We study the strategic interaction between a new good producer and a remanufacturer who use advertising campaigns to compete for a dominant share of the market for a certain good. Each firm chooses one of three possible strategies for running its advertising campaign. The two rival firms care only about capturing a dominant share of the relevant market. Hence, if a firm expects to capture dominant market share with probability p ∈ [0, 1], then its payoff in the game we study is also p. Our analysis leads to four results. First, we provide the normal form representation of the game between the new good producer and the remanufacturer. Second, we specify the game in matrix form. Third, we indicate what happens at each stage of the elimination of strictly dominated strategies. Finally, we show that the iterated elimination of strictly dominated strategies yields a clear and unique prediction about the outcome of the advertising game.