Multistability in a dynamic Cournot game with three oligopolists

The time evolution of a dynamic oligopoly game with three competing firms i s modeled by a discrete dynamical system obtained by the iteration of a thr ee-dimensional non-invertible map. For the symmetric case of identical play ers a complete analytical study of the stability conditions for the fixed p oints, which are Nash equilibria of the game, is given. For the situation o f several coexisting stable Nash equilibria a numerical study of their basi ns of attraction is provided. This gives, evidence of the occurrence of glo bal bifurcations at which the basins are transformed from simply connected sets into nonconnected sets, a basin structure which is peculiar of non-inv ertible maps. The presence of several coexisting attractors (or multistabil ity) is observed even when complex attractors exist. Two different routes t o complexity are presented: one related to the creation of more and more co mplex attractors; the other related to the creation of more and more comple x structures of the basins, Starting from the benchmark case of identical p layers, the effects of heterogeneous behavior of the players, causing the l oss of the symmetry properties of the dynamical system, are investigated th rough numerical explorations. (C) 1999 IMACS/Elsevier Science B.V. All righ ts reserved.