Ah, yeah, you’re right. The separating hyperplane theorem only gives us ≤, and I was assuming <.
I think “admissible if and only if non-dogmatic” may still hold as I stated it, because I don’t see how to set up an example like the one you give when A is finite. I’m editing the post anyway, since (1) I don’t know how to how that at the moment, and (2) the if and only if falls apart for infinite action sets as in your example anyway, which makes it kind of feel “wrong in spirit”.
Ah, yeah, you’re right. The separating hyperplane theorem only gives us ≤, and I was assuming <.
I think “admissible if and only if non-dogmatic” may still hold as I stated it, because I don’t see how to set up an example like the one you give when A is finite. I’m editing the post anyway, since (1) I don’t know how to how that at the moment, and (2) the if and only if falls apart for infinite action sets as in your example anyway, which makes it kind of feel “wrong in spirit”.