  We propose a class of Markovian agent based models for the time evolution of
a share price in an interactive market. The models rely on a microscopic
description of a market of buyers and sellers who change their opinion about
the stock value in a stochastic way. The actual price is determined in
realistic way by matching (clearing) offers until no further transactions can
be performed. Some analytic results for a non-interacting model are presented.
We also propose basic interaction mechanisms and show in simulations that these
already reproduce certain particular features of prices in real stock markets.
