"I can predict that if (the other agent predicts) I choose strategy X, then the other agent will implement strategy Y, and my expected payoff is Z"

...are we allowed to use self-reference?

"I just flipped a fair coin. I decided, before I flipped the coin, that if it came up heads, I would ask you for $1000. And if it came up tails, I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads. The coin came up heads - can I have $1000?"

X = "if the other agent is trustworthy (implicitly: I can trust that the other agent analyzed past-me sufficiently to know that I always use strategy X) then I agree to the bet.

Z = whatever the expected payoff of the bet was before the flip.

In effect, I only agree to a counterfactual bet if :

I know that you are aware that I've pre-committed to taking bets with those who are aware that I've pre-committed to taking bets with those who are aware I've pre-committed to taking bets with those who are aware ...