I think you should either have the entire thing, or none of it (maybe just the conclusion). If I can’t understand what’s going on from your overview, I don’t see the point of it being there.
In particular, I was wondering if I could make this kind of “sacrifice yourself for yourself” situation happen without involving a predictor guessing your choice before you made it. Turns out you can.
In this example, it happens because the predictor guesses your strategy. It might not actually be before you choose the strategy, but since they can’t exactly take advantage of you choosing first and look at it, it’s functionally the same as them guessing your strategy.
What’s the point of the −11 for asking fate? You can’t choose not to. Having eleven fewer util no matter what doesn’t change anything.
Alright, I removed the game tree from the summary.
The −11 was chosen to give a small, but not empty, area of positive-returns in the strategy space. You’re right that it doesn’t affect which strategies are optimal, but in my mind it affects whether finding an optimal strategy is fun/satisfying.
I don’t understand what you’re saying here.
It might help if you gave the utility for the defender, so we can see what’s a good strategy for them.
You followed the link? The game tree image is a decent reference, but a bad introduction.
The answer to your question is that it’s a zero sum game. The defender wants to minimize the score. The attacker wants to maximize it.
I hadn’t followed it.
I think you should either have the entire thing, or none of it (maybe just the conclusion). If I can’t understand what’s going on from your overview, I don’t see the point of it being there.
In this example, it happens because the predictor guesses your strategy. It might not actually be before you choose the strategy, but since they can’t exactly take advantage of you choosing first and look at it, it’s functionally the same as them guessing your strategy.
What’s the point of the −11 for asking fate? You can’t choose not to. Having eleven fewer util no matter what doesn’t change anything.
Alright, I removed the game tree from the summary.
The −11 was chosen to give a small, but not empty, area of positive-returns in the strategy space. You’re right that it doesn’t affect which strategies are optimal, but in my mind it affects whether finding an optimal strategy is fun/satisfying.