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Jiro comments on Open Thread, Apr. 27 - May 3, 2015 - Less Wrong Discussion
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Still More to the Prisoner's Dilemma
After reading http://www.pnas.org/content/early/2012/05/16/1206569109.full.pdf+html , the detail that's caught my attention: "The player with the shortest memory sets the terms of the game." If a strategy remembers 0 turns, and simply Always Cooperates, or Always Defects, or randomly chooses between them, then no matter how clever its opponent might be, it can't do any better than by acting as if it were also a Memory-0 strategy. Tit-for-Tat is a Memory-1 strategy - and despite all the analysis that I've read on it before, I now see it from a new perspective, in that it's one of the few Memory-1 strategies that gracefully falls back to the appropriate Memory-0 strategy when faced with All-C or All-D... and any strategy which tries to implement a more complicated scheme based on longer strings is faced with the fact that Tit-for-Tat simply doesn't remember anything beyond a single turn.
I would like to see if this perspective can be extended to a Memory-2 strategy that falls gracefully back to appropriate Memory-1 strategies such as Tit-for-Tat when faced with Memory-1 strategies, and like Tit-for-Tat, to a suitable Memory-0 strategy when faced with Memory-0 ones.
Does anyone have a link to a suitable set of programs to run some experimental tourneys, and instructions on how to apply them? (If it matters, the OSes I have available are WinXP and Fedora 21.)
This is a neat question, but I think programs being successful is not really about gracefully going down a hierarchy. For example, Tit-for-Tat does not take the correct strategy against always-cooperate (If your opponent is always cooperating, you say thank you and always defect). Tit-for-Tat succeeds for much more ecological reasons. I'd say bigger-memory versions of Tit-for-Tat are going to be something like the class of "peaceful, non-exploitable" strategies. Such strategies are not going to be the first to defect, which means they actually don't get that much information about their opponent. I think the lesson of iterated prisoners dilemmas is that you don't need that information anyhow, as long as your strategy occupies a good ecological niche.