nd of meta-rationality attached to it.
Traveller’s Dilemma
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I’m no game theory expert, but in this type of game, logic only leads to such conclusions (there’s another called the centipede game with a different set up whereby both players could get $100 but end up getting $2 for simliar reasons) if you think along the lines of ‘if we both say the true price, I could deviate by $1 and earn myself the $2 bonus’ but the incentive to behave in such a way is weak when you know that going down that road ends up with you getting $2. Your suggestion of the true price makes sense – one of the justifications for use of the Nash equilibrium concept is that they represent a natural focal point for players, and the true price is a natural focus point in this game that both players might reasonably expect the other to choose.
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Strongly recommend that Mick’s readership look in detail at the latest essay on Bill Whittle’s blog, which expand this idea, another variation on the “prisoner’s dilemma”, to discuss the philosophical and moral concepts of the “remnant”: also evoking the writings of the rather obscure and long-dead American political scientist Albert Jay Nock.
Whitttle’s URL is “ejectejecteject dot com” -
Here is another version.
Let’s say you and I have CONSECUTIVE numbers tattooed to our foreheads, and we can only see each other’s number. The object is to guess the number on our own head.
If I am looking at 100, then I know my number.
If I am looking at 99, then if my partner says he knows then I must have 100 (see the logic above). If he does not know, then I must have 98.
If I am looking at 98, athen I have either 99 and the game plays out as above but with the positions reversed, or I have 97, and the game does not play out as above. But I know my number in either case. (It’s a little too complex to explain in a comment, but I think you get the drift).
The logic follows that I will always know the number on my forehead, which doesn’t seem possible at first. -
Hmmm…if someone was dumb enough to have a big number tattoed on their forehead, I’d question their ability to use any kind of logic. 😉
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