I did not downvote (you were at -3 and -2 when I wrote this), but I think the there are many possible reasons to downvote you depending on the voter's implicit or explicit theory of voting.
This might be seen as a pure "puzzle" post, and you aren't offering a puzzle solution that takes the question at face value. Your program doesn't do anything quine-like (like put its own source code into a input variable), nor does it have any logic engine (even by implication).
This is the kind of solution evolution might work out in very certain specific environments where it happened to "just work", but if you put this code into a place where it actually had to "work for a living" by analyzing other programs using roughly the same routines it uses to analyze itself and it gained or lost by modulation of its behavior with them (and some programs were suckers, some were cheaters, and some could be implicitly bargained with, so there were real opportunities to gain or lose) this code would not give you "optimal play ignoring computation costs" (it is either a sucker or a cheater, depending on what "1" means and in some contexts either of these strategies will lose).
Maybe another way of putting the criticism is that your "clever trick" is in noticing that the problem can sort of be solved in practice by collapsing down to have no extra levels of self awareness. But for theoretical robustness in other circumstances it would be preferable to have a system that scales to infinity, so that agents capable of modeling other agent's models of their own attempts to model other agents can still be "trusted by bad modelers". (Remember that part of the unspoken motivation here is to build skills towards building a verifiably friendly AGI.)
Also, the people here are all super smart, so telling them "just be dumber and people will trust you" isn't an answer they want to hear, and saying this (even indirectly) could maybe be seen as an attempt to troll, or to drag people into a topic area that is too difficult to discus, given LW's current sanity waterline (which is the only reason I personally vote things below zero).
Another possibility is that people don't see the reversed Tortoise and Achilles joke and just think (1) you said something dumb and (2) they should "punish dumbness" in order to maintain LW's purity (IE the signal to noise ratio).
The more reasons to downvote you expose, the more chance you have to accumulate a really low score, and that comment exposed several.
Thanks for the analysis. I'll try to clarify those points, then.
Of course, I'm not suggesting my answer as a solution to the prisoner's dilemma. I actually don't think this kind of mathematical analysis is even relevant to the prisoner's dilemma in practice -- I think the latter is best dealt with by pre-commitments, reputation tracking etc. to change the payoff matrix and in particular change the assumption that the interaction is one-off -- which it typically isn't anyway. (Note that in cases involving actual criminals, we need witness protection program...
You know that automated proof verifiers exist, right? And also that programs can know their own source code? Well, here's a puzzle for you:
Consider a program A that knows its own source code. The algorithm of A is as follows: generate and check all possible proofs up to some huge size (3^^^^3). If A finds a proof that A returns 1, it returns 1. If the search runs to the end and fails, it returns 0. What will this program actually return?
Wait, that was the easy version. Here's a harder puzzle:
Consider programs A and B that both know their own, and each other's, source code. The algorithm of A is as follows: generate and check all proofs up to size 3^^^^3. If A finds a proof that A returns the same value as B, it returns 1. If the search fails, it returns 0. The algorithm of B is similar, but possibly with a different proof system and different length limit. What will A and B return?
This second puzzle is a formalization of a Prisoner's Dilemma strategy proposed by Eliezer: "I cooperate if and only I expect you to cooperate if and only if I cooperate". So far we only knew how to make this strategy work by "reasoning from symmetry", also known as quining. But programs A and B can be very different - a human-created AI versus an extraterrestrial crystalloid AI. Will they cooperate?
I may have a tentative proof that the answer to the first problem is 1, and that in the second problem they will cooperate. But: a) it requires you to understand some logic (the diagonal lemma and Löb's Theorem), b) I'm not sure it's correct because I've only studied the subject for the last four days, c) this margin is too small to contain it. So I put it up here. I submit this post with the hope that, even though the proof is probably wrong or incomplete, the ideas may still be useful to the community, and someone else will discover the correct answers.
Edit: by request from Vladimir Nesov, I reposted the proofs to our wiki under my user page. Many thanks to all those who took the time to parse and check them.