  We lay out a model of games with imperfect information that features explicit
communication actions, by which the entire observation history of a player is
revealed to another player. Such full-information protocols are common in
asynchronous distributed systems; here, we consider a synchronous setting with
a single active player who may communicate with multiple passive observers in
an indeterminate environment. We present a procedure for solving the basic
strategy-synthesis problem under regular winning conditions.
  We present our solution in an abstract framework of games with imperfect
information and we split the proof in two conceptual parts: (i) a generic
reduction schema from imperfect-information to perfect-information games, and
(ii) a specific construction for full-information protocols that satisfies the
requirement of the reduction schema.
  Furthermore we show that the number of passive observers induces a strict
hierarchy, both in terms of expressiveness and complexity: with n observers, a
full-information protocol can express indistinguishability relations (defining
imperfect information for the player in the protocol) that are not expressible
with n-1 observers, and the strategy-synthesis problem is
(n+1)-EXPTIME-complete.
