Here we report on on the Pareto optimal trigger strategy for the 14 service areas in Table 4. We first explain how we search for the Pareto optimal trigger strategy. Next, we discuss some sub-optimal outcomes and suggest what they mean. These outcomes are demonstrated in Figures 1 through 5. Figure 2 shows the best quantity response curves of each provider in service area A. All of the service areas have similar response curves.
Our model resolves the discounted value statements presented in
the previous section. We search for Pareto optimal values over a range
of trigger price values (tp) for a given reversion length (T).
When the Pareto optimal discounted value is found, at a particular tp,
we then run the model again at that tp over a range of different
reversion lengths T. We then repeat the process testing discounted
values at different tp using the new T. The process is repeated
until no higher discounted values can be found. From this procedure
we compute the best response quantities, 
and 
.
We also verify the same response quantities using two different
root finding functions in Mathematica for Windows. We also view the
numerical responses as graphic response curves.
Figure 2 is an example of the Pareto optimal response quantities computed
for service area A. In the figure
the first crosspoint nearest to the axis origin is the
best response quantities for each firm. This first crosspoint
produces the highest discounted values. The next farthest crosspoint
from the origin are the Cournot quantites and they produce lower
discounted values. The furthest crosspoint from the origin
shows another suboptimal equilibria point where
selected quantites produce still lower discounted values.