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From: khorsell@ee.latrobe.edu.au (Kym Horsell)
Subject: Re: Prisoner's Dilemma
Sender: news@lugb.latrobe.edu.au (News System)
Message-ID: <3sqvn5$fj6@laplace.ee.latrobe.edu.au>
Date: Wed, 28 Jun 1995 07:17:57 GMT
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References: <3sdioh$5tf@mars.efn.org> <Ted.Belding-2406951449220001@pm056-27.dialip.mich.net> <Pine.ULT.3.91.950625021800.7629A-100000@rac8.wam.umd.edu> <1995Jun26.150050.30898@rs6000.cmp.ilstu.edu>
Organization: School of Electronic Engineering, La Trobe University
Xref: glinda.oz.cs.cmu.edu comp.ai.genetic:6229 comp.ai.alife:3715

In article <1995Jun26.150050.30898@rs6000.cmp.ilstu.edu>,
Tom Kunka <tskunka@rs6000.cmp.ilstu.edu> wrote:
>Keith Wiley (keithw@wam.umd.edu) wrote:
>: > Nope.  If you're playing a single round, the best strategy is "always
>: > defect".  
>
>: well obviously, tit-for-tat doesn't exactly dictate single round 
>: situations.  What most people don't realize however is that the number of 
>: rounds played must be unknown to all parties involved.  Otherwise the 
>: best strategy is still always defect, because every round is 
>: quintessentially the last round of the match.
>
>I was doing some work with the P.D. and a GA...All in the past :-(
>But anyway just for fun I put the GA to evolve against TFT and found that
>the GA would find a way to consistantly beat TFT.  

If you want to look at _exhaustive_ tests for small automata (up to
4 states at this stage) and some hopefully good simulations for
strategies played by FSA's up to 20 states, look at

	http://www.ee.latrobe.edu.au/~khorsell/ipd/ipd.html

For the 4-state case there are more than 1 million FSA's and around 60 
thousand canonical strategies (FSA's form equivalance classes). Playing off 
all-by-all and allowing for drawing a partner from a population where each 
strategy is represented with equal probability we find the strategy:

State     Output  Next-if-0  Next-if-1
  0:         1/      1           2
  1:         1/      1           1
  2:         1/      3           0
  3:         0/      1           2

does best on average with a payoff of 3.129211. Several others are
close. (In the above input/output of 0 == "co-operate" and 1 == "defect";
the Axelrod payoff values were used).

-- 
R. Kym Horsell
khorsell@EE.Latrobe.EDU.AU              kym@CS.Binghamton.EDU 
