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July 19th, 2011, 11:53 PM   #1
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Can this problem be approached with Game Theory?

Hallo all, I don't know if this is the right place to post but 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 (or at least as much as he can) the elements in Sa by repeatedly "asking" player A if he has an element. 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.

Perhaps the problem above is not clearly stated but that’s the best I could do. I would like to discuss if Game Theory is appropriate for approaching this problem. Thanks in advance
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July 20th, 2011, 06:11 AM   #2
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Re: Can this problem be approached with Game Theory?

I don't see it as game theory, but it's certainly math regardless.

The strategy will depend heavily on what knowledge B has about Sa and what the metric and distance is.
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