The effects of change in transport cost are investigated for homogeneous Cournot duopoly with several regional or international markets and with decreasing marginal costs. A new existence proof is given for the unique Cournot duopoly equilibrium based on an integration of mathematical and diagrammatical approaches. Two cases are analyzed, in one of which the marginal revenue of any firm is assumed to decrease with an increase in the other firm's output, and in the other it is an increasing function of the other firm's output. In both cases the firms are assumed to have decreasing marginal costs.