Strategy correlations and timing of adaptation in Minority Games

TL;DR

This paper analyzes how strategy correlations and timing of adaptation influence the dynamics of Minority Games, revealing qualitative differences with anti-correlated strategies and discussing the implications for ergodicity and mixed populations.

Contribution

It provides an analytical and simulational study of strategy correlations and adaptation timing in Minority Games, extending static replica results to dynamic behavior.

Findings

Timing of adaptation affects game dynamics with correlated strategies.

Standard volatility approximations fail in batch games with anti-correlations.

Oscillations and ergodicity breakdown are linked to strategy correlations.

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 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 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.