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I've skimmed over the beginning of your paper, and I think there might be several problems with it.

  1. I don't see where it is explicitly stated, but I think information "seller's prediction is accurate with probability 0,75" is supposed to be common knowledge. Is it even possible for a non-trivial probabilistic prediction to be a common knowledge? Like, not as in some real-life situation, but as in this condition not being logical contradiction? I am not a specialist on this subject, but it looks like a logical contradiction. And you can prove absolutely anything if your premise contains contradiction.
  2. A minor nitpick compared to the previous one, but you don't specify what you mean by "prediction is accurate with probability 0.75". What kinds of mistakes does seller make? For example, if buyer is going to buy the , then with probability 0.75 the prediction will be "". What about the 0.25? Will it be 0.125 for "none" and 0.125 for ""? Will it be 0.25 for "none" and 0 for ""? (And does buyer knows about that? What about seller knowing about buyer knowing...)

    When you write "$1−P (money in Bi | buyer chooses Bi ) · $3 = $1 − 0.25 · $3 = $0.25.", you assume that P(money in Bi | buyer chooses Bi )=0.75. That is, if buyer chooses the first box, seller can't possibly think that buyer will choose none of the boxes. And the same for the case of buyer choosing the second box. You can easily fix it by writing "$1−P (money in Bi | buyer chooses Bi ) · $3 >= $1 − 0.25 · $3 = $0.25" instead. It is possible that you make some other implicit assumptions about mistakes that seller can make, so you might want to check it.