  The study of societies of adaptive agents seeking minority status is an
active area of research. Recently, it has been demonstrated that such systems
display an intriguing phase-transition: agents tend to {\it self-segregate} or
to {\it cluster} according to the value of the prize-to-fine ratio, $R$. We
show that such systems do {\it not} establish a true stationary distribution.
The winning-probabilities of the agents display temporal oscillations. The
amplitude and frequency of the oscillations depend on the value of $R$. The
temporal oscillations which characterize the system explain the transition in
the global behavior from self-segregation to clustering in the $R<1$ case.
