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stability as the bifurcation parameter
2
tends towards 1. This result is quite surpris-
ing as one would expect a fully cooperative firm to have a stabilizing effect. With
respect to the monotonicity property of the individual quantities mentioned above,
the bifurcation diagram reveals that for an increasing cooperation level of firm 2, the
equilibrium quantity of firm 1 first increases, and then decreases, whereas firm 2's
equilibrium quantity decreases throughout. The counterintuitive destabilizing effect
of an increase in the cooperation level
k
of one of the firms is not a general prop-
erty. This becomes obvious from the diagram shown in Fig. 4.22 (obtained with the
same set of parameters as in Fig. 4.21; the only difference being that the number of
firms has increased to N
D
8). Here, an increase in the cooperation level of firm 2
leads first to a stabilization of the equilibrium through a period halving bifurcation.
Then a further increase in the cooperation level finally causes destabilization and
transition to periodic attractors of increasing period as well as to chaotic behavior.
We close this subsection by remarking that the bifurcation diagrams obtained
with different values of
1
and
2
for increasing values of N or increasing values of
a
k
as bifurcation parameters are qualitatively very similar to those shown in Fig. 3.6
and 3.7 respectively. The only difference is that with higher cooperation levels both
individual quantities and their fluctuations are generally reduced.
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