  We propose a flexible stochastic framework for modeling the market share
dynamics over time in a multiple markets setting, where firms interact within
and between markets. Firms undergo stochastic idiosyncratic shocks, which
contract their shares, and compete to consolidate their position by acquiring
new ones in both the market where they operate and in new markets. The model
parameters can meaningfully account for phenomena such as barriers to entry and
exit, fixed and sunk costs, costs of expanding to new sectors with different
technologies and competitive advantage among firms. The construction is
obtained in a Bayesian framework by means of a collection of nonparametric
hierarchical mixtures, which induce the dependence between markets and provide
a generalization of the Blackwell-MacQueen P\'{o}lya urn scheme, which in turn
is used to generate a partially exchangeable dynamical particle system. A
Markov Chain Monte Carlo algorithm is provided for simulating trajectories of
the system, by means of which we perform a simulation study for transitions to
different economic regimes. Moreover, it is shown that the infinite-dimensional
properties of the system, when appropriately transformed and rescaled, are
those of a collection of interacting Fleming-Viot diffusions.
