Endogenous equity shares in duopoly markets with product differentiation

Abstract

Firms can form partial passive ownership arrangements by acquiring equity shares in competitors' profits. We consider a duopoly model in which products are differentiated along both vertical and horizontal dimensions and one firm may acquire the other firm's equity shares before they engage in strategic competition. We identify equilibrium equity shares and characterize how the choice of equity shares depends on three previously unexplored factors: (i) the size of the market, (ii) the degree of horizontal product differentiation and (iii) the degree of vertical product differentiation. Whether an increase in the size of the market increases firm's incentive to hold a stake in the rival depends on whether the acquiring firm is a high-quality firm or a low-quality firm. The effect of vertical product differentiation also depends on the type of the acquiring firm, high-quality vis-à-vis low-quality. On the contrary, an increase in horizontal product differentiation can increase firm's incentive to hold a stake in the rival, irrespective of the type of the acquiring firm. We also find that the equilibrium levels of consumer welfare and social welfare may be lower compared to the case of no partial passive ownership.