  In this short paper we define the wealth process in a spin model for market
microstructure, for individual agents and in aggregate. The agents in our model
try to balance their desire to belong to the local majority (herding behavior),
defined over random network neighborhoods, and the occasional advantage of
belonging to the global minority (contrarian trading). We arrive at a
classification of the martingale properties of this wealth process and use it
to determine the strategic stability of the agents' interactions. Our goal is
to add a behavioral interpretation to this stochastic agent-based model for
market fluctuations.
