In this paper, we study the impacts of cross-ownership structure on double marginalization problem (DMP) and social welfare under downstream the Bertrand and Cournot competition. We find that in the Bertrand competition, DMP is more serious under backward cross-ownership than under forward cross-ownership. Under forward cross-ownership, because the upstream firm internalizes part of a retailer's profit, it alleviates the DMP. However, for the whole society, forward cross-ownership is beneficial with respect to backward cross-ownership. The mark-up ratio under forward cross-ownership is the largest, followed by that under vertical separation. The lowest one is under backward cross-ownership. The results hold under Cournot competition as well.

中文翻译：

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纵向交叉所有权、双重边缘化与社会福利

本文研究了伯特兰和古诺竞争下游的交叉所有制结构对双重边缘化问题（DMP）和社会福利的影响。我们发现，在Bertrand竞争中，后向交叉所有权下的DMP比前向交叉所有权下的DMP更为严重。在远期交叉所有权下，由于上游公司将零售商的部分利润内部化，因此减轻了 DMP。但对于整个社会来说，前向交叉所有权相对于后向交叉所有权是有利的。远期交叉持股下的加成率最大，其次是垂直分离下的加成率。最低的是落后的交叉所有制。该结果在古诺竞争下也成立。