This paper studies the choice of strategic variables by firms in a symmetric oligopoly in which each firm produces differentiated goods and maximizes its relative profit, that is the difference between its profit and the average profit of the other firms. We consider a two-stage game such that in the first stage the firms choose their strategic variables, quantity or price, and in the second stage they determine the values of their strategic variables. We show that the choice of strategic variables is irrelevant in the sense that the equilibrium quantities and prices are the same in all firms whichever each firm chooses in the first stage, so any combination of strategy choice by the firms constitutes a sub-game perfect equilibrium in the two-stage game.
