h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

You should have some tit-for-tat (and variants) strategies in there I think. Also, try making the payoff in the co-operation game (c,c) and see what happens when you vary c - in particular it would be interesting to know if there is a phase transition as c passes through 5.

Regarding Tit for tat, it would be an idea to do the same as with the Bayesian strategies - one optimistic variant that always cooperates on the first move, and a pessimistic one that always defects on the first move. I'd like to back the strategy I outlined in the FFFF forum the other day, which attempts to maximise, not its own individual rewards, but the overall rewards for both players - ie, their aggregate result when added together. To safeguard against naivety it includes a three move memory to keep check on the other player and make sure that they're not habitually defecting; but, as long as they're not, it cooperates. It goes as follows... ... always cooperate for the first three moves, to give mutual cooperation a good chance to get established; then, after that, if the other player defected more than once in the opening three moves start to play 'Tit for tat', and continue with that unless or until the other player goes for three consecutive moves without defecting; if they do, then simply keep running through the original 'cooperate for three moves' strategy unless the other player starts habitually defecting again. GTB kindly worked out the lookup tables for that strategy. They're on that FFFF thread if you need them, here :- http://www.bbc.co.uk/dna/h2g2/classic/F80629?thread=155651&post=3407231#p3407046 I'd like to call it 'Everyone a winner?' with a question mark, because I'm not so sure it'll work out that way in a blind mixed game. Lear

I've actually analysed directly what happens when the co-operation payoff is 5 or lower; the mixed game actually behaves the same as the prisoners' dilemma. The payoff needs to be higher than 5 for the co-operation game to be analytically different to the prisoners' dilemma. 8 is just a handy value. We can't really draw quantitative conclusions from this, but we can draw qualitative conclusions. 8 gives us a nice threshold for qualitative behaviour.

I'll add the Tit-for-tat strategies.

Actually, I can't really have a co-op first move for a Bayesian strategy without violating what the Bayesian strategy is supposed to do. The optimistic and pessimistic Bayesian strategies are actually much the same concept rendered into Bayesian language.

I'll also add the '3 co-op' strategy. Actually, we may have a whole family here; with the tolerance before the state change to Tit-fir-tat. The one we have already has tolerance 1, we can also make strategies for tolerance 0 or tolerance 2.

How about an 'unforgiving' strategy that co-operates until the first defection then defects forever?

Also, should r be known to the stategies? My gut feeling is no, but then that widens the scope of possible strategies too large for confort. I think we can probably let the strategies know what r is wlog.

I've come up with a couple of other strategies...

>"I'll also add the '3 co-op' strategy. Actually, we may have a whole family here; with the tolerance before the state change to Tit-for-tat. The one we have already has tolerance 1, we can also make strategies for tolerance 0 or tolerance 2."


That sounds like an interesting idea, for the purpose of comparison. I assume you mean a small family of related strategies, like '2 co-op' and '4 co-op'. And then again maybe also one that only needs the other player to cooperate twice consecutively before it moves back out of Tit for tat mode, and then another one for four... etc...

I imagine that '2 co-op' would be likely to fare better in the Prisoner's Dilemma rounds and '4 co-op' in the Co-operation Game.

What about throwing in a RANDOM strategy as well, for the hell of it?


Lear

I think we need to restrict the number of n co-op strategies in the mix to avoid flooding the system with similar types; perhaps if we have:

'3 co-op tolerance 1'
'2 co-op tolerance 0'
'4 co-op tolerance 2'

Where the co-op number is the sample for the decision to move over to tit-for-tat or back again and the tolerance is the number of defections the system will allow without going tit-for-tat.

How about the tit for tat variant by which it performs the opposite after a consective run of 10. Also it remembers if it was the one that started the defection if so it allows one free hit.
This means if it is stuck in 10 defects it will go for it. Equally 10 trusting results then defects.