  We study team decision problems where communication is not possible, but
coordination among team members can be realized via signals in a shared
environment. We consider a variety of decision problems that differ in what
team members know about one another's actions and knowledge. For each type of
decision problem, we investigate how different assumptions on the available
signals affect team performance. Specifically, we consider the cases of
perfectly correlated, i.i.d., and exchangeable classical signals, as well as
the case of quantum signals. We find that, whereas in perfect-recall trees
(Kuhn [1950], [1953]) no type of signal improves performance, in
imperfect-recall trees quantum signals may bring an improvement. Isbell [1957]
proved that in non-Kuhn trees, classical i.i.d. signals may improve
performance. We show that further improvement may be possible by use of
classical exchangeable or quantum signals. We include an example of the effect
of quantum signals in the context of high-frequency trading.
