  In our previous work, we have shown that the use of a quantum architecture in
decentralised control allows access to a larger space of control strategies
beyond what is classically implementable through common randomness, and can
lead to an improvement in the cost -- a phenomenon we called the quantum
advantage. In the previous part of this two part series, we showed, however,
that not all decision problems admit such an advantage. We identified a
decision-theoretic property of the cost called the `coordination dilemma' as a
necessary condition for the quantum advantage to manifest. In this article, we
investigate the impact on the quantum advantage of a scalar parameter that
captures the extent of the coordination dilemma. We show that this parameter
can be bounded within an open interval for the quantum advantage to exist, and
for some classes, we precisely identify this range of values. This range is
found to be determined by the information of the agents.
