In an oligopolistic setting under a Cournot scheme, the strategy of each economic player depends on its own quantity decision, but also on its rivals' reaction. Since Puu's seminal work, different oligopoly games have been studied in terms of their stability, as nonlinear discrete time varying systems. Most works in this line of research have concentrated on single markets with linear production structures (i.e. assuming constant returns to scale). Nevertheless, oligopolistic competition seems today to present multi-market phenomena, exhibiting, in some cases, important economies of scale, especially in the retail and service industry. In this paper, we study the stability of a multi-market Cournot-Nash equilibrium with global economies of scale. In other words, we look at the scale level that is related to the total production of firms, in all markets, as opposed to local economies of scale presented at each store individually. The modeling confirms the fact that economies and diseconomies of scale make the Cournot equilibrium very unstable for certain values of the scale of the producers. On the other hand, stability is achieved when the firm reaches absolute advantage with respect to its competition.