In this paper, we report on an equilibrium with market dominance that exists in a simple two-firm model that features neither entry barriers nor sophisticated punishment strategies. This equilibrium induces an intertemporal market division in which the two firms alternate as monopolists – despite the fact that the model also sustains a cournot duopoly. Even when initially both firms are active in the market, the alternating monopoly reveals itself rather quickly. Moreover, it pareto dominates the cournot equilibrium – as it is close to the cartel outcome. Several examples of what well may be such alternating monopolies are presented.