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Nonlinear dynamics in a Cournot duopoly with relative profit delegation

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  • Fanti, Luciano
  • Gori, Luca
  • Sodini, Mauro

Abstract

This paper analyses the dynamics of a nonlinear Cournot duopoly with managerial delegation and homogeneous players. We assume that the owners of both firms hire a manager and delegate output decisions to him or her. Each manager receives a fixed salary plus a bonus based on relative (profit) performance. Managers of both firms may collude or compete. In cases of both collusion and a low degree of competition, we find that synchronised dynamics take place. However, when the degree of competition is high, the dynamics may undergo symmetry-breaking bifurcations, which can cause significant global phenomena. Specifically, there is on–off intermittency and blow-out bifurcations for several parameter values. In addition, several attractors may coexist. The global behaviour of the noninvertible map is investigated through studying a transverse Lyapunov exponent and the folding action of the critical curves of the map. These phenomena are impossible under profit maximisation.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:12:p:1469-1478
    DOI: 10.1016/j.chaos.2012.08.008
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    as
    1. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    2. Robert Gibbons & Kevin J. Murphy, 1990. "Relative Performance Evaluation for Chief Executive Officers," ILR Review, Cornell University, ILR School, vol. 43(3), pages 30, April.
    3. Fershtman, Chaim & Judd, Kenneth L, 1987. "Equilibrium Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 77(5), pages 927-940, December.
    4. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
    5. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    6. 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.
    7. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    8. Steven D. Sklivas, 1987. "The Strategic Choice of Managerial Incentives," RAND Journal of Economics, The RAND Corporation, vol. 18(3), pages 452-458, Autumn.
    9. 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.
    10. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    11. 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.
    12. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    13. 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.
    14. Ahmad Naimzada & Fabio Tramontana, 2010. "A Dynamic Model of a Boundedly Rational Consumer with a Simple Least Squared Learning Mechanism," Computational Economics, Springer;Society for Computational Economics, vol. 36(1), pages 47-56, June.
    15. 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.
    16. Reitman, David, 1994. "Partial Ownership Arrangements and the Potential for Collusion," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 313-322, September.
    17. 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.
    18. Cyert, Richard M & DeGroot, Morris H, 1973. "An Analysis of Cooperation and Learning in a Duopoly Context," American Economic Review, American Economic Association, vol. 63(1), pages 24-37, March.
    19. Anna Agliari & Laura Gardini & Tonu Puu, 2006. "Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-20.
    20. M. Kopel & F. Szidarovszky, 2006. "Resource Dynamics under Partial Cooperation in an Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 393-410, February.
    21. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    22. 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.
    23. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    24. Arjen van Witteloostuijn & Thijs Jansen & Arie van Lier, 2007. "Bargaining over managerial contracts in delegation games: managerial power, contract disclosure and cartel behavior," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(8), pages 897-904.
    25. 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.
    26. Rajesh K. Aggarwal & Andrew A. Samwick, 1999. "Executive Compensation, Strategic Competition, and Relative Performance Evaluation: Theory and Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 1999-2043, December.
    27. Grossman, Sanford J & Stiglitz, Joseph E, 1977. "On Value Maximization and Alternative Objectives of the Firm," Journal of Finance, American Finance Association, vol. 32(2), pages 389-402, May.
    28. Cánovas, José S. & Puu, Tönu & Ruíz, Manuel, 2008. "The Cournot–Theocharis problem reconsidered," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1025-1039.
    29. G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
    30. 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.
    31. Jensen, Michael C & Murphy, Kevin J, 1990. "Performance Pay and Top-Management Incentives," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 225-264, April.
    32. Agliari, Anna & Chiarella, Carl & Gardini, Laura, 2006. "A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 60(4), pages 526-552, August.
    33. Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, vol. 41(6), pages 1043-1048, November.
    34. Chiarella, Carl, 1986. "Perfect foresight models and the dynamic instability problem from a higher viewpoint," Economic Modelling, Elsevier, vol. 3(4), pages 283-292, October.
    35. 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.
    36. 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.
    37. Vickers, John, 1985. "Delegation and the Theory of the Firm," Economic Journal, Royal Economic Society, vol. 95(380a), pages 138-147, Supplemen.
    38. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    39. Agliari, Anna & Gardini, Laura & Puu, Tönu, 2005. "Some global bifurcations related to the appearance of closed invariant curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(3), pages 201-219.
    40. 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.
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    Cited by:

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    2. 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.
    3. 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.
    4. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    5. 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.
    6. Giovanni Dosi & Mauro Sodini & Maria Virgillito, 2015. "Profit-driven and demand-driven investment growth and fluctuations in different accumulation regimes," Journal of Evolutionary Economics, Springer, vol. 25(4), pages 707-728, September.
    7. Brianzoni, Serena & Campisi, Giovanni & Colasante, Annarita, 2022. "Nonlinear banking duopoly model with capital regulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.
    9. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    10. 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).
    11. Xin Su & Shengsen Duan & Shubing Guo & Haolong Liu, 2018. "Evolutionary Games in the Agricultural Product Quality and Safety Information System: A Multiagent Simulation Approach," Complexity, Hindawi, vol. 2018, pages 1-13, March.
    12. Gori, Luca & Sodini, Mauro & Fanti, Luciano, 2015. "A nonlinear Cournot duopoly with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 178-190.

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    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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