Advertising with spillover effects in a differential oligopoly game with differentiated goods

We consider a differentiated oligopoly where firms compete à la Cournot in the market phase, and each firm may invest in advertising activity, to enlarge its market size. Each firm's advertising effort has positive external effects on the market size of all rivals. We derive the open-loop (and the coincident closed-loop) Nash equilibrium, and the optimal behaviour of a cartel involving all firms setting both quantities and advertising efforts so as to maximize joint profits. The comparative assessment of these equilibria shows that a cartel may produce a steady state where social welfare is higher than the social welfare level associated with the non-cooperative setting. This is due to the positive externalities from advertising activity.