling the presence of a large number of NE. Here we study the number of NE both analytically and numerically. We then analyse the stability of the recently obtained replica-symmetric solution and, in the region where it becomes unstable, derive the solution within one-step RSB approximation. We are finally able to draw a detailed phase diagram of the model.
Replica symmetry breaking in the minority game / De Martino, A.; Marsili, M.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 34:12(2001), pp. 2525-2537. [10.1088/0305-4470/34/12/301]
Replica symmetry breaking in the minority game
De Martino A.;
2001
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 related to the ground states of a disordered Hamiltonian with replica symmetry breaking (RSB), signalling the presence of a large number of NE. Here we study the number of NE both analytically and numerically. We then analyse the stability of the recently obtained replica-symmetric solution and, in the region where it becomes unstable, derive the solution within one-step RSB approximation. We are finally able to draw a detailed phase diagram of the model.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2976747