Is Optimal Interlocking Cross-Ownership for the Network Industry?

Common wisdom suggests that noncontrolling, interlocking crossholdings is always profitable in a Cournot duopoly model. Therefore, the maximal profit is obtained by a reciprocal share of ownership of about 50%, which allows for the monopoly profit. By contrast, we analyze a network industry and show that crossholdings can be unprofitable under network effects and variable degree of product compatibility between firms. In particular, an optimal percentage value of crossholdings significantly less than 50%—or even 0%—always exist. Thus, we provide a new reason for unprofitable crossholdings. This result offers a policy warning to anti-trust agencies.