SYNCHRONIZATION, INTERMITTENCY AND CRITICAL CURVES IN A DUOPOLY GAME

The phenomenon of synchronization of a two-dimensional discrete dynami cal system is studied for the model of an economic duopoly game, whose time evolution is obtained by the iteration of a noninvertible map of the plane. In the case of identical players the map has a symmetry pr operty that implies the invariance of the diagonal x(1)=x(2), so that synchronized dynamics is possible. The basic question is whether an at tractor of the one-dimensional restriction of the map to the diagonal is also an attractor for the two-dimensional map, and in which sense. In this paper, a particular dynamic duopoly game is considered for whi ch the local study of the transverse stability, in a neighborhood of t he invariant submanifold in which synchronized dynamics takes place, i s combined with a study of the global behavior of the map. When measur e theoretic, but not topological, attractors are present on the invari ant diagonal, intermittency phenomena are observed. The global behavio r of the noninvertible map is investigated by studying of the critical manifolds of the map, by which a two-dimensional region is defined th at gives an upper bound to the amplitude of intermittent trajectories. Global bifurcations of the basins of attraction are evidenced through contacts between critical curves and basin boundaries. (C) 1998 IMACS /Elsevier Science B.V.