Hallo all, I would like some insight on this one:
There are two players A and B each having a countable set of naturals lets say Sa and Sb. Initially Sa has cardinality n and Sb has cardinality 0 (empty set) and player B does not know the elements on Sa.
The goal is for player B to "take" all the elements in Sa (or at least as much as he can) by repeatedly "asking" player A if he has an element and place them in Sb. Player A responds if the element asked is “near” an element on his set. Therefore player A has a rule like “if the distance of input with one or more of my elements is less than x then give it”. Player A always follows this rule.
Player B may have some knowledge on the elements of Sa (like the max or min number in the set) therefore he could make “smart” questions or may have no knowledge therefore he asks randomly. If player B does not find much elements after a number of questions, he loses. If player A responds with “I have no more elements” then player B wins.
I would like to discuss if Game Theory is appropriate for approaching this problem. Thanks in advance