  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.
