  In light of the growing interest in agent-based market models, we bring
together several earlier works in which we considered the topic of
self-consistent market modelling. Building upon the binary game structure of
Challet and Zhang, we discuss generalizations of the strategy reward scheme
such that the agents seek to maximize their wealth in a more direct way. We
then examine a disturbing feature whereby such reward schemes, while appearing
microscopically acceptable, lead to unrealistic market dynamics (e.g.
instabilities). Finally, we discuss various mechanisms which are responsible
for re-stabilizing the market in reality. This discussion leads to a `toolbox'
of processes from which, we believe, successful market models can be
constructed in the future.
