This paper shows that imperfect competition can be a rich source of sunspots equilibria and coordination failures. This is demonstrated in a dynamic general equilibrium model that has no major distortions except imperfect competition. In the absence of fundamental shocks, the model has a unique certainty (fundamental) equilibrium. But there is also a continuum of stochastic (sunspots) equilibria that are not mere randomizations over fundamental equilibria. Markup is always counter-cyclical in sunspots equilibria, which is consistent with empirical evidence. The paper provides a justification for exogenous variations over time in desired markups, which play an important role as a source of cost-push shocks in the monetary policy literature. We show that fluctuations driven by self-fulfilling expectations (or sunspots) look very similar to fluctuations driven by technology shocks, and we prove that such fluctuations are welfare reducing.