One intelligence system non-randomly affecting the impression made on another intelligent system, so as to effect the latter's behavioral response to this impression. Only in the definition of magic, it can be reflexive. Although maybe you'd say your definition of communication can be reflexive, i.e. someone informing their own behavior.
Yeah and so we all are hip to "impression management," either in our own life experience or Goffman's writings. That we care about and regulate the mask, etc.
The key that at least the early works of Goffman's miss (I haven't read his later, 80s-90s stuff) is that this impression management is always contextual to the game at hand. So while a general principle of appearing more intelligent, attractive, witty etc seems appealing to argue for, we get in caught in games where we play humble, downplay our endowments, etc!
So the impressions we try to foster are always contingent on the kind of game played, i.e. who the other agents are, what our goals are, etc
A "game" in my factoring is just an interaction between an agent and an environment (which includes other agents). The agent has goals, preferred states (like "food in my belly") and these goals turn the environment into a landscape of affordances and obstacles.