Abstract
Competitive implications of cross-holdings have been extensively analyzed in the literature. Incentives for engaging cross-holdings and welfare effects were however rarely studied. Although a similar logic as with the merger paradox holds for Cournot oligopolies with homogeneous products and symmetric technologies, we show that there are profit incentives for firms to engage cross-holdings with asymmetric technologies. Furthermore, we show that social welfare could be enhanced with cross-holdings even though the market becomes more concentrated. We also discuss the robustness of both the submodularity of the Cournot model with respect to the presence of cross-holdings and our results with respect to product differentiation.
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We thank the editor, Nicholas Yannelis, the associate editor, and two anonymous reviewers for their constructive comments and suggestions that have helped to greatly improve the paper. We also thank Rabah Amir, Masaki Aoyagi, Yongmin Chen, Zhiqi Chen, Gautam Gowrisankaran, Patrick Legros and the audience in the 2016 international conference on innovation and industrial economics in Nanjing for insightful comments and suggestions. Financial support from the Humanity and Social Science Planning Foundation of the Ministry of Education of China (Grant No. 20YJA790001), the Humanity and Social Science Youth Foundation of the Ministry of Education of China (Grant No. 18YJC790115), and the National Science Foundation of China (Grant No. 72103210, 71721001) are gratefully acknowledged.
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Ma, H., Qin, CZ. & Zeng, C. Incentive and welfare implications of cross-holdings in oligopoly. Econ Theory 77, 975–997 (2024). https://doi.org/10.1007/s00199-021-01398-x
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DOI: https://doi.org/10.1007/s00199-021-01398-x