I will answer your comment in two sections, because it's really two comments in one:
The metaphor didn't really have anything to offer, before the preceding paragraph made it clear that the strategy is first-order Markov (it did state very plainly that you only remember the last position).
I don't understand the consequence. It seems to me that you aren't forcing the opponent to commit to a first-order Markov strategy themselves, you just make it easier on them to do that, because they don't need any more moves in the past.
Of course, you're doing this to simplify your own life, and because (I guess) first-order strategies work just as well as higher-order ones. Their conclusion seems to verify this, because they state that you really don't need (since you can't do any better than first-order) higher-order strategies, since you can model the opponent effectively with just the last move (which is the exact model the opponent is using).
Taking more moves into account, you would either just be trying to predict randomness (since that's the whole difference, if the opponent only remembers one move), or you would be "decompressing" their strategy into thousands of moves (since you can express a thousand moves of tit-for-tat with just "my move is the opponent's last move").
Literally, knowing any states further than the last gives you exactly zero extra information. Thus, it's useless.
I think in the second half of what you said you began to understand what you started out saying that you "don't understand."
Think of "the consequence" here in a purely security-theory way. In some sense that's what we're doing, securing ourselves from exploitation.
Press and Dyson are expressing the radical idea that "if I protect myself from some stupid attackers, I protect myself from all smarter ones." How does this work? It works precisely because there is a threshold above which "smarter doesn't matter" -- a smarter attacker has the exact same payoffs as a stupid attacker playing a different strategy. In that sense there are no higher-order strategies for exploiting a sufficiently stupid strategy: sure you can program a smarter attack, but it cannot do better than a different, stupid attack.
So if I intentionally choose my strategy to be stupid and show that, for all of your stupid strategies, the expected payoff is the same -- then for all of your smart strategies, the expected payoff is also the same!
It's not quite "trying to predict randomness", it's "if I dumb myself down I can also assume, without loss of generality, that my adversaries are dumb."
I think we're saying the same thing, yeah. I was remarking that any clever strategy doesn't confer any advantage to the attacker because there is no advantage to confer. They have perfect knowledge of your strategy just by knowing one previous move, and perfect knowledge is the most you can get.
Unless I'm confused again, it seems to me that there's just no advantage to them remembering more moves, since they know everything you're going to do from that last one. It's not that your strategy being stupid actively forces them to be stupid, they're not losing anything by being cleverer, they just don't gain anything because they already have it all.
The metaphor didn't really have anything to offer, before the preceding paragraph made it clear that the strategy is first-order Markov (it did state very plainly that you only remember the last position).
I don't understand the consequence. It seems to me that you aren't forcing the opponent to commit to a first-order Markov strategy themselves, you just make it easier on them to do that, because they don't need any more moves in the past.
Of course, you're doing this to simplify your own life, and because (I guess) first-order strategies work just as well as higher-order ones. Their conclusion seems to verify this, because they state that you really don't need (since you can't do any better than first-order) higher-order strategies, since you can model the opponent effectively with just the last move (which is the exact model the opponent is using).
Taking more moves into account, you would either just be trying to predict randomness (since that's the whole difference, if the opponent only remembers one move), or you would be "decompressing" their strategy into thousands of moves (since you can express a thousand moves of tit-for-tat with just "my move is the opponent's last move").
Literally, knowing any states further than the last gives you exactly zero extra information. Thus, it's useless.