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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?

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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.

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  • $\begingroup$ I've accepted your answer but I do ponder if the assumption of nature move establishing the players' types (and with a common prior knowledge of those type assignment probabilities) is really capturing all I'm asking about. I'm guessing that players sending each other signals about their types prior to playing the actual game make this a 3-step game (instead of just nature move followed by a static game). $\endgroup$
    – fantastic peace and prosperity
    Commented Apr 10, 2019 at 7:30
  • $\begingroup$ This is possible in Bayesian games, there can be many steps. For an example see Kuhn poker. $\endgroup$
    – Giskard
    Commented Apr 10, 2019 at 7:54
  • $\begingroup$ Actually it looks like the narrowest fitting type is called signalling game, although in that one only one of the players (the "sender") chooses [and sends] a message after being dealt a type by nature. $\endgroup$
    – fantastic peace and prosperity
    Commented Apr 10, 2019 at 8:10

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