Is there a general name for the setup in which payoffs are not known exactly but players try to influence each other's perception of the payoffs? A recent question elsewhere made me look at the "madman strategy" which actually consists of trying to make the opposite player think that he is playing a game of chicken instead of prisoner's dilemma. This can only work, of course, because in reality the payoffs are not known apriori, so an inversion of the non-cooperation payoff with the "tentation" payoff does this game switch.

Is there a general name for a "meta-game" (my term) situation in which the payoffs are not known exactly and players are trying to influence each others' perception of the payoffs?
What players are trying to do is always up for interpretation, it is not coded into the mathematics of game theory. 

The madman strategy can be modelled as a Bayesian game, with different types having different payoffs, and one player sending a signal about their type, the other player observing the signal. A situation in which types are indistinguishable based on their signals is called a pooling equilibrium.