I will continue to pick at nits here and suggest that there may be a relative (and more importantly, uncertain) autonomy between everyday rationality and formal rationality as Oaksford & Chater discuss in Bayesian Rationality (2007). This limits but does not negate the effectiveness of experimental modeling of economic actions where the premise for rationality is strictly one of choice among/between payoffs, especially in one-shot moments.
Ann --------------- Subject: Re: PD simplified From: ken hanly <[EMAIL PROTECTED]> Date: Tue, 7 Aug 2007 19:30:42 -0700 Yes. It is assumed that each player knows the payoff to each player for each of the four possible combination of choices. It is also assumed that the players are both rational in that they want to minimize their time spent in jail. There is no need to communicate with the other person. There is no assumption of omniscience just knowledge of the payoffs for each combination and that the other person and you are both rational. Perhaps a short cut way of understanding the reasoning for both to adopt the co-operation strategy is this. Both are rational and the situation is symmetrical so both will chose the same strategy. This means that there are only two possible strategies that rational players could choose: both defect or both co-operate. But both defecting does not minimize the time of each spent in jail whereas both co-operating does. Therefore both will chose to co-operate. Of course the traditionalists point out that two of the possible combinations have been left out of the reasoning. True enough but because both will choose the same strategy, being rational, a different choice by each is not really a possibility. In fact allowing them as possibilities is what leads to the traditional "irrational" solution. Cheers, Ken Hanly --- Jim Devine <[EMAIL PROTECTED]> wrote:
ken hanly wrote:
> >It is not that some definition of rational is contradictory it is that the traditional solution of the dilemma is not rational according to the standard definition because it does not lead to the least time served for the players. < if you are an individualistic prisoner (thinking only of your own fate), if you don't have any information except the offers that your captors tell you about, and if you can't communicate with the other prisoner, how can you conceivably act to minimize your time served? are you assuming that the "players" know the game matrix? To say that the "traditional solution" is not "rational" because it "does not lead to the least time" seems to assume that rationality involves omniscience. It's "social rationality," but most people don't think -- or can't think -- in those terms. Again, I bow before anyone's superior knowledge of game theory.
> > The actual solution is rational. For some reason that I dont fathom Hosfstadter wants to distinguish rationality from super-rationality and call the standard solution rational but his super-rational.< maybe "super-rationality" involves the aforementioned omniscience? -- Jim Devine / "Segui il tuo corso, e lascia dir le genti." (Go your own way and let people talk.) -- Karl, paraphrasing Dante.
