  We explore various extensions of Challet and Zhang's Minority Game in an
attempt to gain insight into the dynamics underlying financial markets. First
we consider a heterogeneous population where individual traders employ
differing `time horizons' when making predictions based on historical data. The
resulting average winnings per trader is a highly non-linear function of the
population's composition. Second, we introduce a threshold confidence level
among traders below which they will not trade. This can give rise to large
fluctuations in the `volume' of market participants and the resulting market
`price'.
