  In this paper we extend the series of our studies on the properties of an
interacting particle model for market microstructure. In our earlier work we
defined a Markov process on the majority opinion of the agents, obtained the
transition probabilities and analyzed the martingale properties of the ensuing
wealth process. Here we relax the assumption on the choices of individual
agents by allowing mixed strategies, offering opportunities for the agents to
gain intermediate submartingale exposure for their individual wealth processes.
We develop a novel two-dimensional spin system to model the critical regions of
the wealth process as a reflection of the agents' behaviors. We exhibit
strategic conflicts between individual market participants and the market as a
whole, and identify a new source of uncertainty arising from `reinforced
expectations'.
