  A quantum system with variables in Z(d) is considered. Coherent density
matrices and coherent projectors of rank n are introduced, and their properties
(e.g., the resolution of the identity) are dis- cussed. Cooperative game theory
and in particular the Shapley methodology, is used to renormalize coherent
states, into a particular type of coherent density matrices (dressed coherent
states). The Q-function of a Hermitian operator, is then renormalized into a
physical analogue of the Shapley values. Both the Q-function and the Shapley
values, are used to study the relocation of a Hamilto- nian in phase space as
the coupling constant varies, and its effect on the ground state of the system.
The formalism is also generalized for any total set of states, for which we
have no resolution of the identity. The dressing formalism leads to density
matrices that resolve the identity, and makes them practically useful.
