Strategy correlations and timing of adaptation in Minority Games

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Galla, Tobias; Sherrington, David;
  • Related identifiers: doi: 10.1140/epjb/e2005-00242-0
  • Subject: Condensed Matter - Statistical Mechanics | Condensed Matter - Disordered Systems and Neural Networks

We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach a la De Dominicis we compute the phase diagram and the behaviour of batch and on-... View more
  • References (31)
    31 references, page 1 of 4

    28. Heimel J A F 2001, PhD thesis, King's College London

    29. Mosetti G, Challet D, Marsili M, Zhang Y-C 2005 (in This work was supported by EPSRC (UK) under research preparation) grant GR/M04426 and studentship 00309273. TG acknowl- 30. Challet D 1999, PhD thesis, University of Fribourg edges the award of a Rhodes Scholarship and support 31. Challet D, De Martino A, Marsili M, Perez Castillo I 2004, by Balliol College, Oxford. Financial support by the ESF preprint cond-mat/0407595 programme SPHINX and by the European Community's 32. We measure c1 in the stationary state as c1 = (2T )−1 P2T Human Potential Programme under contract HPRN-CT- τ=T |C(τ + M ) − C(τ )|, where T corresponds to 2002-00319, STIPCO is gratefully acknowledged. The au- 25 effective updates, i.e. T = 25M on-line steps. While the thors would like to thank A C C Coolen, J P Garrahan, data for the uncorrelated case (ρ = 1/2) does not seem to M Marsili, E Moro, G Mosetti, M K Y Wong and Y C exhibit any strong dependence on the sample size P , the Zhang for helpful discussions. running time or the details of the numerical procedure of determining c1 in the simulations, we find that the quantitative values of the data for the uncorrelated case (ρ = 0) can depend on these parameters. This does not, however, References affect the key qualitative observation of an increasing oscillation amplitude as M is increased.

    33. The data for ρ = 0 and M = 10P appears to lie (slightly) below the random trading limit σ2 = 1 in an interval around αc(ρ = 0) = 1. This seems to persist also for larger values of P or M and/or for longer running times. It is at present unclear whether this constitutes a systematic effect or whether it is an artifact due to limitations in the numerical simulations. Note also that similar observations were made for the on-line case with real market histories (ρ = 0 and M = 1) [30].

    34. Galla T 2004, D.Phil. thesis, University of Oxford

    1. Challet D and Zhang Y-C 1997 Physica A 246 407

    2. Challet D, Marsili M and Zhang Y-C 2000 Physica A 276 284

    3. Challet D, Marsili M and Zecchina R 2000 Phys. Rev. Lett. 84 1824

    4. Marsili M, Challet D and Zecchina R 2000 Physica A 280 522

    5. Garrahan J P, Moro E and Sherrington D 2000 Phys. Rev E 62 R9

    6. Heimel J A F and Coolen A C C 2001 Phys. Rev. E 63 056121

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