General Oligopolies - Nonlinear Oligopolies: Stability and Bifurcations - page 137

the critical curve LC, the basin of E 1 is transformed from a simply connected set
into a disconnected set.
In summary, in the case of non-identical adjustment speeds, parameter changes
may also result in global bifurcations. Such bifurcations are related to a contact
between a basin boundary and critical curves and change the qualitative structure of
the basins. Since the whole basin of E 1 is given by the union of the infinitely many
preimages of its immediate basin .E 1 / D S k0 T k .

B 0 .E 1 //,
the unfolding action of the inverses of the map T can result in disconnected por-
tions of the basin which are quite far away from the Nash equilibrium. In a sense,
this gives rise to a higher degree of uncertainty with respect to the possibility of pre-
dicting the effects of any small change in the initial market share of the competitors
on the long-run outcome of the duopoly game.

B 0 .E 1 /,thatis B