We compare two formulations of relative profit maximization in duopoly with differentiated goods: (1) (difference case) maximization of the difference between the profit of one firm and that of the other firm and (2) (ratio case) maximization of the ratio of the profit of one firm to the total...

We study a symmetric free entry oligopoly in which firms produce differentiated goods so as to maximize their relative profits. The relative profit of each firm is the difference between its profit and the average of the profits of other firms. We show that, whether firms determine their outputs...