Dynamics of the Time Horizon Minority Game

We present exact analytic results for a new version of the Minority Game (MG) in which strategy performance is recorded over a finite time horizon. The dynamics of this Time Horizon Minority Game (THMG) exhibit many distinct features from the MG and depend strongly on whether the participants are fed real, or random, history strings. The THMG equations are equivalent to a Markov Chain, and yield exact analytic results for the volatility given a specific realization for the quenched strategy disorder.