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ReevesAnd comments on Open Thread, Apr. 27 - May 3, 2015 - Less Wrong Discussion

3 Post author: Gondolinian 27 April 2015 12:18AM

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Comment author: DataPacRat 27 April 2015 01:18:34AM 14 points [-]

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.)

Comment author: ReevesAnd 29 April 2015 07:19:16PM 2 points [-]

[Tit for Tat is] 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.

I am not clear on how this is the case. It seems to me that the appropriate strategy when faced with any Memory-0 strategy is to go All-D, since your defections would optimize your own score while having no influence on the future behavior of your opponent. Tit for Tat does not default to All-D unless the opponent is All-D.

Comment author: DataPacRat 30 April 2015 08:11:36PM 0 points [-]

All-D is the /optimal/ strategy for Memory-0 - but if your goal for Memory-0 interactions is merely to avoid getting the Sucker's payoff, and /also/ to be able to deal with Memory-1 strategies, then defaulting to All-C versus All-C isn't that bad a compromise.