  In the evolutionary version of the minority game, agents update their
strategies (gene-value $p$) in order to improve their performance. Motivated by
recent intriguing results obtained for prize-to-fine ratios which are smaller
than unity, we explore the system's dynamics with a strategy updating rule of
the form $p \to p \pm \delta p$ ($0 \leq p \leq 1$). We find that the strategy
distribution depends strongly on the values of the prize-to-fine ratio $R$, the
length scale $\delta p$, and the type of boundary condition used. We show that
these parameters determine the amplitude and frequency of the the temporal
oscillations observed in the gene space. These regular oscillations are shown
to be the main factor which determines the strategy distribution of the
population. In addition, we find that agents characterized by $p={1 \over 2}$
(a coin-tossing strategy) have the best chances of survival at asymptotically
long times, regardless of the value of $\delta p$ and the boundary conditions
used.
