Skip to main content

Advertisement

SpringerLink
Log in

Complexity analysis of remanufacturing duopoly game with different competition strategies and heterogeneous players

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we consider a repeated remanufacturing duopoly game with different competition strategies and heterogeneous players by assuming that the original equipment manufacturer is boundedly rational and takes profit maximization as his business objective, and the third-party remanufacturer is adaptive and takes share maximization on the basis of obtaining a certain profit as his business objective. We study the equilibrium points and their stability in two situations: Consumer’s willingness-to-pay (WTP) is higher and lower. Numerical simulations show complex dynamic behaviors of this two-dimensional discrete system. We find that in the first situation, the stability of the system has nothing to do with the adjustment speed of the third-party remanufacturer. Under different conditions, the WTP has different impact on the stability region of the conditional equilibrium point. The system can lose stability through two different bifurcation routes (flip and Neimark–Sacker bifurcations). In the second situation, the stability region of the Nash equilibrium becomes large with WTP increasing. A higher WTP can enhance the stability of the Nash equilibrium. The third-party remanufacturer’s business objective can expand the stability region. A fiercer competition can have a stronger stabilization effect to the Nash equilibrium. The stability of the system can be lost only through flip bifurcation. The results of system performance measuring show that unstable behavior is not all harmful to both manufacturers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Mitra, S., Webster, S.: Competition in remanufacturing and the effects of government subsidies. Int. J. Prod. Econ. 111(2), 287–298 (2008)

    Article  Google Scholar 

  2. Örsdemir, A., Kemahlıoğlu-Ziya, E., Parlaktürk, A.K.: Competitive quality choice and remanufacturing. Prod. Oper. Manag. 23(1), 48–64 (2014)

    Article  Google Scholar 

  3. Atasu, A., Sarvary, M., Van Wassenhove, L.N.: Remanufacturing as a marketing strategy. Manag. Sci. 54(10), 1731–1746 (2008)

    Article  Google Scholar 

  4. Subramanian, R., Ferguson, M.E., Toktay, L.B.: Remanufacturing and the component commonality decision. Prod. Oper. Manag. 22(1), 36–53 (2013)

    Article  Google Scholar 

  5. Atasu, A., Guide, V.D.R., Van Wassenhove, L.N.: So what if remanufacturing cannibalizes new product sales? Calif. Manag. Rev. 52(2), 56–76 (2010)

    Article  Google Scholar 

  6. Ferrer, G., Swaminathan, J.M.: Managing new and remanufactured products. Manag. Sci. 52(1), 15–26 (2006)

    Article  Google Scholar 

  7. Ferguson, M.E., Toktay, L.B.: The effect of competition on recovery strategies. Prod. Oper. Manag. 15(3), 351–368 (2006)

    Article  Google Scholar 

  8. Majumder, P., Groenevelt, H.: Competition in remanufacturing. Prod. Oper. Manag. 10(2), 125–141 (2001)

    Article  Google Scholar 

  9. Ferrer, G., Swaminathan, J.M.: Managing new and differentiated remanufactured products. Eur. J. Oper. Res. 203(2), 370–379 (2010)

    Article  MATH  Google Scholar 

  10. Cournot, A.: Recherches sur les Principes Mathématiques de la Théoris des Richesses. Hachette, Paris (1838)

    Google Scholar 

  11. Bertrand, J.: Théorie mathématique de la richesse sociale. J. Savants 48, 499–508 (1883)

    Google Scholar 

  12. Puu, T.: Chaos in duopoly pricing. Chaos Soliton Fractals 1(6), 573–581 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Puu, T.: Complex dynamics with three oligopolists. Chaos Soliton Fractals 7(12), 2075–2081 (1996)

    Article  MathSciNet  Google Scholar 

  14. Kopel, M.: Simple and complex adjustment dynamics in Cournot duopoly models. Chaos Soliton Fractals 7(12), 2031–2048 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  15. Puu, T.: The chaotic duopolists revisited. J. Econ. Behav. Organ. 33(3–4), 385–394 (1998)

    Article  Google Scholar 

  16. Agiza, H.N.: On the stability, bifurcations, chaos and chaos control of Kopel map. Chaos Soliton Fractals 10(11), 1909–1916 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Bischi, G.I., Naimzada, A.: Global analysis of a dynamic duopoly game with bounded rationality. In: Filar, J.A., Gaitsgory, V., Mizukami, K. (eds.) Advanced in Dynamics Games and Application. Birkhauser, Switzerland (1999)

    Google Scholar 

  18. Agiza, H.N., Hegazi, A.S., Elsadany, A.A.: The dynamics of Bowley’s model with bounded rationality. Chaos Soliton Fractals 12(9), 1705–1717 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Agiza, H.N., Hegazi, A.S., Elsadany, A.A.: Complex dynamics and synchronization of a duopoly game with bounded rationality. Math. Comput. Simul. 58(2), 133–146 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rassenti, S., Reynolds, S.S., Smith, V.L., Szidarovszky, F.: Adaptation and convergence of behavior in repeated experimental Cournot games. J. Econ. Behav. Organ. 41(2), 117–146 (2000)

    Article  Google Scholar 

  21. Bischi, G.I., Kopel, M.: Equilibrium selection in a nonlinear duopoly game with adaptive expectations. J. Econ. Behav. Organ. 46(1), 73–100 (2001)

    Article  Google Scholar 

  22. Onazaki, T., Sieg, G., Yokoo, M.: Stability, Chaos and multiple attractors: a single agent makes a difference. J. Econ. Dyn. Control 27(10), 1917–1938 (2003)

    Article  Google Scholar 

  23. Agiza, H.N., Elsadany, A.A.: Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Phys. A 320, 512–524 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Agiza, H.N., Elsadany, A.A.: Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Appl. Math. Comput. 149(3), 843–860 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. Zhang, J.X., Da, Q.L., Wang, Y.H.: Analysis of nonlinear duopoly game with heterogeneous players. Econ. Model. 24(1), 138–148 (2007)

    Article  Google Scholar 

  26. Dubiel-Teleszynski, T.: Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale. Commun. Nonlinear Sci. 16(1), 296–308 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  27. Angelini, N., Dieci, R., Nardini, F.: Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioral rules. Math. Comput. Simul. 79(10), 3179–3196 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Tramontana, F.: Heterogeneous duopoly with isoelastic demand function. Econ. Model. 27(1), 350–357 (2010)

    Article  MathSciNet  Google Scholar 

  29. Agliari, A., Gardini, L., Puu, T.: The dynamics of a triopoly Cournot game. Chaos Soliton Fractals 11(15), 2531–2560 (2000)

  30. Elsadany, A.A.: Competition analysis of a triopoly game with bounded rationality. Chaos Soliton Fractals 45(11), 1343–1348 (2012)

    Article  Google Scholar 

  31. Elabbasy, E.M., Agiza, H.N., Elsdany, A.A.: Analysis of nonlinear triopoly game with heterogeneous players. Comput. Math. Appl. 57(3), 488–499 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  32. Tramontana, T., Elsadany, A.A.: Heterogeneous triopoly game with isoelastic demand function. Nonlinear Dyn. 68(1–2), 187–193 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  33. Elsadany, A.A., Agiza, H.N., Elabbasy, E.M.: Complex dynamics and chaos control of heterogeneous quadropoly game. Appl. Math. Comput. 219(24), 11110–11118 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  34. Ma, J.H., Zhang, J.L.: Research on the price game and the application of delayed decision in oligopoly insurance market. Nonlinear Dyn. 52(9–10), 1479–1489 (2012)

    Google Scholar 

  35. Yu, H.J., Cai, G.L., Li, Y.X.: Dynamic analysis and control of a new hyperchaotic finance system. Nonlinear Dyn. 67(3), 2171–2182 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  36. Li, T., Ma, J.H.: The complex dynamics of R&D competition models of three oligarchs with heterogeneous players. Nonlinear Dyn. 72(4), 45–54 (2013)

    Article  Google Scholar 

  37. Li, T., Ma, J.H.: Complexity analysis of the dual-channel supply chain model with delay decision. Nonlinear Dyn. 78(4), 2617–2626 (2014)

    Article  Google Scholar 

  38. Bell, D., Keeney, R., Little, J.D.: A market share theorem. J. Mark. Res. 12(2), 136–141 (1975)

    Article  Google Scholar 

  39. Szymanski, D.M., Bharadwaj, S.G., Varadarajan, P.R.: An analysis of the market share-profitability relationship. J. Mark. 57(3), 1–18 (1993)

    Article  Google Scholar 

  40. Prescott, J.E., Kohli, A.K., Venkatraman, N.: The market share-profitability relationship: an empirical assessment of major assertions and contradictions. Strateg. Manag. J. 7(4), 377–394 (1986)

    Article  Google Scholar 

  41. Venkatraman, N., Prescott, J.E.: The market share-profitability relationship: testing temporal stability across business cycles. J. Manag. 16(4), 783–805 (1990)

    Google Scholar 

  42. Bischi, G.I., Gardini, L., Kopel, M.: Analysis of global bifurcations in a market share attraction model. J. Econ. Dyn. Control 24(5), 855–879 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  43. Bischi, G.I., Kopel, M.: Multistability and path dependence in a dynamic brand competition model. Chaos Soliton Fractals 18(3), 561–576 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  44. Li, T., Ma, J.H.: Complexity analysis of dual-channel game model with different manager’s business objectives. Commun. Nonlinear Sci. 20(1), 199–208 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  45. Puu, T.: Attractors, Bifurcation and Chaos: Nonlinear Phenomena in Economics. Springer, Berlin (2003)

    Book  Google Scholar 

Download references

Acknowledgments

We would like to thank the anonymous referees very much for their valuable comments and suggestions. This work was supported by Major Program of National Natural Science Foundation of China (71390521) and by National Natural Science Foundation of China (71101067 and 71271103).

Author information

Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Lian Shi & Zhaohan Sheng

  2. School of Management and Engineering, Nanjing University, Nanjing, 210093, China

    Zhaohan Sheng & Feng Xu

Authors
  1. Lian Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhaohan Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, L., Sheng, Z. & Xu, F. Complexity analysis of remanufacturing duopoly game with different competition strategies and heterogeneous players. Nonlinear Dyn 82, 1081–1092 (2015). https://doi.org/10.1007/s11071-015-2218-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2218-7

Keywords

Search

Navigation