The Nash Equilibrium and the traveller's dilemma

[CallMeIshmael]

"A cannot "pretend" to be irrational while still being rational, as that would be predicted by C, being perfectly rational. "

How?

Like, how does C know exactly what A is thinking? The definition that they are both rational, simply means they are going to examine the structure of the game, and use logic and mathematics to deduce the optimal strategy.

Mutual assumption of rationality doesnt equal telepathy

Is A constantly thinking "maybe I should play 99... no, [censored], wait, he just heard that... no, 100.. we gotta play 100"?

[PairTheBoard]

On the other hand, A,B may play 100 irrationally according to you while C makes the Game Theory rational choice of 2. Now who does better after all the matchups?

According to the Scientific American article this problem remains open. It requires creative thinking. Game theory as it presently stands is simply not adequate. I'm inclined to look at the "Parasite Dilemma" for further investigation into what's going on here.

The simple Prisoner's Dilemma has a Dominating Strategy of Defection when played only once. Yet if played repeatedly in a population of opponents the constant Defect strategy does worse than ones which encourage Cooperation. It looks to me that the Traveler's Dilemma effectively telescopes repetitions of the Prisoner's Dilemma into a one time decision. The Repetitions become Virtual Ones contained in the Thinking of the participants rather than actual ones being physically transacted. The Tit-for-Tat type strategies employed in Repeated Prisoner's Dilemmas become incorporated into the one time decision of the Traveler's Dilemma. These are the kinds of concepts that need to be looked at in my opinion. I leave it to the professional game theoreticians to continue work on it.

Meanwhile, I'm interested in what people in SMP have to say about the Parasite Dilemma I presented on another thread. I think it may further isolate some of these concepts.

PairTheBoard

[CallMeIshmael]

GMontag,

Back to what you said about the prisoner's dilemma

Assume that both players in the game are perfectly rational. Also assume that one player goes first, and the response (coop/defect) is wrtitten down on a piece of paper.

That paper is brought into the other person's room, but they are not allowed to look at it.


It is your belief that, regardless of what the second player chooses, it was ALWAYS be the same as what is on the paper, yes?

[GMontag]

[ QUOTE ]
"A cannot "pretend" to be irrational while still being rational, as that would be predicted by C, being perfectly rational. "

How?

Like, how does C know exactly what A is thinking? The definition that they are both rational, simply means they are going to examine the structure of the game, and use logic and mathematics to deduce the optimal strategy.

Mutual assumption of rationality doesnt equal telepathy

Is A constantly thinking "maybe I should play 99... no, [censored], wait, he just heard that... no, 100.. we gotta play 100"?

[/ QUOTE ]

It's not telepathy. It is merely a consequence of the fact that C being perfectly rational and having accurate knowledge of A's rationality and the rest of the infinite inductive chain, will be able to come to the same conclusion as A. That is, unless there are two different valid rational arguments that lead to different strategies.

[GMontag]

[ QUOTE ]
GMontag,

Back to what you said about the prisoner's dilemma

Assume that both players in the game are perfectly rational. Also assume that one player goes first, and the response (coop/defect) is wrtitten down on a piece of paper.

That paper is brought into the other person's room, but they are not allowed to look at it.


It is your belief that, regardless of what the second player chooses, it was ALWAYS be the same as what is on the paper, yes?

[/ QUOTE ]

If you state that as one of the premises of the problem, as was done in this problem, then yes. It's not the rationality that does it, it's the knowledge of the other player's rationality, et al that is the condition for superrationality.

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
GMontag,

Back to what you said about the prisoner's dilemma

Assume that both players in the game are perfectly rational. Also assume that one player goes first, and the response (coop/defect) is wrtitten down on a piece of paper.

That paper is brought into the other person's room, but they are not allowed to look at it.


It is your belief that, regardless of what the second player chooses, it was ALWAYS be the same as what is on the paper, yes?

[/ QUOTE ]

If you state that as one of the premises of the problem, as was done in this problem, then yes. It's not the rationality that does it, it's the knowledge of the other player's rationality, et al that is the condition for superrationality.

[/ QUOTE ]

Here's the problem with this:

Under your framework, the answer to the question "what is the solution to a one shot prisoner's dilemma under the common knowledge assumption of rationality?" is "Cooperate"

But, that is not the accepted answer.

Now, it IS sort of lame to appeal to what is essentially a tautology, but it is what it is.

The common use of the "assumption of common rationality" isnt used the way you want to use it. I mean, I understand what you mean, but that is not what the term means.

[GMontag]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
GMontag,

Back to what you said about the prisoner's dilemma

Assume that both players in the game are perfectly rational. Also assume that one player goes first, and the response (coop/defect) is wrtitten down on a piece of paper.

That paper is brought into the other person's room, but they are not allowed to look at it.


It is your belief that, regardless of what the second player chooses, it was ALWAYS be the same as what is on the paper, yes?

[/ QUOTE ]

If you state that as one of the premises of the problem, as was done in this problem, then yes. It's not the rationality that does it, it's the knowledge of the other player's rationality, et al that is the condition for superrationality.

[/ QUOTE ]

Here's the problem with this:

Under your framework, the answer to the question "what is the solution to a one shot prisoner's dilemma under the common knowledge assumption of rationality?" is "Cooperate"

But, that is not the accepted answer.

Now, it IS sort of lame to appeal to what is essentially a tautology, but it is what it is.

The common use of the "assumption of common rationality" isnt used the way you want to use it. I mean, I understand what you mean, but that is not what the term means.

[/ QUOTE ]

Then the common use of the "assumption of common rationality" is different than the "assumption of infinite rationality" that you used in setting up this problem. It is that premise that I'm basing my argument for (100,100) on, and my statement about the PD was if you use that premise there as well, the solution would be (keep silent, keep silent).

[CallMeIshmael]

[ QUOTE ]
Then the common use of the "assumption of common rationality" is different than the "assumption of infinite rationality" that you used in setting up this problem.

[/ QUOTE ]

Nope.

http://en.wikipedia.org/wiki/Common_knowledge_(logic)

[GMontag]

[ QUOTE ]
[ QUOTE ]
Then the common use of the "assumption of common rationality" is different than the "assumption of infinite rationality" that you used in setting up this problem.

[/ QUOTE ]

Nope.

http://en.wikipedia.org/wiki/Common_knowledge_(logic)

[/ QUOTE ]

Then the accepted answer is wrong. Come up with a couterargument that isn't an argument from authority.

[Sephus]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Then the common use of the "assumption of common rationality" is different than the "assumption of infinite rationality" that you used in setting up this problem.

[/ QUOTE ]

Nope.

http://en.wikipedia.org/wiki/Common_knowledge_(logic)

[/ QUOTE ]

Then the accepted answer is wrong. Come up with a couterargument that isn't an argument from authority.

[/ QUOTE ]

someone smarter than i am can probably do this better, but my best guess is there's some sort of circularity i can't quite pin down.

maybe the entire rationality of your strategy depends on it being the rational strategy.

maybe it's a problem that you expect to use the same strategy because only one solution is rational, and you use that fact to decide which is the rational one.

maybe you have to say "we will both choose the same solution given that we choose the rational one" and not just "we will both choose the same solution." (100/100) maximizes your payoff if you both choose the same strategy, which we know happens if you both choose the rational strategy, which makes 100 the rational strategy. it seems like there could be a problem somewhere.

even though you say you are sure that 100 is the only rational solution, you don't claim that you know for sure (beforehand) that your rational opponent will bid 100. it seems like it should follow from "there is only one rational solution" that you also know your opponent will play it ahead of time.

maybe once you start assuming that your opponents bid depends on your own, you've already left rationality behind, even though the whole thing appears to be rational on the surface.

playing 100 maximizes your payoff as long as it's the rational strategy, and it's the rational strategy because it maximizes your payoff. but of course it doesn't maximize your payoff against an opponent playing "the rational strategy," but we've already proven it's the rational strategy, so it must be the case that sometimes the rational strategy does not maximize its own payoff given the rational strategy of the opponent.

i dont know, [censored] it.