From: Ray Tayek <rtayek@ca.rr.com> Subject: [math-fun] ON "ITERATED PRISONER?S DILEMMA CONTAINS STRATEGIES THAT DOMINATE ANY EVOLUTIONARY OPPONENT" The highly technical paper, <http://www.pnas.org/content/early/2012/05/16/1206569109.abstract>" Prisoner?s Dilemma contains strategies that dominate any evolutionary opponent" by William H. Press and Freeman J. Dyson has now been published in PNAS (May 22, 2012), which was followed by a PNAS Commentary by Alexander Stewart and Joshua Plotkin of the Department of Biology, University of Pennsylvania

--based on trying to figure out what they are doing without actually reading it, it seems they are arguing that if the opponent in IPD generates his moves via a Markov chain... which presumably is necessarily true for any real opponent given the laws of physics since that opponent is bounded, i.e. has a finite bounded number of states, and has access to a source of randomness, and hence must be a Markov chain on those states... then you, where by "you" I mean a Turing machine, can outplay him asymptotically by learning his markov model and then predicting his play. This is probably completely irrelevant to real life because the "number of states" of a human being containing 10^27 atoms is going to be around 2^(10^27) if each atom could store 1 bit, so the time it takes to learn your opponent's Markov chain in real life is going to far exceed the lifetime of that human, or for that matter of the universe. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)