  We present a general theorem for distributed synthesis problems in
coordination games with $\omega$-regular objectives of the form: If there
exists a winning strategy for the coalition, then there exists an "essential"
winning strategy, that is obtained by a retraction of the given one. In
general, this does not lead to finite-state winning strategies, but when the
knowledge of agents remains bounded, we can solve the synthesis problem. Our
study is carried out in a setting where objectives are expressed in terms of
events that may \emph{not} be observable. This is natural in games of imperfect
information, rather than the common assumption that objectives are expressed in
terms of events that are observable to all agents. We characterise decidable
distributed synthesis problems in terms of finiteness of knowledge states and
finite congruence classes induced by them.
