Advertisement

Endogenous Choice of the Timing of Setting Incentive Parameters and the Strategic Contracts in a Managerial Mixed Duopoly with a Welfare-Based Delegation Contract and a Sales Delegation Contract

  • Yasuhiko NakamuraEmail author
Article
  • 24 Downloads

Abstract

This study explores the game in which both the timing of setting the welfare-based incentive parameter of a public firm with a welfare-maximizing owner and the sales incentive parameter of a private firm and the contents of their strategic contracts in a managerial mixed duopoly with a welfare-based delegation à la (Nakamura in Int Rev Econ Financ 35:262–277, 2015) and a sales delegation are endogenously determined by their owners. We show two market structures: (1) the market structure in which the owner of the public (private) firm with a quantity contract is the leader (follower) in the determination of the incentive parameters and (2) the market structure in which the owner of the public (private) firm with a quantity (price) contract is the follower (leader) in the determination of the incentive parameters. The equilibrium market structures and highest social welfare are achieved in market structure (1). Therefore, in a managerial mixed duopoly with a welfare-based delegation and a sales delegation, it is not as necessary for the relevant authority including the government to regulate the free determination of both the timing of setting the welfare-based incentive parameter of the public firm and the sales incentive parameter of the private firm and the contents of their strategic contracts by their owners. The payoffs of the owners of both the public firm and the private firm stay relatively low in market structure (2), another equilibrium market structure. Finally, we confirm the robustness of the results on the equilibrium market structures against the change in the cost functions of both the public firm and the private firm from their constant marginal costs to their increasing marginal costs on the basis of the quadratic cost functions with their quantities.

Keywords

Cournot competition Bertrand competition Endogenous timing of incentive parameters Mixed duopoly Welfare-based delegation Sales delegation 

JEL Classification

L13 D43 D21 

Notes

Acknowledgments

We thank an anonymous referee and the Editor-in-Chief Professor Kai Hueschelrath for helpful comments and suggestions. All remaining errors are our own.

Funding Information

We are grateful for the financial support of the Seimeikai Foundation (16-002), KAKENHI (16H03624) and KAKENHI (16K03665).

Supplementary material

10842_2018_291_MOESM1_ESM.pdf (167 kb)
(PDF 168 KB)

References

  1. Amir R (1995) Endogenous timing in two-player games: a counterexample. Games Econom Behav 9:234–237CrossRefGoogle Scholar
  2. Amir R (2005) Supermodularity and complementarity in economics: an elementary survey. South Econ J 71:636–660CrossRefGoogle Scholar
  3. Amir R, Grilo I (1999) Stackelberg versus Cournot equilibrium. Games Econom Behav 26:1–21CrossRefGoogle Scholar
  4. Bárcena-Ruiz R, Paz Espinoza M (1999) Long-term or short-term managerial contracts. J Econ Manag Strateg 5:343–359CrossRefGoogle Scholar
  5. Bárcena-Ruiz JC (2007) Endogenous timing in a mixed duopoly: price competition. J Econ 91:263–272CrossRefGoogle Scholar
  6. Bárcena-Ruiz JC (2009) The decision to hire managers in mixed markets under bertrand competition. Jpn Econ Rev 60:376–388CrossRefGoogle Scholar
  7. Bárcena-Ruiz JC, Garzón MB (2010) Endogenous timing in a mixed oligopoly with semipublic firms. Port Econ J 9:97–113CrossRefGoogle Scholar
  8. Bárcena-Ruiz JC (2013) Endogenous timing of incentive contracts in mixed markets under Bertrand competition. Manch Sch 81:340–355CrossRefGoogle Scholar
  9. Barros F (1995) Incentive schemes as strategic variables: an application to a mixed duopoly. Int J Ind Organ 13:373–386CrossRefGoogle Scholar
  10. Chirco A, Scrimitore M (2013) Choosing price or quantity? the role of delegation and network externalities. Econ Lett 121:482–486CrossRefGoogle Scholar
  11. Chirco A, Colombo C, Scrimitore M (2014) Organizational structure and the choice of price vs quantity in a mixed duopoly. Jpn Econ Rev 65:521–542CrossRefGoogle Scholar
  12. 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
  13. Dixit A (1979) A model of duopoly suggesting a theory of entry barriers. Bell J Econ 10:20–32CrossRefGoogle Scholar
  14. Fershtman C, Judd K (1987) Equilibrium incentives in oligopoly. Am Econ Rev 77:927–940Google Scholar
  15. Fershtman C, Judd K, Klemperer E (1991) Observable contracts: Strategic delegation and cooperation. Int Econ Rev 93:551–559CrossRefGoogle Scholar
  16. Goering GE (2012) Corporate social responsibility and marketing channel coordination. Res Econ 66:142–148CrossRefGoogle Scholar
  17. Hamilton JH, Slutsky SM (1990) Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games Econom Behav 2:29–46CrossRefGoogle Scholar
  18. Harsanyi JC , Selten R (1988) A general theory of equilibrium selection in games. MIT Press, CambridgeGoogle Scholar
  19. Kopel T, Brand B (2013) Socially responsible firms and endogenous choice of strategic incentives. Econ Model 29:982–989CrossRefGoogle Scholar
  20. Lee S-H, Xu L (2017) Endogenous timing in private and mixed duopolies with emission taxes, forthcoming in Journal of EconomicsGoogle Scholar
  21. Lambertini L (2000a) Extended games played by managerial firms. Jpn Econ Rev 51:274–283CrossRefGoogle Scholar
  22. Lambertini L (2000b) Strategic delegation and the shape of market competition. Scottish Journal of Political Economy 47:550–570CrossRefGoogle Scholar
  23. Matsumura T (1998) Partial privatization in mixed duopoly. J Public Econ 70:473–483CrossRefGoogle Scholar
  24. Matsumura T, Ogawa A (2010) On the robustness of private leadership in mixed duopoly. Aust Econ Pap 49:149–160CrossRefGoogle Scholar
  25. Matsumura T, Ogawa A (2012) Price versus quantity in a mixed duopoly. Econ Lett 116:174–177CrossRefGoogle Scholar
  26. 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
  27. Méndez-Naya J (2015) Endogenous timing in a mixed duopoly model. J Econ 116:47–61Google Scholar
  28. Nakamura Y (2015) 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
  29. 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
  30. 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
  31. Nakamura Y (2018c) Combining the endogenous choice of the timing of setting the levels of strategic contracts and their contents in a managerial mixed duopoly. MimeographGoogle Scholar
  32. Nakamura Y (2019) Combining the endogenous choice of the timing of setting incentive parameters and the contents of strategic contracts in a managerial mixed duopoly. Int Rev Econ Financ 59:207–233CrossRefGoogle Scholar
  33. Nakamura Y, Inoue T (2007) Endogenous timing in a mixed duopoly: the managerial delegation case. Econ Bull 12(27):1–7Google Scholar
  34. Nakamura Y, Inoue T (2009) Endogenous timing in a mixed duopoly: Price competition with managerial delegation. Manag Decis Econ 30:325–333CrossRefGoogle Scholar
  35. Nishimori A, Ogawa H (2005) Long-term and short-term contract in a mixed market. Aust Econ Pap 44:275–289CrossRefGoogle Scholar
  36. Pal D (1998) Endogenous timing in a mixed oligopoly. Econ Lett 61:181–185CrossRefGoogle Scholar
  37. Polo M, Tedeschi P (1992) Managerial contracts, collusion and mergers. Ric Econ 46:281–302Google Scholar
  38. Sadanand A, Sadanand V (1996) Firm scale and the endogenous timing of entry: a choice between commitment and flexibility. J Econ Theory 70:516–530CrossRefGoogle Scholar
  39. Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15:546–554CrossRefGoogle Scholar
  40. Sklivas SD (1987) The strategic choice of management incentives. RAND J Econ 18:452–458CrossRefGoogle Scholar
  41. Sun CH (2013) Combining the endogenous choice of price/quantity and timing. Econ Lett 120:364–368CrossRefGoogle Scholar
  42. Van Damme E, Hurkens S (1999) Endogenous stackelberg leadership. Games Econom Behav 28:105–129CrossRefGoogle Scholar
  43. Vickers J (1985) Delegation and the theory of the firm. Econ J 95:138–147CrossRefGoogle Scholar
  44. 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 2019

Authors and Affiliations

  1. 1.College of EconomicsNihon UniversityTokyoJapan

Personalised recommendations