Verbal communication is a game, in the game theoretic sense. In a game with your enemy, like zero-sum heads-up poker, you’re trying minimize how much value you communicate with your words, in the sense that you when you say “call”, you want your opponent to be indifferent between their replies (so they have no best option to choose from, no economic profit available). You want to “maximize the entropy” of their subjective state after you communicate, or minimize the the information[1] communicated.
Now what if the the other player has a compute advantage? If you’re playing a game with the devil, or an exploitative chess engine, they’re going to try to hack you. Your best strategy isn’t necessarily ignoring them, but it’s a little tricker. It’s something like...instead of using your raw value function to chose your actions, come up with an ensemble of value functions you think are plausible for an entity with greater compute, figure out your best action in each of those guess-of-greater-compute-value-functions, and then marginalize out the guess-of-greater-compute-value-functions and choose the best action that way?[2] Which may also be how you “maximize” the value a friend with more compute can help you?
This is related to why you can bluff in chess. You make a “scary” looking move that’s actually bad, but the other player may still have to play like you see something they don’t.
I think you like riffing, so I’ll riff.
Verbal communication is a game, in the game theoretic sense. In a game with your enemy, like zero-sum heads-up poker, you’re trying minimize how much value you communicate with your words, in the sense that you when you say “call”, you want your opponent to be indifferent between their replies (so they have no best option to choose from, no economic profit available). You want to “maximize the entropy” of their subjective state after you communicate, or minimize the the information[1] communicated.
Now what if the the other player has a compute advantage? If you’re playing a game with the devil, or an exploitative chess engine, they’re going to try to hack you. Your best strategy isn’t necessarily ignoring them, but it’s a little tricker. It’s something like...instead of using your raw value function to chose your actions, come up with an ensemble of value functions you think are plausible for an entity with greater compute, figure out your best action in each of those guess-of-greater-compute-value-functions, and then marginalize out the guess-of-greater-compute-value-functions and choose the best action that way?[2] Which may also be how you “maximize” the value a friend with more compute can help you?
I think the type of the thing you’re minimizing is more like “value of information” in utils rather than raw quantity of information in bits?
This is related to why you can bluff in chess. You make a “scary” looking move that’s actually bad, but the other player may still have to play like you see something they don’t.