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Combining the Endogenous Choice of the Timing of Setting the Levels of Strategic Contracts and Their Contents in a Managerial Mixed Duopoly

  • Yasuhiko Nakamura
Article

Abstract

This study considers a game in which both, the timing of setting the levels of strategic contracts and their contents, are endogenized in a managerial mixed duopoly composed of a public firm with a welfare-maximizing owner and a private firm with a profit-maximizing owner. We suppose that the managers of both, the public firm and the private firm, adopt sales delegation contracts that are equal to the weighted sum of their profits and sales revenue with respect to the incentive parameters. We show that the market structure such that the manager of the public firm with a quantity contract is the follower and the manager of the private firm with a price contract is the leader can become the unique equilibrium market structure in the game in which both, the timing of setting the levels of strategic contracts and their contents, are endogenized in a managerial mixed duopoly. In addition, highest social welfare can be achieved in such a unique equilibrium market structure. Therefore, it is not necessary for the relevant authority, including the government, to regulate free decisions on the timing of the levels of the strategic contracts for the owners of both, the public firm and the private firm.

Keywords

Cournot competition Bertrand competition Endogenous competition Endogenous timing Mixed duopoly Managerial delegation 

JEL Classification

L13 D43 D21 

Notes

Acknowledgments

We are grateful to the two anonymous referees for their feedback. All remaining errors are our own. This study was conducted with the financial support of the Seimeikai Foundation (16-002), KAKENHI (16H03624), and KAKENHI (16K03665).

Supplementary material

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References

  1. Bakó B, Tasnádi A (2017) The Kreps–Scheinkman game in mixed duopolies. J Inst Theor Econ 173:753–768CrossRefGoogle Scholar
  2. Balogh TL, Tasnádi A (2012) Does timing of decisions in a mixed duopoly matter? J Econ 106:233–249CrossRefGoogle Scholar
  3. Bárcena-Ruiz JC (2007) Endogenous timing in a mixed duopoly: price competition. J Econ 91:263–272CrossRefGoogle Scholar
  4. Bárcena-Ruiz JC (2009) The decision to hire managers in mixed markets under Bertrand competition. Jpn Econ Rev 60:376–388CrossRefGoogle Scholar
  5. Bárcena-Ruiz JC (2013) Endogenous timing of incentive contracts in mixed markets under Bertrand competition. Manch Sch 81:340–355CrossRefGoogle Scholar
  6. Bárcena-Ruiz JC, Garzón MB (2010) Endogenous timing in a mixed oligopoly with semipublic firms. Port Econ J 9:97–113CrossRefGoogle Scholar
  7. Barros F (1995) Incentive schemes as strategic variables: an application to a mixed duopoly. Int J Ind Organ 13:373–386CrossRefGoogle Scholar
  8. Chirco A, Scrimitore M (2013) Choosing price or quantity? The Role of Delegation and Network Externalities Economics Letters 121:482–486Google Scholar
  9. Chirco A, Colombo C, Scrimitore M (2014) Organizational structure and the choice of price versus quantity in a mixed duopoly. Jpn Econ Rev 65:521–542CrossRefGoogle Scholar
  10. Din H-R, Sun C-H (2016) Combining the endogenous choice of timing and competition version in a mixed duopoly. J Econ 118:141–166CrossRefGoogle Scholar
  11. Dixit A (1979) A model of duopoly suggesting a theory of entry barriers bell. J Econ 10:20–32Google Scholar
  12. Fershtman C, Judd K (1987) Equilibrium incentives in oligopoly. Am Econ Rev 77:927–940Google Scholar
  13. Hamilton JH, Slutsky SM (1990) Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games Econ Behav 2:29–46CrossRefGoogle Scholar
  14. Haraguchi J, Matsumura T (2014) Price versus quantity in a mixed duopoly with foreign penetration. Res Econ 68:338–353CrossRefGoogle Scholar
  15. Haraguchi J, Matsumura T (2016) Cournot/Bertrand comparison in a mixed oligopoly. J Econ 117:117–136CrossRefGoogle Scholar
  16. Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, CambridgeGoogle Scholar
  17. Heywood JS, Ye G (2009) Delegation in a mixed oligopoly: the case of multiple private firms. Manag Decis Econ 30:71–82CrossRefGoogle Scholar
  18. Hoernig S (2012) Strategic delegation under price competition and network effects. Econ Lett 117:487–489CrossRefGoogle Scholar
  19. Katz ML, Shapiro C (1985) Network externalities, competition, and compatibility. Am Econ Rev 75:424–440Google Scholar
  20. Klemperer P, Meyer M (1986) Price competition vs. quantity competition: the role of uncertainty. RAND J Econ 17:618–638CrossRefGoogle Scholar
  21. Kreps DM, Scheinkman JA (1983) Quantity precommitment and Bertrand competition yield cournot outcomes. Bell J Econ 14:326–337CrossRefGoogle Scholar
  22. Lambertini L (2000) Extended games played by managerial firms. Jpn Econ Rev 51:274–283CrossRefGoogle Scholar
  23. Maggi G (1996) Strategic trade policies with endogenous mode of competition. Am Econ Rev 86:237–258Google Scholar
  24. Matsumura T (1998) Partial privatization in mixed duopoly. J Public Econ 70:473–483CrossRefGoogle Scholar
  25. Matsumura T, Ogawa A (2010) On the robustness of private leadership in mixed duopoly. Aust Econ Pap 49:149–160CrossRefGoogle Scholar
  26. Matsumura T, Ogawa A (2012) Price versus quantity in a mixed duopoly. Econ Lett 116:174–177CrossRefGoogle Scholar
  27. Matsumura T, Ogawa A (2014) Corporate social responsibility or payoff asymmetry? A study of an endogenous timing game. South Econ J 81:457–473CrossRefGoogle Scholar
  28. Méndez-Naya J (2015) Endogenous Timing in a Mixed Duopoly Model. J Econ 116:47–61Google Scholar
  29. Nakamura Y (2015a) Endogenous choice of strategic incentives in a mixed duopoly with a new managerial delegation contract for the public firm. Int Rev Econ Financ 35:262–277CrossRefGoogle Scholar
  30. Nakamura Y (2015b) Price versus quantity in a mixed duopoly: the case of relative profit maximization. Ecol Model 35:37–43CrossRefGoogle Scholar
  31. Nakamura Y (2017a) Price versus quantity in a duopolistic market with bargaining over managerial delegation contracts. Manag Decis Econ 83:326–343CrossRefGoogle Scholar
  32. Nakamura Y (2017b) Price versus quantity in a duopoly with a unilateral effect and with bargaining over managerial contracts. J Indus Compet Trade 17:83–119CrossRefGoogle Scholar
  33. Nakamura Y (2018a) Endogenous timing of incentive contracts in a managerial oligopoly focusing on asymmetric strategic contracts and the relation between each firm’s goods. MimeographGoogle Scholar
  34. Nakamura Y (2018b) Combining the endogenous choice of the timing of setting the incentive parameters and content of strategic contracts in a managerial duopoly. MimeographGoogle Scholar
  35. Nakamura Y (2018c) Combining the endogenous choice of the timing of setting incentive parameters and the contents of strategic contracts in a managerial mixed duopoly. MimeographGoogle Scholar
  36. Nakamura Y, Inoue T (2007) Endogenous timing in a mixed duopoly: the managerial delegation case. Econ Bull 12(27):1–7Google Scholar
  37. Nakamura Y, Inoue T (2009) Endogenous timing in a mixed duopoly: price competition with managerial delegation. Manag Decis Econ 30:325–333CrossRefGoogle Scholar
  38. Pal D (1998) Endogenous timing in a mixed oligopoly. Econ Lett 61:181–185CrossRefGoogle Scholar
  39. Scrimitore M (2013) Price or quantity? The strategic choice of subsidized firms in a mixed duopoly. Econ Lett 118:337–341CrossRefGoogle Scholar
  40. Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15:546–554CrossRefGoogle Scholar
  41. Sklivas SD (1987) The strategic choice of management incentives. RAND J Econ 18:452–458CrossRefGoogle Scholar
  42. Sun CH (2013) Combining the endogenous choice of price/quantity and timing. Econ Lett 120:364–368CrossRefGoogle Scholar
  43. Thisse J-F, Vives X (1998) On the strategic choice of spatial price policy. Am Econ Rev 78:122–137Google Scholar
  44. Tomaru Y, Nakamura Y, Saito M (2011) Strategic managerial delegation in a mixed duopoly with capacity choice: partial delegation or full delegation. Manch Sch 79:811–838CrossRefGoogle Scholar
  45. Vickers J (1985) Delegation and the theory of the firm. Econ J 95:138–147CrossRefGoogle Scholar
  46. White MD (2001) Managerial incentives and the decision to hire managers in markets with public and private firms. Eur J Polit Econ 17:877–896CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of EconomicsNihon UniversityTokyoJapan

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