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Endogenous equity shares in duopoly markets with product differentiation

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  • Yi Li

Abstract

Firms can form partial passive ownership arrangements by acquiring equity shares in competitors' profits. We consider a duopoly model in which products are differentiated along both vertical and horizontal dimensions and one firm may acquire the other firm's equity shares before they engage in strategic competition. We identify equilibrium equity shares and characterize how the choice of equity shares depends on three previously unexplored factors: (i) the size of the market, (ii) the degree of horizontal product differentiation and (iii) the degree of vertical product differentiation. Whether an increase in the size of the market increases firm's incentive to hold a stake in the rival depends on whether the acquiring firm is a high‐quality firm or a low‐quality firm. The effect of vertical product differentiation also depends on the type of the acquiring firm, high‐quality vis‐à‐vis low‐quality. On the contrary, an increase in horizontal product differentiation can increase firm's incentive to hold a stake in the rival, irrespective of the type of the acquiring firm. We also find that the equilibrium levels of consumer welfare and social welfare may be lower compared to the case of no partial passive ownership. Actions participatives endogènes sur les marchés duopolistiques avec différenciation des produits. Les entreprises peuvent conclure des accords de participation passive partielle en acquérant des actions participatives de leurs concurrents. Nous considérons un modèle de duopole dans lequel les produits sont différenciés à la fois verticalement et horizontalement et où une entreprise peut acquérir des actions participatives de l'autre avant de se lancer dans une concurrence stratégique. Nous déterminons l'équilibre du nombre d'actions participatives et caractérisons la façon dont le choix des actions participatives dépend de trois facteurs jusqu'ici inexplorés : i) la taille du marché; ii) le degré de différenciation horizontale des produits; iii) le degré de différenciation verticale des produits. La question de savoir si une augmentation de la taille du marché augmente le désir de l'entreprise de détenir une participation dans l'entreprise rivale dépend du fait que l'entreprise acquéreuse est une entreprise de haute ou de faible qualité. L'effet de la différenciation verticale des produits dépend également du type d'entreprise acquéreuse, de haute ou de faible qualité. Au contraire, un accroissement de la différenciation horizontale des produits peut augmenter le désir de l'entreprise de détenir une participation dans l'entreprise rivale, quel que soit le type de l'entreprise acquéreuse. Nous constatons également que les niveaux d'équilibre du bien‐être des consommateurs et du bien‐être social peuvent être plus faibles que dans le cas où il n'y a pas de participation passive partielle.

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  • Yi Li, 2025. "Endogenous equity shares in duopoly markets with product differentiation," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 58(1), pages 227-246, February.
  • Handle: RePEc:wly:canjec:v:58:y:2025:i:1:p:227-246
    DOI: 10.1111/caje.12750
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    1. José Azar & Martin C. Schmalz & Isabel Tecu, 2018. "Anticompetitive Effects of Common Ownership," Journal of Finance, American Finance Association, vol. 73(4), pages 1513-1565, August.
    2. Brito, Duarte & Ribeiro, Ricardo & Vasconcelos, Helder, 2019. "Can partial horizontal ownership lessen competition more than a monopoly?," Economics Letters, Elsevier, vol. 176(C), pages 90-95.
    3. Foros, Øystein & Jarle Kind, Hans & Shaffer, Greg, 2011. "Mergers and partial ownership," European Economic Review, Elsevier, vol. 55(7), pages 916-926.
    4. Malueg, David A., 1992. "Collusive behavior and partial ownership of rivals," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 27-34, March.
    5. Flath, David, 1991. "When is it rational for firms to acquire silent interests in rivals?," International Journal of Industrial Organization, Elsevier, vol. 9(4), pages 573-583, December.
    6. Arghya Ghosh & Hodaka Morita, 2017. "Knowledge transfer and partial equity ownership," RAND Journal of Economics, RAND Corporation, vol. 48(4), pages 1044-1067, December.
    7. Brito, Duarte & Ribeiro, Ricardo & Vasconcelos, Helder, 2020. "Overlapping ownership, endogenous quality, and welfare," Economics Letters, Elsevier, vol. 190(C).
    8. Bourreau, Marc & Jullien, Bruno, 2018. "Mergers, investments and demand expansion," Economics Letters, Elsevier, vol. 167(C), pages 136-141.
    9. Papadopoulos, Konstantinos G. & Petrakis, Emmanuel & Skartados, Panagiotis, 2019. "Product innovation transfer under passive partial ownership holdings," Economics Letters, Elsevier, vol. 177(C), pages 22-25.
    10. Amrita Nain & Yan Wang, 2018. "The Product Market Impact of Minority Stake Acquisitions," Management Science, INFORMS, vol. 64(2), pages 825-844, February.
    11. David Gilo & Yossi Moshe & Yossi Spiegel, 2006. "Partial Cross Ownership and Tacit Collusion," RAND Journal of Economics, The RAND Corporation, vol. 37(1), pages 81-99, Spring.
    12. Symeonidis, George, 2003. "Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 39-55, January.
    13. Shelegia, Sandro & Spiegel, Yossi, 2012. "Bertrand competition when firms hold passive ownership stakes in one another," Economics Letters, Elsevier, vol. 114(1), pages 136-138.
    14. Joseph Farrell & Carl Shapiro, 1990. "Asset Ownership and Market Structure in Oligopoly," RAND Journal of Economics, The RAND Corporation, vol. 21(2), pages 275-292, Summer.
    15. George Symeonidis, 2000. "Price and Nonprice Competition with Endogenous Market Structure," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 9(1), pages 53-83, March.
    16. Reynolds, Robert J. & Snapp, Bruce R., 1986. "The competitive effects of partial equity interests and joint ventures," International Journal of Industrial Organization, Elsevier, vol. 4(2), pages 141-153, June.
    17. Bárcena-Ruiz, Juan Carlos & Campo, María Luz, 2017. "Taxes versus standards under cross-ownership," Resource and Energy Economics, Elsevier, vol. 50(C), pages 36-50.
    18. David Gilo & Yossi Moshe & Yossi Spiegel, 2006. "Partial cross ownership and tacit collusion," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 81-99, March.
    19. Reitman, David, 1994. "Partial Ownership Arrangements and the Potential for Collusion," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 313-322, September.
    20. Leonardos, Stefanos & Petrakis, Emmanuel & Skartados, Panagiotis & Stamatopoulos, Giorgos, 2021. "Partial passive ownership holdings and licensing," Economics Letters, Elsevier, vol. 204(C).
    21. Bresnahan, Timothy F. & Salop, Steven C., 1986. "Quantifying the competitive effects of production joint ventures," International Journal of Industrial Organization, Elsevier, vol. 4(2), pages 155-175, June.
    22. Dietzenbacher, Erik & Smid, Bert & Volkerink, Bjorn, 2000. "Horizontal integration in the Dutch financial sector," International Journal of Industrial Organization, Elsevier, vol. 18(8), pages 1223-1242, December.
    23. Li, Sanxi & Ma, Hongkun & Zeng, Chenhang, 2015. "Passive cross holding as a strategic entry deterrence," Economics Letters, Elsevier, vol. 134(C), pages 37-40.
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