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Inefficient but Robust Public Leadership

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Abstract

We investigate endogenous timing in a mixed duopoly in a differentiated product market. We find that private leadership is better than public leadership from a social welfare perspective if the private firm is domestic, regardless of the degree of product differentiation. Nevertheless, the public leadership equilibrium is risk-dominant, and it is thus robust if the degree of product differentiation is high. We also find that regardless of the degree of product differentiation, the public leadership equilibrium is risk-dominant if the private firm is foreign. These results may explain the recent revival of public financial institutions in Japan.

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Notes

  1. See Horiuchi and Sui (1993). It is globally observed that public sectors play an important role in lending markets. See Bose et al. (2014).

  2. For example, three major state-owned public enterprises, the Japan Railway group, Japan Tobacco Incorporated, and Nippon Telegraph and Telephone Corporation, were privatized.

  3. The literature on mixed oligopolies has rich and diverse discussions on the observable delay game. Tomaru and Kiyono (2010) generalized the demand and cost functions. Matsumura (2003b) introduced foreign competition. Tomaru and Saito (2010) considered a subsidized mixed duopoly, and Bárcena-Ruiz (2007) investigated price competition and showed that Bertrand emerges in a mixed duopoly. Bárcena-Ruiz and Sedano (2011) discussed a different type of objective in a public firm. For the importance of sequential-move games in mixed oligopolies, see also Heywood and Ye (2009a), Ino and Matsumura (2010), Wang and Mukherjee (2012), Gelves and Heywood (2013), and Wang and Lee (2013). For the recent development of mixed oligopolies, see also Ishida and Matsushima (2009), Bose et al. (2014), and Matsumura and Tomaru (2013).

  4. If the shadow cost is high, the unique equilibrium is a Cournot.

  5. For a discussion on this commitment, see Ino and Matsumura (2010).

  6. They established another great contribution. They showed that the profit of each private firm can be increasing in the number of private firms in their mixed oligopolies. For this discussion, see also Matsumura and Sunada (2013).

  7. This never holds in private oligopolies. See Ino and Matsumura (2012). However, their result does not hold when the number of firms is given exogenously. Moreover, they did not discuss the robustness of public leadership.

  8. Wang and Lee (2013) showed that foreign ownership share in private firms affects welfare implication of public leadership. For pioneering works discussing foreign competition in mixed oligopolies, see Corneo and Jeanne (1994), Fjell and Pal (1996), and Pal and White (1998). Foreign ownership is important in the context of public policies in mixed oligopolies. See also Bárcena-Ruiz and Garzón (2005a, ??b) Heywood and Ye (2009b), and Lin and Matsumura (2012).

  9. In the literature on the endogenous timing game, risk dominance is a fairly powerful and popular tool for equilibrium choice. See van Damme and Hurkens (2004), Amir and Stepanova (2006), and Hirata and Matsumura (2011). For a convincing rationalization of this concept, see van Damme and Hurkens (2004).

  10. The assumption that m 0≥m 1 is popular in the literature and we believe that this is a reasonable assumption. For the theoretical and empirical discussion on the cost difference between public and private firms, see Matsumura and Matsushima (2004) and Megginson and Netter (2001), respectively. However, we can show that our results hold without this assumption unless the difference of these two costs is too large.

  11. Similarly, the private firm’s optimal output is less sensitive to the public leader’s output when δ is smaller. However, the private firm’s optimal output is less sensitive to the rival’s output and δ than the public firm’s, and thus, a change in δ more significantly affects the leader’s incentive when the follower is the public firm than when it is the private firm.

  12. Even in the private duopoly, it is possible that both firms prefer to the more-efficient firm’s leadership to the less-efficient firm’s one. For the pioneering studies in this field, see Ono (1978, 1982).

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Authors and Affiliations

  1. Institute of Social Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Toshihiro Matsumura

  2. College of Liberal Arts, International Christian University, 3-10-2, Osawa, Mitaka-shi, Tokyo, 181-8585, Japan

    Akira Ogawa

Authors
  1. Toshihiro Matsumura
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  2. Akira Ogawa
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Correspondence to Akira Ogawa.

Additional information

We are indebted to an anonymous referee for their precious and constructive comments and suggestions. We acknowledge financial supports from JSPS KAKENHI Grant Numbers (15K03347) and Zengin Foundation for Studies on Economics and Finance.

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Matsumura, T., Ogawa, A. Inefficient but Robust Public Leadership. J Ind Compet Trade 17, 387–398 (2017). https://doi.org/10.1007/s10842-017-0248-1

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