The dynamics of a triopoly Cournot game

This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused. ” 2000 Elsevier Science Ltd. All rights reserved.

[1]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[2]  David A. Rand,et al.  Exotic phenomena in games and duopoly models , 1978 .

[3]  Tönu Puu,et al.  The chaotic duopolists revisited , 1998 .

[4]  G. Bischi,et al.  Multistability in a dynamic Cournot game with three oligopolists , 1999, Mathematics and Computers in Simulation.

[5]  Laura Gardini,et al.  Multistability and cyclic attractors in duopoly games , 2000 .

[6]  M. Bernhard.  Introduction to Chaotic Dynamical Systems , 1992 .

[7]  Laura Gardini,et al.  On New Phenomena in Dynamic Promotional Competition Models with Homogeneous and Quasi-homogeneous Firms , 2000 .

[8]  H. Agiza,et al.  Dynamics of a Cournot Game with n-Competitors , 1998 .

[9]  Christian Mira,et al.  Basin bifurcations of two-dimensional noninvertible maps : Fractalization of basins , 1994 .

[10]  T. Puu.  Nonlinear economic dynamics , 1989 .

[11]  Mauro Gallegati,et al.  Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games , 1999, Ann. Oper. Res..

[12]  Luciano Stefanini,et al.  Synchronization, intermittency and critical curves in a duopoly game , 1998 .

[13]  Laura Gardini,et al.  Global dynamics in a non-linear model of the equity ratio , 2000 .

[14]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[15]  Michael Kopel,et al.  Simple and complex adjustment dynamics in Cournot duopoly models , 1996 .

[16]  Gian Italo Bischi,et al.  Global Analysis of a Dynamic Duopoly Game with Bounded Rationality , 2000 .

[17]  H. N. Agiza,et al.  On the Analysis of Stability, Bifurcation, Chaos and Chaos Control of Kopel Map , 1999 .

[18]  Christian Mira,et al.  Chaotic Dynamics in Two-Dimensional Noninvertible Maps , 1996 .

[19]  Laura Gardini,et al.  Analysis of global bifurcations in a market share attraction model , 2000 .

[20]  Giancarlo Gandolfo,et al.  Economic Dynamics, Methods and Models , 1980 .

[21]  Tönu Puu,et al.  Complex dynamics with three oligopolists , 1996 .

[22]  Christian Mira,et al.  On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps , 1997 .

[23]  Tönu Puu,et al.  Chaos in duopoly pricing , 1991 .