Strategy correlations and timing of adaptation in Minority Games |
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Authors: | Email author" target="_blank">T?GallaEmail author D?Sherrington |
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Institution: | (1) The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK;(2) International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy and Istituto Nazionale per la Fisica della Materia (INFM), Trieste-SISSA Unit, V. Beirut 2-4, 34014 Trieste, Italy |
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Abstract: | 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 à 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
approximations for the volatility in terms of persistent order
parameters in the stationary ergodic states become unreliable in batch
games under such circumstances. We then comment on the role of
oscillations and the relation to the breakdown of ergodicity. Finally,
it is discussed how the generating functional formalism can be used to
study mixed populations of so-called ‘producers’ and ‘speculators’ in
the context of the batch Minority Games. |
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Keywords: | |
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