If you just look for the proofs of statements of the form
(action=A1 => U=U1) AND (action=A2 => U=U2) AND (U1>=U2)
where U1 and U2 are variables, and A1 and A2 are different constants (cooperate and defect in some order), up to some sufficient timeout (after which you act randomly), and perform A1 the moment you see the first one, you’ll play correctly against your near-copy (with different timeout or syntactic differences), and defecting and cooperating rocks.
Conjecture:
If you just look for the proofs of statements of the form
where U1 and U2 are variables, and A1 and A2 are different constants (cooperate and defect in some order), up to some sufficient timeout (after which you act randomly), and perform A1 the moment you see the first one, you’ll play correctly against your near-copy (with different timeout or syntactic differences), and defecting and cooperating rocks.
Maybe my math intuition is utterly failing me today, but I find this conjecture very hard to believe. Could you try proving it?