Eur. Phys. J. B 46, 153-168 (2005)
https://doi.org/10.1140/epjb/e2005-00242-0

Strategy correlations and timing of adaptation in Minority Games

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

Corresponding author: ^a galla@ictp.trieste.it

Received: 1 April 2005
Published online: 8 August 2005

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.