Nonlinear dynamics in a Cournot duopoly with relative profit delegation
The present study analyses the dynamics of a nonlinear Cournot duopoly with managerial delegation and bounded rational players. Problems concerning strategic delegation (based on relative performance evaluations) have recently received in depth attention in both the theoretical and empirical industrial economics literatures. In this paper, we take a dynamic view of this problem and assume that the owners of both firms hire a manager and delegate output decisions to him. Each manager receives a fixed salary plus a bonus offered in a publicly observable contract. The bonus entitled to the manager hired by the owner of every firm is based on relative (profit) performance. Managers of both firms may collude or compete. In such a context, we find, in either cases of collusion and low degree of competition, that synchronised dynamics takes place. However, when the degree of competition increases the dynamics can undergo symmetry-breaking bifurcations that may cause relevant global phenomena. In particular, on-off intermittency and blow-out bifurcations are observed for several parameter values. Moreover, coexistence of attractors may also occur. The global behaviour of the noninvertible map is investigated through the study of the transverse Lyapunov exponent and the folding action of the critical curves of the map. These phenomena are impossible under profit maximisation.
|Date of creation:||04 Apr 2012|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Ahmad Naimzada & Fabio Tramontana, 2010. "A Dynamic Model of a Boundedly Rational Consumer with a Simple Least Squared Learning Mechanism," Computational Economics, Society for Computational Economics, vol. 36(1), pages 47-56, June.
- Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
- Gibbons, R. & Murphy, K.J., 1989.
"Relative Performance Evaluation For Chief Executive Officers,"
532, Massachusetts Institute of Technology (MIT), Department of Economics.
- Robert Gibbons & Kevin J. Murphy, 1990. "Relative performance evaluation for chief executive officers," Industrial and Labor Relations Review, ILR Review, Cornell University, ILR School, vol. 43(3), pages 30-51, February.
- Robert Gibbons & Kevin J. Murphy, 1989. "Relative Performance Evaluation for Chief Executive Officers," NBER Working Papers 2944, National Bureau of Economic Research, Inc.
- Robert Gibbons & Kevin Murphy, 1989. "Relative Performance Evaluation for Chief Executive Officers," Working Papers 628, Princeton University, Department of Economics, Industrial Relations Section..
- 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 225-64, April.
- Fabio Tramontana & Laura Gardini & Tönu Puu, 2008.
"Cournot Duopoly when the Competitors Operate Multiple Production Plants,"
0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- 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.
- Chaim Fershtman & Kenneth L Judd, 1984.
"Equilibrium Incentives in Oligopoly,"
642, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- Fanti, Luciano & Gori, Luca, 2012.
"The dynamics of a differentiated duopoly with quantity competition,"
Elsevier, vol. 29(2), pages 421-427.
- Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a differentiated duopoly with quantity competition," MPRA Paper 33477, University Library of Munich, Germany.
- Luciano Fanti & Luca Gori, 2011. "The dynamics of a differentiated duopoly with quantity competition," Discussion Papers 2011/121, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
- Vickers, John, 1985. "Delegation and the Theory of the Firm," Economic Journal, Royal Economic Society, vol. 95(380a), pages 138-47, Supplemen.
- 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 107-22, February.
- 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.
- 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.
- Rajesh Aggarwal & Andrew A. Samwick, 1996.
"Executive Compensation, Strategic Competition, and Relative Performance Evaluation: Theory and Evidence,"
NBER Working Papers
5648, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, vol. 41(6), pages 1043-48, November.
- 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.
- Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
- 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.
- 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.
- 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 301-25, June.
- 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.
- Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:37834. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)
If references are entirely missing, you can add them using this form.