I don't want to pick nits here, but it does seem that using Hofstadter ( 'genius' capital notwithstanding) doesn't quite address the limitations (as Doyle hinted at) of language as a form of (prison-house) information, since we get into further problems when concepts of super-rationality imply a sub-rationality that is ( or isn't ) irrationality (and where sub-optimality is not the same as sub-rationality). The hint to this is whether Hofstadter's version of Kant can include issues of practical reason for the PD; an example of this would be issues of asymmetric information which (as exchanged linguistic signs) can complicate the IPD and make the closed bag "leaky" before, during, and after its exchange. I agree with Ken's point, but don't think that the actual solution is necessarily rational for the same Kantian reasons. As with my earlier post regarding common-pool resources, historically contingent or situated spatio-temporal actions complicate GT models to the point where they become first steps in a longer, more critical explanatory process.
Ann ------------------ Subject: PD simplified From: ken hanly <[EMAIL PROTECTED]> Date: Mon, 6 Aug 2007 21:44:52 -0700 The Game Tucker began with a little story, like this: two burglars, Bob and Al, are captured near the scene of a burglary and are given the "third degree" separately by the police. Each has to choose whether or not to confess and implicate the other. If neither man confesses, then both will serve one year on a charge of carrying a concealed weapon. If each confesses and implicates the other, both will go to prison for 10 years. However, if one burglar confesses and implicates the other, and the other burglar does not confess, the one who has collaborated with the police will go free, while the other burglar will go to prison for 20 years on the maximum charge. The strategies in this case are: confess or don't confess. The payoffs (penalties, actually) are the sentences served. We can express all this compactly in a "payoff table" of a kind that has become pretty standard in game theory. Here is the payoff table for the Prisoners' Dilemma game: Table 3-1 Al confess don't Bob confess 10,10 0,20 don't 20,0 1,1 The table is read like this: Each prisoner chooses one of the two strategies. In effect, Al chooses a column and Bob chooses a row. The two numbers in each cell tell the outcomes for the two prisoners when the corresponding pair of strategies is chosen. The number to the left of the comma tells the payoff to the person who chooses the rows (Bob) while the number to the right of the column tells the payoff to the person who chooses the columns (Al). Thus (reading down the first column) if they both confess, each gets 10 years, but if Al confesses and Bob does not, Bob gets 20 and Al goes free. So: how to solve this game? What strategies are "rational" if both men want to minimize the time they spend in jail? Al might reason as follows: "Two things can happen: Bob can confess or Bob can keep quiet. Suppose Bob confesses. Then I get 20 years if I don't confess, 10 years if I do, so in that case it's best to confess. On the other hand, if Bob doesn't confess, and I don't either, I get a year; but in that case, if I confess I can go free. Either way, it's best if I confess. Therefore, I'll confess." But Bob can and presumably will reason in the same way -- so that they both confess and go to prison for 10 years each. Yet, if they had acted "irrationally," and kept quiet, they each could have gotten off with one year each. Dominant Strategies What has happened here is that the two prisoners have fallen into something called a "dominant strategy equilibrium." DEFINITION Dominant Strategy: Let an individual player in a game evaluate separately each of the strategy combinations he may face, and, for each combination, choose from his own strategies the one that gives the best payoff. If the same strategy is chosen for each of the different combinations of strategies the player might face, that strategy is called a "dominant strategy" for that player in that game. This is typical of the standard conclusion to describe the strategy that would result in a lesser time for each player as "irrational". My point is simply that it is not the strategy that would give them the least time in jail and therefore it is not rational. The conclusion contradicts the definition of rational--choosing the strategy that would give the least time in jail. Now you may object that this ignores the two cells where choices are opposite but that is another issue. (As Hofstadter notes the symmetry ensures that both will chose the same strategy or as in mine and other arguments there is a two stage reasoning process the first arriving at the standard strategy and the second rejecting it as not Pareto optimal, leading to adoption of co-operation.) Anyway I hope this clears up my point. 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. 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. Blog: http://kenthink7.blogspot.com/index.html Blog: http://kencan7.blogspot.com/index.html
