Algorithmic complexity in the minority game

In this paper, we present our approach for the study of the complexity of Minority Game using tools from thermodynamics and statistical physics. Previous attempts were based on the behavior of volatility, an observable of the financial markets. Our approach focuses on some properties of the binary stream of outcomes of the game. Physical complexity, a magnitude rooted in Kolmogorov-Chaitin theory, allows us to explain some properties of collective behavior of the agents. Mutual information function, a measure related to Shannon’s information entropy, was useful to observe a kind of phase transition when applied to the binary string of the whole history of the game.