Fanti, Luciano and Gori, Luca and Sodini, Mauro (2012): Nonlinear dynamics in a Cournot duopoly with relative profit delegation.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Nonlinear dynamics in a Cournot duopoly with relative profit delegation|
|English Title:||Nonlinear dynamics in a Cournot duopoly with relative profit delegation|
|Keywords:||Cournot; Managerial delegation; Nonlinear dynamics; Oligopoly; Relative profits|
|Subjects:||L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets
D - Microeconomics > D4 - Market Structure and Pricing > D43 - Oligopoly and Other Forms of Market Imperfection
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium
|Depositing User:||Luca Gori|
|Date Deposited:||04. Apr 2012 12:55|
|Last Modified:||14. Feb 2013 09:37|
Aggarwal R.K., Samwick, A.A., 1999. Executive compensation, strategic competition and relative performance evaluation: theory and evidence. Journal of Finance 54, 1999–2043.
Agiza, H.N., 1999. On the analysis of stability, bifurcation, chaos and chaos control of Kopel map. Chaos, Solitons and Fractals 10, 1909–1916.
Agiza, H.N., Elsadany, A.A., 2003. Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica A 320, 512–524.
Agiza, H.N., Elsadany, A.A., 2004. Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Applied Mathematics and Computation 149, 843–860.
Agliari, A., Bischi, G.I., Gardini, L., 2002. Some methods for the global analysis of dynamic games represented by iterated noninvertible maps. In: Puu, T., Sushko, I., Eds., Oligopoly Dynamics. Models and Tools, Ch. 3, 31–84. Berlin Heidelberg: Springer-Verlag.
Agliari, A., Gardini, L., Puu, T., 2005. Some global bifurcations related to the appearance of closed invariant curves. Mathematics and Computers in Simulation 68, 201–219.
Agliari, A., Chiarella, C., Gardini, L., 2006. A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis. Journal of Economic Behavior & Organization 60, 526–552.
Agliari, A., Gardini, L., Puu, T., 2006. Global bifurcations in duopoly when the Cournot point is destabilized via a subcritical Neimark bifurcation. International Game Theory Review 8, 1–20.
Ashwin, P., Buescu, J., Stewart, I., 1996. From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity 9, 703–737.
Baumol, W., 1958. On the theory of oligopoly. Economica 25, 187–198.
Bischi, G.I., Gardini, L., 1998. Role of invariant and minimal absorbing areas in chaos synchronization. Physical Review E 58, 5710–5719.
Bischi, G.I., Gardini, L., 2000. Global properties of symmetric competition models with riddling and blowout phenomena. Discrete Dynamics in Nature and Society 5, 149–160.
Bischi, G.I., Kopel, M., 2001. Equilibrium selection in a nonlinear duopoly game with adaptive expectations. Journal of Economic Behavior and Organization 46, 73–100.
Bischi, G.I., Kopel, M., 2003. Multistability and path dependence in a dynamic brand competition model. Chaos, Solitons & Fractals 18, 561–576.
Bischi, G.I., Naimzada, A., 2000. Global analysis of a dynamic duopoly game with bounded rationality. In: Filar, J.A., Gaitsgory, V., Mizukami, K., Eds., Advances in Dynamics Games and Application, Vol. 5., 361–385. Boston: Birkhäuser.
Bischi, G.I., Gallegati, M., Naimzada, A., 1999. Symmetry-breaking bifurcations and representative firm in dynamic duopoly games. Annals of Operations Research 89, 253–272.
Bischi, G.I., Mammana, C., Gardini, L., 2000. Multistability and cyclic attractors in duopoly games. Chaos, Solitons & Fractals 11, 543–564.
Bischi, G.I., Stefanini, L., Gardini, L., 1998. Synchronization, intermittency and critical curves in duopoly games. Mathematics and Computers in Simulations 44, 559–585.
Bischi, G.I., Chiarella, C., Kopel, M., Szidarovszky, F., 2010. Nonlinear Oligopolies. Stability and Bifurcations. Berlin Heidelberg: Springer-Verlag.
Burmeister, E., 1980. On some conceptual issues in rational expectations modelling. Journal of Money, Credit and Banking 12, 217–228.
Chiarella, C., 1986. Perfect foresight models and the dynamic instability problem from a higher viewpoint. Economic Modelling 3, 283–292.
Chiarella, C., 1990. The Elements of a Nonlinear Theory of Economic Dynamics. Berlin: Springer Verlag.
Correa-López, M., Naylor, R.A., 2004. The Cournot-Bertrand profit differential: a reversal result in a differentiated duopoly with wage bargaining. European Economic Review 48, 681–696.
Cournot, A., 1838. Recherches sur les Principes Mathématiques de la Théorie des Richessess. Paris: Hachette.
Cyert, R.M., DeGroot, M.H., 1973. An analysis of cooperation and learning in a duopoly context. American Economic Review 63, 24–37.
Devaney, R.L., 1989. An Introduction to Chaotic Dynamical Systems. Second Edition. Redwood City (CA): Addison-Wesley.
Dixit, A.K., 1986. Comparative statics for oligopoly. International Economic Review 27, 107–122.
Fama, E.F., Jensen, M.C., 1983. Separation of ownership and control. Journal of Law and Economics 26, 301–325.
Fanti, L., Gori, L., 2012. The dynamics of a differentiated duopoly with quantity competition. Economic Modelling 29, 421–427.
Fershtman, C., 1985. Managerial incentives as a strategic variable in duopolistic environment. International Journal of Industrial Organization 3, 245–253.
Fershtman, C., Judd, K., 1987. Equilibrium incentives in oligopoly. American Economic Review 77, 927–940.
Gibbons, R., Murphy, K.J., 1990. Relative performance evaluation for chief executive officers. Industrial and Labor Relations Review 43, 30–51.
Gibson, C.G., 2003. Elementary Euclidean Geometry. Cambridge: Cambridge University Press.
Grossman, S.J., Stiglitz, J.E., 1977. On value maximization and alternative objectives of the firm. Journal of Finance 32, 389–402.
Jansen, T., Lier, A. van, Witteloostuijn, A. van, 2007. A note on strategic delegation: the market share case. International Journal of Industrial Organization 25, 531–539.
Jansen, T., Lier A. van, Witteloostuijn, A. van, 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 30, 141–153.
Jensen, M.C., Murphy, K.J., 1990. Performance pay and top management incentives. Journal of Political Economy 98, 225–264.
Kopel, M., 1996. Simple and complex adjustment dynamics in Cournot duopoly models. Chaos, Solitons and Fractals 12, 2031–2048.
Kopel, M., Szidarovszky, F., 2006. Resource dynamics under partial cooperation in an oligopoly. Journal of Optimization Theory and Applications 128, 393–410.
Kopel, M., Bischi, G.I., Gardini, L., 2000. On new phenomena in dynamic promotional competition models with homogeneous and quasi-homogeneous firms. In: Delli Gatti, D., Gallegati, M., Kirman, A.P., Eds., Interaction and Market Structure. Essays on Heterogeneity in Economics, 57–87. Berlin Heidelberg: Springer-Verlag.
Li, T.Y., Yorke, J.A., 1975. Period three implies chaos. American Mathematical Monthly 82, 985–992.
Lucas, R.E., Jr., 1972. Expectations and the neutrality of money. Journal of Economic Theory 4, 103–124.
Maistrenko, Y.L., Maistrenko, V.L., Popovich, A., Mosekilde, E., 1998. Transverse instability and riddled basins in a system of two coupled logistic maps. Physical Review E 57, 2713–2724.
Miller, N., Pazgal, A., 2002. Relative performance as a strategic commitment mechanism. Managerial and Decision Economics 23, 51–68.
Mira, C., Gardini, L., Barugola, A., Cathala, J.C., 1996. Chaotic Dynamics in Two-Dimensional Noninvertible Maps. Singapore: World Scientific Publishing.
Mosekilde, E., Maistrenko, Y.L., Postnov, D., 2002. Chaos Synchronization. Application to Living Systems. Singapore: World Scientific.
Muth, J.F., 1961. Rational expectations and the theory of price movements. Econometrica 29, 315–335.
Naimzada, A.K., Tramontana, F., 2010. A dynamic model of a boundedly rational consumer with a simple least squared learning mechanism. Computational Economics 36, 47–56.
Puu, T., 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals 1, 573–581.
Puu, T., 1998. The chaotic duopolists revisited. Journal of Economic Behavior & Organization 33, 385–394.
Salas Fumas, V., 1992. Relative performance evaluation of management: the effects on industrial competition and rick sharing. International Journal of Industrial Organization 10, 473–489.
Sargent, T.J., 1993. Bounded Rationality in Macroeconomics. New York (NY): Oxford University Press.
Sargent, T.J., Wallace, N., 1973. The stability of models of money and growth with perfect foresight. Econometrica 41, 1043–1048.
Shin, G.S., 2003. Interwoven basin structures of double logistic map at the edge of chaos. Working Paper http://arxiv.org/abs/nlin/0303028.
Simon, H., 1957. Simon, Herbert (1957). A behavioral model of rational choice. In: Models of Man, Social and Rational: Mathematical Essays on Rational Human Behavior in a Social Setting. New York (NY): Wiley.
Sklivas, S., 1987. The strategic choice of managerial incentives. RAND Journal of Economics 18, 452–458.
Theocharis R.D. 1960. On the stability of the Cournot solution on the oligopoly problem. Review of Economic Studies 27, 133–134.
Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357.
Tramontana, F., Gardini, L., Puu, T., 2009. Cournot duopoly when the competitors operate multiple production plants. Journal of Economic Dynamics and Control 33, 250–265.
Vickers, J., 1985. Delegation and the theory of the firm. Economic Journal 95, 138–147.
Witteloostuijn, A. van, Jansen, T., Lier, A. van, 2007. Bargaining over managerial contracts in delegation games: managerial power, contract disclosure and cartel behavior. Managerial and Decision Economics 28, 897–904.
Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148.