This paper analyses a differential game of duopolistic rivalry through time where firms can use advertising and price as competitive tools. Two cases are considered whereby: (1) advertising has the main effect of increasing market size and firms differ in production efficiency; (2) advertising has both predatory and cooperative effects in a symmetric market. The former shows that market shares and advertising shares are positively correlated and that market size increases with the difference in firms' relative efficiency. The latter highlights the differences in the feedback and open-loop strategies. It is shown that firms' advertising are strategic complements and that profits are higher in the feedback equilibrium because firms advertise more. The applicability of the model in markets where franchise contracts and dealership agreements operate is also discussed.