  Quantum guessing games form a versatile framework for studying different
tasks of information processing. A quantum guessing game with posterior
information uses quantum systems to encode messages and classical communication
to give partial information after a quantum measurement has been performed. We
present a general framework for quantum guessing games with posterior
information and derive structure and reduction theorems that enable to analyze
any such game. We formalize symmetry of guessing games and characterize the
optimal measurements in cases where the symmetry is related to an irreducible
representation. The application of guessing games to incompatibility detection
is reviewed and clarified. All the presented main concepts and results are
demonstrated with examples.
