Recent empirical research demonstrates that cross-holding engenders significant anti-competitive effect even though it confers no decisive influence on the target firm. This research has obtained wide attention, which leads to both calls for and actual changes in antitrust policy. However, the effects of cross-holding on competition are not well established. This paper examines the collusive effect of cross-holding with asymmetry in cost functions across firms in an infinitely repeated Cournot duopoly game. The two firms have a different share of capital that affects marginal costs. We find that cross-holding facilitates collusion when a small firm (i.e., a firm with a small capital capacity) increases its passive ownership in a big firm (i.e., a firm with a large capital capacity), and the size of initial ownership is relatively small. Unexpectedly, collusion becomes more difficult to be sustained when a big firm increases ownership in a small firm, or when a small firm increases ownership in a big firm but the initial ownership is relatively large. Our result that cross-holding may either facilitate or hinder collusion, under certain circumstances, generates important implications for antitrust policy.

最近的经验研究表明，交叉持股即使对目标公司没有决定性影响，也能产生显着的反竞争效果。这项研究已引起广泛关注，从而导致反托拉斯政策的呼吁和实际变化。但是，交叉控股对竞争的影响尚不明确。本文研究了在无限次重复的古诺双寡头博弈中跨持股不对称对企业成本函数的合谋效应。两家公司的资本份额不同，这会影响边际成本。我们发现，当小公司（即资本能力小的公司）增加其在大公司（即资本能力大的公司）中的被动所有权时，交叉持股会促进勾结。相对较小。出乎意料的是，当大公司增加对小公司的所有权时，或者当小公司增加对大公司的所有权但初始所有权相对较大时，串通变得更加难以维持。在某些情况下，交叉控股可能促进或阻碍串通的结果对反托拉斯政策产生了重要影响。