Third obvious possibility: B maximises u~Σpivi, subject to the constraints E(Σpivi|B) ≥ E(Σpivi|A) and E(u|B) ≥ E(u|A). where ~ is some simple combining operation like addition or multiplication, or “the product of A and B divided by the sum of A and B”.
I think these possibilities all share the problem that the constraint makes it essentially impossible to choose any action other than what A would have chosen. If A chose the action that maximized u, then B cannot choose any other action while satisfying the constraint E(u|B) ≥ E(u|A) unless there were multiple actions that had the exact same payoff (which seems unlikely if payoff values are distributed over the reals, rather than over a finite set). And the first possibility (to maximize u while respecting E(Σpivi|B) ≥ E(Σpivi|A) ) just results in choosing the exact same action as A would have chosen, even if there’s another action that has an identical E(u) AND higher E(Σpivi).
The fact that it’s the same phrasing used in the literature is really concerning, because it means the interpretation the literature gives is wrong: Many subjects may in fact be generating a mental model (based on deductive reasoning, no less!) which is entirely compatible with the problem-as-stated and yet which produces a different answer than the one the researchers expected.
One could certainly write ‘(Ace is present OR King is present) XOR (Queen is present OR Ace is present)’ which trivially reduces to ‘(King is present OR Queen is present) AND (Ace is not present)‘, but that gives the game away a bit—as perhaps it should! The fact that phrasing the knowledge formally rather than in ad-hoc English makes the correct answer so much more obvious is a strong indicator that this is a deficiency in the original researchers’ grasp of idiomatic English, not in their research subjects’ grasp of logic.
It’s difficult for me to look at the problem with fresh eyes, so I can’t be entirely certain whether the added ‘black box’ note helps. It doesn’t look helpful.
What would be really useful would be a physical situation in which the propositional-logic reading of the statements is the only correct interpretation. There is luckily a common silly-logic-puzzle trope which evokes this: