IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v69y2014icp253-270.html
   My bibliography  Save this article

Local and global dynamics in a duopoly with price competition and market share delegation

Author

Listed:
  • Fanti, Luciano
  • Gori, Luca
  • Mammana, Cristiana
  • Michetti, Elisabetta

Abstract

This paper aims at studying a nonlinear dynamic duopoly model with price competition and horizontal product differentiation augmented with managerial firms, where managers behave according to market share delegation contracts. Ownership and management are then separate and managers are paid through adequate incentives in order to achieve a competitive advantage in the market. In this context, we show that complexity arises, related both to the structure of the attractors of the system and the structure of their basins, as multistability occurs. The study is conducted by combining analytical and numerical techniques, and aims at showing that slight different initial conditions may cause very different long-term outcomes.

Suggested Citation

  • Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2014. "Local and global dynamics in a duopoly with price competition and market share delegation," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 253-270.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:253-270
    DOI: 10.1016/j.chaos.2014.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914001775
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.10.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Kopel & L. Lambertini, 2012. "On the (non) existence of a price equilibrium in delegation games with relative performance compensation," Working Papers wp807, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Fumas, Vicente Salas, 1992. "Relative performance evaluation of management : The effects on industrial competition and risk sharing," International Journal of Industrial Organization, Elsevier, vol. 10(3), pages 473-489, September.
    3. Bischi Gian Italo & Lamantia Fabio, 2012. "Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    4. Qiu, Larry D., 1997. "On the Dynamic Efficiency of Bertrand and Cournot Equilibria," Journal of Economic Theory, Elsevier, vol. 75(1), pages 213-229, July.
    5. Chaim Fershtman & Kenneth L. Judd, 2006. "Equilibrium Incentives in Oligopoly: Corrigendum," American Economic Review, American Economic Association, vol. 96(4), pages 1367-1367, September.
    6. Susan C Borkowski, 1999. "International Managerial Performance Evaluation: A Five Country Comparison," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 30(3), pages 533-555, September.
    7. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    8. Thijs Jansen & Arie van Lier & Arjen van Witteloostuijn, 2009. "On the impact of managerial bonus systems on firm profit and market competition: the cases of pure profit, sales, market share and relative profits compared," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 141-153.
    9. Giant-italo Bischi & Laura Gardini, 2000. "Global properties of symmetric competition models with riddling and blowout phenomena," Discrete Dynamics in Nature and Society, Hindawi, vol. 5, pages 1-12, January.
    10. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2012. "Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-22, December.
    11. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    12. Michael Kopel & Luca Lambertini, 2013. "On Price Competition with Market Share Delegation Contracts," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 34(1), pages 40-43, January.
    13. Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-414, May.
    14. Fershtman, Chaim, 1985. "Managerial incentives as a strategic variable in duopolistic environment," International Journal of Industrial Organization, Elsevier, vol. 3(2), pages 245-253, June.
    15. Leonard Wang & Ya-Chin Wang & Lihong Zhao, 2009. "Market Share Delegation and Strategic Trade Policy," Journal of Industry, Competition and Trade, Springer, vol. 9(1), pages 49-56, March.
    16. Leonard Wang & Ya-Chin Wang, 2010. "Input Pricing and Market Share Delegation in a Vertically Related Market: Is the Timing Order Relevant?," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 17(2), pages 207-221.
    17. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    18. Ritz, Robert A., 2008. "Strategic incentives for market share," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 586-597, March.
    19. Lopez, Monica Correa & Naylor, Robin A., 2004. "The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining," European Economic Review, Elsevier, vol. 48(3), pages 681-696, June.
    20. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    21. Jansen, Thijs & van Lier, Arie & van Witteloostuijn, Arjen, 2007. "A note on strategic delegation: The market share case," International Journal of Industrial Organization, Elsevier, vol. 25(3), pages 531-539, June.
    22. Bignami Fernando & Agliari Anna, 2010. "Synchronization and On-Off Intermittency Phenomena in a Market Model with Complementary Goods and Adaptive Expectations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-31, March.
    23. Vickers, John, 1985. "Delegation and the Theory of the Firm," Economic Journal, Royal Economic Society, vol. 95(380a), pages 138-147, Supplemen.
    24. Fershtman, Chaim & Judd, Kenneth L, 1987. "Equilibrium Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 77(5), pages 927-940, December.
    25. Fama, Eugene F & Jensen, Michael C, 1983. "Separation of Ownership and Control," Journal of Law and Economics, University of Chicago Press, vol. 26(2), pages 301-325, June.
    26. Steven D. Sklivas, 1987. "The Strategic Choice of Managerial Incentives," RAND Journal of Economics, The RAND Corporation, vol. 18(3), pages 452-458, Autumn.
    27. Miller, Nolan H & Pazgal, Amit I, 2001. "The Equivalence of Price and Quantity Competition with Delegation," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 284-301, Summer.
    28. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    29. Nolan Miller & Amit Pazgal, 2002. "Relative performance as a strategic commitment mechanism," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 23(2), pages 51-68.
    30. Gray, Sidney, 1995. "Cultural perspectives on the measurement of corporate success," European Management Journal, Elsevier, vol. 13(3), pages 269-275, September.
    31. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
    32. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    33. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    34. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
    35. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2013. "The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 73-86.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luca Gori & Nicolò Pecora & Mauro Sodini, 2017. "Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 905-931, November.
    2. Zhou, Jie & Zhou, Wei & Chu, Tong & Chang, Ying-xiang & Huang, Meng-jia, 2019. "Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 358-378.
    3. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    4. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Liu, Cui & He, Rui-chun & Zhou, Wei & Li, Hui, 2021. "Dynamic analysis of airline bidding game based on nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    6. Brianzoni, Serena & Gori, Luca & Michetti, Elisabetta, 2015. "Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 191-203.
    7. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    2. Luca Gori & Nicolò Pecora & Mauro Sodini, 2017. "Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 905-931, November.
    3. Evangelos Mitrokostas & Emmanuel Petrakis, 2014. "Organizational structure, strategic delegation and innovation in oligopolistic industries," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 23(1), pages 1-24, January.
    4. Fanti, Luciano & Gori, Luca, 2011. "Stability analysis in a Cournot duopoly with managerial sales delegation and bounded rationality," MPRA Paper 33828, University Library of Munich, Germany.
    5. Yasuhiko Nakamura, 2015. "Endogenous Choice of Strategic Variables in an Asymmetric Duopoly with Respect to the Demand Functions that Firms Face," Manchester School, University of Manchester, vol. 83(5), pages 546-567, September.
    6. Cellini, Roberto & Lambertini, Luca & Ottaviano, Gianmarco I.P., 2020. "Strategic inattention, delegation and endogenous market structure," European Economic Review, Elsevier, vol. 121(C).
    7. Luciano Fanti & Nicola Meccheri, 2015. "On the Cournot–Bertrand Profit Differential and the Structure of Unionisation in a Managerial Duopoly," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 266-287, December.
    8. Ya‐chin Wang & Leonard F.s. Wang, 2009. "Equivalence Of Competition Mode In A Vertically Differentiated Duopoly With Delegation," South African Journal of Economics, Economic Society of South Africa, vol. 77(4), pages 577-590, December.
    9. Werner Neus & Manfred Stadler, 2018. "Common holdings and strategic manager compensation: The case of an asymmetric triopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 39(7), pages 814-820, October.
    10. Chen, Tai-Liang & Yang, Mingjie, 2024. "Brand loyalty, managerial delegation and position choices: Bertrand versus Cournot competition," Regional Science and Urban Economics, Elsevier, vol. 109(C).
    11. Nicola Meccheri & Luciano Fanti, 2012. "Managerial Delegation Schemes in a Duopoly with Endogenous Production Costs: A Comparison of Sales and Relative Profit Delegation under Centralised Unionisation," Working Paper series 44_12, Rimini Centre for Economic Analysis.
    12. Leonard F. S. Wang, 2020. "Relative Performance Versus Market Share Delegation in a Vertically Related Market," Arthaniti: Journal of Economic Theory and Practice, , vol. 19(1), pages 16-27, June.
    13. Constantine Manasakis & Evangelos Mitrokostas & Emmanuel Petrakis, 2010. "Endogenous managerial incentive contracts in a differentiated duopoly, with and without commitment," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 31(8), pages 531-543, December.
    14. Barreda-Tarrazona, Iván & Georgantzís, Nikolaos & Manasakis, Constantine & Mitrokostas, Evangelos & Petrakis, Emmanuel, 2016. "Endogenous managerial compensation contracts in experimental quantity-setting duopolies," Economic Modelling, Elsevier, vol. 54(C), pages 205-217.
    15. Luciano Fanti & Nicola Meccheri, 2013. "Managerial Delegation under Alternative Unionization Structures," LABOUR, CEIS, vol. 27(1), pages 38-57, March.
    16. Jumpei Hamamura & Vinay Ramani, 2024. "The welfare effect of release timing of relative performance evaluation under quantity competition and asymmetric costs," Scottish Journal of Political Economy, Scottish Economic Society, vol. 71(3), pages 416-438, July.
    17. Bian, Junsong & Li, Kevin W. & Guo, Xiaolei, 2016. "A strategic analysis of incorporating CSR into managerial incentive design," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 83-93.
    18. Stadler, Manfred & Neus, Werner, 2018. "Cross Holdings and Strategic Manager Compensation. The Case of an Asymmetric Triopoly," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181534, Verein für Socialpolitik / German Economic Association.
    19. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    20. Xubei Lian & Kai Zhang & Leonard F. S. Wang, 2023. "Managerial delegation, network externalities and loan commitment," Manchester School, University of Manchester, vol. 91(1), pages 37-54, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:253-270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.