In a three-stage vertical differentiated-products duopoly model, profit-maximizing owner first choose quality, and then incentive schemes in order to influence their managers’ behavior. In the third stage, basing the manager’s objective function on a linear combination of the firm’s profit and its rival’s profit, the managers compete either both in quantities, both in prices, or one in quantity and the other in price. If the owners have sufficient power to manipulate their managers’ incentives, the equilibrium outcome is the same regardless of how the firms compete in the market. If equivalence outcome holds, the equilibrium qualities do not depend on the mode of product-market competition. In the delegation game when one firm competes by setting price, the other firms will positive weight on coefficient of co-operation. Conversely, when one firm competes in quantity, the equilibrium incentive scheme puts negative weight or no delegation on coefficient of co-operation. In contrast with the existing literature in this area, two important differences are (i) coefficient of co-operation are different between high quality firm and low quality firm because of asymmetric vertical differentiated model, and (ii) high-quality firm have the strategic advantage even though the firms move simultaneously at all the stages.