Quantifying complexity in the minority game

A Lempel–Ziv complexity measure is introduced into the theory of a minority game in order to capture some features that volatility, one of the central quantities in this model of interacting agents, is not able to. Extracted solely from the binary string of outcomes of the game complexity offers new and valuable information on collective behavior of players. Also, we show that an expression for volatility may be included in the analytical expression for complexity.