Why does reverse psychology work?
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Consider a simple game with a single binary choice. You hide a coin in one hand, other player has to guess which it is. The payoffs/utilities are common knowledge (you don’t want to lose the coin, the other player wants to get the coin, everyone knows, everyone knows everyone knows, etc.), but he doesn’t know what strategy you’re using. Also you can talk.
Now, the optimal thing to do is to pick a hand completely randomly, for both players. You can’t do better against an optimal player. But humans don’t play optimally – random choices are difficult to make (maybe you unconsciously favor your right hand), consistently suck at estimating chances and hallucinate patterns all the time, and also you can use cheap talk to influence how the other player thinks. If the other player is confident that you’re giving him information about what hand the coin is in, he could choose a hand with 80% chance, or 100% chance, or anything other than 50%, for more expected gains.
This can take many forms – “he favors his right hand”, or “he’s trying to hint that he favors his right hand, expecting me to pick it, which he knows, and he would only play a winning strategy for him, so it’s not there, so I should pick the left hand”, or “he expects I would use _that_ thought process, so I should pick the right hand after all”, etc. – 0, 1, 2, or more layers of reverse psychology. As you see, for this game, all odd/even numbers are the same. You can work out something like “he outright told me it’s his right hand, based on his smirk I expect him to be using reverse psychology once with 68% chance, twice with 3% chance, otherwise be straightforward with 29% chance” then sum odds/evens. Of course, in some sense, frustrating those estimates is the whole point of the game. We’re not perfect – maybe you’re playing well, maybe your opponent is better than you at reading you and hiding that he’s reading you and you didn’t pick up on that and you’ve already lost.
This is all still a big simplification, of course. There’s a lot of literature on iterated games, signaling, and so on. We can be unaware of signals we send unconsciously, fake awareness or unawareness, act predictably to set up surprises later, fake all sorts of things, have other factors like history or future influence decisions, make commitments… But in general, reverse psychology works sometimes, when two people thinking they can outsmart each other play at different levels.
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