The effects of cross-holdings receive increasing attention among scholars and policymakers. For instance, European Commission (2014) highlights the possibility of anti-competitive effects caused by minority acquisitions and proposes a system for reviewing the acquisition of minority shareholdings. Heim et al. (2022) report 10,699 cases of minority acquisitions in rival firms across 63 countries between 1990 and 2013.
The related research highlights possible adverse (and desirable) effects of cross-holdings: an acquirer firm internalizes part of the competitive externality imposed on the rival, thus cross-holdings can soften competition and hurt consumers. Cross-holdings (CH) can also produce coordinated effects when firms interact repeatedly in a market.
The present paper deals with cross-holdings in vertical markets. More precisely, we consider a two-tier vertical market where two upstream firms (suppliers) are locked in exclusive relations with two downstream retailers over linear tariffs. Each downstream firm owns part of the equity of its rival with no control rights.
Under a general demand function, we show that downstream CH decrease upstream collusive profits. For a wide family of demand functions that exhibit constant elasticity of slope, we find that CH reduce the profit of an upstream firm in the punishment (competition) phase, while they can increase the profit for a firm that deviates from collusion. Considering stylized cases of demand functions from this wide family, including linear demand, we show that downstream CH reduces upstream collusion.
The present paper is related to the literature on (i) collusion in vertical markets, and (ii) the coordinated effects of cross-ownership. Malueg (1992) and Gilo et al. (2006) study the effect of partial ownership under repeated interaction in oligopolistic industries. The former extends Reynolds and Snapp (1986) and shows that partial ownership (a) facilitates collusion by reducing the short-run gain from cheating because firms internalize some of the cost imposed on rivals (b) hinders collusion because it softens the punishment phase of the trigger strategy. Gilo et al. (2006) show that cross-ownership facilitates collusion in a Bertrand oligopoly with homogeneous goods. Brito et al. (2018) propose an empirical methodology to evaluate the coordinated effects of partial horizontal acquisitions and de Haas and Paha (2020) examine how competition policy affects the impact of minority shareholdings on the sustainability of collusion.
The present paper is also related to the literature on collusion in vertical markets. This literature studies the effects of vertical mergers (Nocke and White, 2007 and Normann, 2009), retailers’ managerial incentives (Bian et al., 2013), exclusive territories (Piccolo and Reisinger, 2011), passive vertical ownership (Charistos et al., 2022) on upstream collusion.
The effect of the structure of the distribution channel on tacit collusion between manufacturers is studied in Reisinger and Thomes (2017). They show that when selling through a common (in contrast to an independent and exclusive) retailer, (a) manufacturers raise the collusive wholesale price above the industry profit maximizing level, in an attempt to mitigate the retailer’s threat of rejecting a manufacturer’s offer, (b) they realize lower competitive profit along the punishment phase and (c) the ratio between deviation and collusive profits is higher as deviation makes the common retailer to reject the offer of the non-deviating firm leading to the monopolization of the downstream market. Reisinger and Thomes (2017) shows that common retailing implies an unambiguously higher incentive to deviate and hinders collusion between manufacturers compared to independent retailing.
Finally, Hu et al. (2022) stresses the impact of downstream CH on the decision of the upstream supplier to engage in R&D investments. They show that (a) the amount of upstream R&D decreases (b) the total surplus may increase, while the consumer surplus always decreases with the degree of downstream CH.