  We study nonzero-sum stochastic switching games. Two players compete for
market dominance through controlling (via timing options) the discrete-state
market regime $M$. Switching decisions are driven by a continuous stochastic
factor $X$ that modulates instantaneous revenue rates and switching costs. This
generates a competitive feedback between the short-term fluctuations due to $X$
and the medium-term advantages based on $M$. We construct threshold-type
Feedback Nash Equilibria which characterize stationary strategies describing
long-run dynamic equilibrium market organization. Two sequential approximation
schemes link the switching equilibrium to (i) constrained optimal switching,
(ii) multi-stage timing games. We provide illustrations using an
Ornstein-Uhlenbeck $X$ that leads to a recurrent equilibrium $M^\ast$ and a
Geometric Brownian Motion $X$ that makes $M^\ast$ eventually "absorbed" as one
player eventually gains permanent advantage. Explicit computations and
comparative statics regarding the emergent macroscopic market equilibrium are
also provided.
