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On the Profitability of Cross-Ownership in Cournot Oligopolies: Stock Sizes Matter

Author

Listed:
  • Hassan Benchekroun
  • Miao Dai
  • Ngo Van Long
Abstract
We examine the profitability of cross-ownership in an oligopolistic industry where firms compete as Cournot rivals. We consider a symmetric cross-ownership structure in which a subset of k firms engage in cross-shareholding and each firm has an equal silent financial interest in the other firms, while the remaining (n – k) firms stay independent. We show that a symmetric cross-ownership is never profitable for any levels of non-controlling minority shareholdings if the participation ratio (k/n) is less than or equal to (n+1)/(2n), while there exists a large range of cross-ownership for which it can be profitable beyond that participation ratio. This result may be called a cross-ownership paradox, analogous to the merger paradox. With the presence of stock constraints, however, we find some of the results from the cross-ownership paradox do not carry over to the case of non-renewable resource industries. The profitability of a symmetric cross-ownership can be positive even when the participation ratio (k/n) is less than or equal to (n+1)/(2n) and is always positive when the participation ratio (k/n) is greater than (n+1)/(2n), provided that the initial resource stock owned by each firm is small enough. We also highlight that cross-ownership can be preferable to a horizontal merger under Cournot competition. Not only is it more profitable to do so, more importantly, it constitutes a shrewd strategy to avoid possible legal challenges. Nous examinons la rentabilité de la propriété croisée dans une industrie oligopolistique où les entreprises se font concurrence en tant que rivales de Cournot. Nous considérons une structure de propriété croisée symétrique dans laquelle un sous-ensemble de k entreprises s'engagent dans des participations croisées, chaque entreprise ayant un intérêt financier silencieux égal dans les autres (k-1) entreprises du sous-ensemble, alors que (n - k) entreprises restent indépendantes. Nous montrons qu'une participation croisée symétrique n'est jamais rentable si le ratio de participation (k /n) est inférieur ou égal à (n + 1) / (2n), alors qu’il existe un large domaine de valeurs de k/n au-delà de (n+1)/(2n) pour lesquelles la participation croisée est rentable. Ce résultat peut être qualifié de paradoxe de la propriété croisée, analogue au paradoxe de la fusion. Cependant, dans le cas des industries de ressources non-renouvelables, avec la présence de contraintes de stock, nous constatons que certains des résultats du paradoxe de la propriété croisée ne se répercutent pas. La rentabilité d'une propriété croisée symétrique peut être positive même lorsque le taux de participation (k / n) est inférieur ou égal à (n + 1) / (2n) et est toujours positive lorsque le taux de participation (k / n) est supérieur à (n +1) / (2n), à condition que le stock initial de ressources détenu par chaque entreprise soit suffisamment petit. Nous soulignons également que la propriété croisée peut être préférable à une fusion horizontale sous la concurrence de Cournot. Non seulement il est plus rentable de le faire, mais surtout, cela constitue une stratégie astucieuse pour éviter d'éventuelles contestations judiciaires.

Suggested Citation

  • Hassan Benchekroun & Miao Dai & Ngo Van Long, 2020. "On the Profitability of Cross-Ownership in Cournot Oligopolies: Stock Sizes Matter," CIRANO Working Papers 2020s-43, CIRANO.
    • Handle: RePEc:cir:cirwor:2020s-43
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    References listed on IDEAS

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    More about this item

    Keywords

    Cross-ownership; Profitability; Oligopoly; Non-renewable Resources; Resource Stock; Horizontal Merger; Competition Policy; Antitrust Laws; Propriété croisée; Rentabilité; Oligopole; Ressources non-renouvelables; Stock de ressources; Fusion horizontale; Politique de la concurrence; Lois antitrust;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices
    • Q3 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation

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