I think the idea OP is aiming at is discussed in this Wiki article:
Superrationality - Wiki
From Link:
Quote:
The concept of superrationality (or renormalized rationality) was coined by Douglas Hofstadter, in his article series and book Metamagical Themas.[1] Superrationality represents an alternative type of rational decision making different from the widely-accepted game-theoretic one, since a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a game-theoretically rational player will defect. Superrationality is not a mainstream model within game theory.
I tried to promote this idea a while back in SMP with a situation I believe I called, "The Parasite Problem". It's really a souped up version of the PD but with a community of players I thought gave it a different feel.
The setup is, you are 1 of 100 players. The most important fact here is that you are all equally optimally most rational as possible And you all know that fact And you all know that you all know. You must all choose independently and in secret from each other whether you want to be a Contributor or a Parasite. There will be a community treasury with funds provided by an outside source according to the rule, $1000 added for each Contributor and $2000 subtracted for each Parasite. After everyone has choosen, the treasury is divided between the 100 players according to 1 share to each Contributor and 2 shares to each Parasite. The treasury can go negative in which case players must pay the outside source according to their number of shares as well.
The question then is, what is your optimal most rational choice knowing that all the other players will also be coming to the optimal most rational choice?
The Nash Equilibrium choice for an individual is probabilistic, where the individual flips a weighted coin so as to Contribute with 2/3 chance and Parasite with 1/3 chance. If everyone does this then the game is 0 EV. The expected treasury will be 0.
But people can also recognize that if everyone Contributes then everyone makes $1000. Surely that's a more rational choice under the most important fact of the setup, that everyone is equally as rational as possible and everyone knows that everyone knows that fact. Those who recognize this and choose to contribute - which should be everyone under the assumption - are being superrational as described in the Wiki article. In a group of 100 who are free to be superrational knowing the important fact, they all make $1000. In another group where everyone is "Nash" rational their EV is to all go home with nothing.
You can argue that in the superrational case, someone might go a step further and think that everyone else will be superrational so he might as well decide to be a Parasite and go home with close to $2000. That thought would likely cross his mind, but then being logical he would realize that if he did so it would contradict the most important fact about the setup. So he doesn't do it.
Like I said, this is really a souped of version of the PD and the same argument would hold in PD for cooperating under the "most important fact" assumption. However, I like the feel that the community gives it. Plus I thought it up myself.
PairTheBoard
Last edited by PairTheBoard; 05-29-2013 at 05:29 PM.