Relevance of memory in Minority Games

Abstract

By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits strings, each node standing for a given string, i.e. a history in the Minority Game. We show that the frequency of visit of each history is not given by $1/2^M$ in the limit of large $M$ when the transition probabilities are biased. Consequently all quantities of the model do significantly depend on whether the histories are real, or uniformly and randomly sampled. We expose a self-consistent theory of the case of real histories, which turns out to be in very good agreement with numerical simulations.

10 pages, 9 figures, using RevTex

References in corpus (4)

• Statistical mechanics of systems with heterogeneous agents: Minority Games
• Modeling Market Mechanism with Minority Game
• Phase Transition and Symmetry Breaking in the Minority Game
• Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

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