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In this paper, two competing firms selling a homogeneous good are considered. The market consists of many small consumers who choose a specific brand based only on the accumulated goodwill of each companies. Each firm chooses the best advertising strategy to maximize its firm value over the planning horizon. Three different equilibrium solutions - Nash equilibrium policy, Pareto optimal policy and partial cooperative policy - have been derived for a simulated situation using an iterative solution method. We were mainly interested in the sensitivity of the production cost function. One firm was supposed to have a lower fixed cost, and/but steeper cost function than the other. The former is smaller in size than the latter. The most distinctive difference between the Nash and Pareto policies was found in the competitive strategies. In the Nash solution, both players increased their investments on competitive advertising gradually when we assigned a positive value to the terminal weight. The Pareto policy showed, however, a switching pattern in competitive advertising. The larger firm’s strategy was to decrease its expenditures, and the smaller firm’s strategy was to increase its activities with time. In each period, the competitive advertising was carried out by one of the firms. The cooperative strategies had a down-sloping stream for both policies, and was initiated by the larger firm. The larger firm invests more and longer both in absolute amounts and in ratio to total spending.