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Nonlinear dynamics in a Cournot duopoly with relative profit delegation. (English) Zbl 1258.91040
Summary: 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.

91A40 Other game-theoretic models
91A80 Applications of game theory
90B50 Management decision making, including multiple objectives
37N40 Dynamical systems in optimization and economics
Full Text: DOI
[1] Baumol, W., On the theory of oligopoly, Economica, 25, 187-198, (1958)
[2] Fama, E.F.; Jensen, M.C., Separation of ownership and control, J law econ, 26, 301-325, (1983)
[3] Vickers, J., Delegation and the theory of the firm, Econ J, 95, 138-147, (1985)
[4] Fershtman, C., Managerial incentives as a strategic variable in duopolistic environment, Int J ind organ, 3, 245-253, (1985)
[5] Fershtman, C.; Judd, K., Equilibrium incentives in oligopoly, Am econ rev, 77, 927-940, (1987)
[6] Sklivas, S., The strategic choice of managerial incentives, RAND J econ, 18, 452-458, (1987)
[7] Salas Fumas, V., Relative performance evaluation of management: the effects on industrial competition and rick sharing, Int J ind organ, 10, 473-489, (1992)
[8] Miller, N.H.; Pazgal, A.I., The equivalence of price and quantity competition with delegation, RAND J econ, 32, 284-301, (2001)
[9] Miller, N.H.; Pazgal, A.I., Relative performance as a strategic commitment mechanism, Managerial dec econ, 23, 51-68, (2002)
[10] Jansen, T.; van Lier, A.; van Witteloostuijn, A., 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 dec econ, 30, 141-153, (2009)
[11] Gibbons, R.; Murphy, K.J., Relative performance evaluation for chief executive officers, Ind lab relat rev, 43, 30-51, (1990)
[12] Aggarwal, R.K.; Samwick, A.A., Executive compensation, strategic competition and relative performance evaluation: theory and evidence, J finance, 54, 1999-2043, (1999)
[13] Bischi, G.I.; Chiarella, C.; Kopel, M.; Szidarovszky, F., Nonlinear oligopolies, Stability and bifurcations, (2010), Springer-Verlag Berlin, Heidelberg · Zbl 1182.91001
[14] Dixit, A.K., Comparative statics for oligopoly, Int econ rev, 27, 107-122, (1986) · Zbl 0584.90012
[15] Bischi, G.I.; Naimzada, A., Global analysis of a dynamic duopoly game with bounded rationality, (), 361-385 · Zbl 0957.91027
[16] Puu, T., Chaos in duopoly pricing, Chaos soliton fract, 1, 573-581, (1991) · Zbl 0754.90015
[17] Kopel, M., Simple and complex adjustment dynamics in Cournot duopoly models, Chaos soliton fract, 12, 2031-2048, (1996) · Zbl 1080.91541
[18] Bischi, G.I.; Stefanini, L.; Gardini, L., Synchronization, intermittency and critical curves in duopoly games, Math comput simulat, 44, 559-585, (1998) · Zbl 1017.91500
[19] Bischi, G.I.; Gallegati, M.; Naimzada, A., Symmetry-breaking bifurcations and representative firm in dynamic duopoly games, Ann oper res, 89, 253-272, (1999) · Zbl 0939.91017
[20] Tramontana, F., Heterogeneous duopoly with isoelastic demand function, Econ modell, 27, 350-357, (2010)
[21] Correa-López, M.; Naylor, R.A., The cournot – bertrand profit differential: a reversal result in a differentiated duopoly with wage bargaining, Eur econ rev, 48, 681-696, (2004)
[22] Cyert, R.M.; DeGroot, M.H., An analysis of cooperation and learning in a duopoly context, Am econ rev, 63, 24-37, (1973)
[23] Kopel, M.; Szidarovszky, F., Resource dynamics under partial cooperation in an oligopoly, J optim theory appl, 128, 393-410, (2006) · Zbl 1181.91251
[24] Reitman, D., Partial ownership arrangements and the potential for collusion, J ind econ, 42, 313-322, (1994)
[25] Kopel M, Lambertini L. On the (non) existence of a price equilibrium in delegation games with relative performance compensation. Working Paper No. 807, Department of Economics, University of Bologna; 2012.
[26] Cánovas, J.S.; Puu, T.; Ruíz, M., The cournot – theocharis problem reconsidered, Chaos soliton fract, 37, 1025-1039, (2008) · Zbl 1140.91444
[27] Mira, C.; Gardini, L.; Barugola, A.; Cathala, J.C., Chaotic dynamics in two-dimensional noninvertible maps, (1996), World Scientific Singapore · Zbl 0906.58027
[28] Agliari, A.; Bischi, G.I.; Gardini, L., Some methods for the global analysis of dynamic games represented by iterated noninvertible maps, (), 31-84, [chapter 3] · Zbl 1072.91013
[29] Bischi, G.I.; Gardini, L., Role of invariant and minimal absorbing areas in chaos synchronization, Phys rev E, 58, 5710-5719, (1998)
[30] Devaney, R.L., An introduction to chaotic dynamical systems, (1989), Addison-Wesley Redwood City (CA) · Zbl 0695.58002
[31] Maistrenko, Y.L.; Maistrenko, V.L.; Popovich, A.; Mosekilde, E., Transverse instability and riddled basins in a system of two coupled logistic maps, Phys rev E, 57, 2713-2724, (1998)
[32] Bischi, G.I.; Gardini, L., Global properties of symmetric competition models with riddling and blowout phenomena, Discrete dyn nat soc, 5, 149-160, (2000) · Zbl 0973.91028
[33] Kopel, M.; Bischi, G.I.; Gardini, L., On new phenomena in dynamic promotional competition models with homogeneous and quasi-homogeneous firms, (), 57-87 · Zbl 1158.91436
[34] Bischi, G.I.; Kopel, M., Multistability and path dependence in a dynamic brand competition model, Chaos soliton fract, 18, 561-576, (2003) · Zbl 1056.91046
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