I agree entirely. My initial proposal was to score according to totals, not to win differentials, though I may not have expressed that clearly. i.e. it's better to cooperate and get minorly exploited than to get locked into a cycle of retaliation where hardly anyone gets any points in the entire match, even if you end up being the winner. Bit of a pyrrhic victory in the latter case.
In the intial prisoner's dilemma game, the tit-for-tat strategy prevailed. e.g. cooperate whenever the opponent cooperated on the last turn, defect whenever the opponent defected on the last turn. It's pretty much exploitation-proof, and enforces cooperation despite being forgiving enough to oftentimes avoid infinite cycles of recrimination. When the contest was run again, after post mortem analysis, some individuals submitted programs designed specifically to defeat tit-for-tat strategies. For example, one program simply defected in every round. Which means that it beat tit-for-tat programs whose initial move was to cooperate by successfully exploiting these programs for one round, after which games would get locked into score-neutral successive mutual defections. End result: these programs did beat tit-for-tat like programs, and in some cases won the majority of their matches, but in the overall points analysis, they were completely swamped out by other programs who happily cooperated with each other during their own games and racked up huge score totals. That's the kind of thing I envision here, where you can't simply expect to win by narrowly edging out other programs in a zero-sum fashion. Absolute score totals are most important. As for Kerim's $19 to $1 example, I'm not sure what you're getting at. Yes, $1 is better than nothing, and so a rational decision maker takes the dollar if that's all that's at stake. This occurs, for example, when this is definitely the last interaction between two agents. Which is why I proposed, as Kerim did, that it should be difficult to tell when the round is set to end, exactly. But I don't think Kerim's point about the "larger societal game" applies in this type of tournament, because the only rationale behind not accepting a $1 offer is to force your opponent/partner to offer you more the next time e is the proposer (it being equally true that for the proposer, $15 is better than $0). Unless we start allowing for reputation effects and inspection of results of past games by programs (which I think would add a little too much complexity at least for an initial round), the "larger societal game" aspect doesn't come into it, since how my program interacts with Kerim's program won't have any impact on whether or not Kerim's program chooses to cooperate with root's, e.g. Then again, it could be interesting eventually to set winning conditions such that both absolute and relative scores, i.e. cooperative and cutthroat styles of play, are rewarded.... THAT would make for quite the interesting mix. BP On Wed, Nov 26, 2008 at 12:48 PM, Kerim Aydin <[EMAIL PROTECTED]>wrote: > > While we're debating executables for this, I thought I'd raise another > issue: scoring. > > One of the features of "cooperation" experiments is that, rationally, > how well your opponent does shouldn't affect you. For example, if your > opponent offers you $1 and keeps $19, the point of the game is that > rationally you should be happy because $1 is better than none, and > the $19 doesn't matter because in game terms, the total # of dollars > in "the whole game" (real life) is such that your opponent's total > only very, very distantly hurts the value of yours. > > The interesting part of the psychology comes in because people are > willing punish the greedy $19-receivers at a cost to themselves, > showing that they are "evolved" to play the larger societal game of > punishing unfairness before they maximize their dollar. > > For our purposes, that means there's the danger that "traditional > scoring" that would turn this experiment into a different kind > of game, more cutthroat and zero-sum, especially if each round is > scored based on differences. Example, take outcomes for three > players, Greedy, Friendly, and Dupe: > > Results: > Greedy vs. Dupe : 11 (Greedy), 1 (Dupe) Diff: +10 Greedy > Friendly vs. Dupe : 100 (Friendly), 98 (Dupe) Diff: +2 Friendly > Greedy vs. Friendly : 50 (Greedy), 50 (Friendly) Diff: 0 > > Ranked by per-game win average (suggested in contest proto I think): > Greedy 5 > Friendly 1 > Dupe -4 > > Ranked by total: > Friendly 150 > Dupe 99 > Greedy 61 > > So the first method awards cutthroat play rather than cooperation (keep > totals down as long as per-game difference is high) while second awards > "cooperation", where Dupe, who didn't win any game directly, does > better than Greedy. Of course since the game domain ultimately is small, > even the cooperative players have to assume some level of zero-sum-ness: > in the second method, the best play is probably "cooperate until the > 'last minute' then do a quick betrayal for the game-winning point". > (This latter strategy can be defused somewhat by making the # of rounds > in one match random within a range so that there's no certain last round). > > [Side note: we actually experimented in this in a contest I ran a few > years ago for players directly: a common pool resource game where you > tried to harvest fish---maximize your own catch against others while > leaving enough to grow into the next round. Quickly learned that > uncertainty about when the "last round" was is v. important. > Incidentally, at the time I was wondering if people would form private > contracts to protect the resource: they didn't in part because contract > law was much less developed, maybe a partner of AAA should extend into > fishing?] > > Just something to think about as it's very relevant to think about > ahead of time, as it affects the types of strategies that end up being > the best. Thoughts? > > -Goethe > > > >
