publication . Article . Preprint . 2005

Strategy correlations and timing of adaptation in Minority Games

Tobias Galla; David Sherrington;
Open Access
  • Published: 01 Jul 2005 Journal: The European Physical Journal B, volume 46, pages 153-168 (issn: 1434-6028, eissn: 1434-6036, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: United Kingdom
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-line games with correlated strategies, complementing exisiting replica studies of their statics. It is shown that the timing of adaptation can be relevant; while conventional games with uncorrelated strategies are nearly insensitive to the choice of on-line versus batch learning, we find qualitative differences when anti-correlations are present in the strategy assignments. The available standard ...
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free text keywords: Electronic, Optical and Magnetic Materials, Condensed Matter Physics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Complex system, Game theory, Ergodicity, Mathematical economics, Sequential game, Functional approach, Ergodic theory, Artificial neural network, Decision theory, Computer science
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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.

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