It doesn't guarantee a perfect allocation, but one that is compatible with everyone's preferences. A is willing to pay up to $750 for the nice room and up to $250 for the bad room. B is willing to pay up to $500 for either room. Any solution where A takes the expensive room for $500-$750 and B takes the cheap room for $250-$500 will leave both content with their choice. B could do better by being strategic and switching his preference to only taking the cheap room for no more than $300, however.
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It doesn't guarantee a perfect allocation, but one that is compatible with everyone's preferences. A is willing to pay up to $750 for the nice room and up to $250 for the bad room. B is willing to pay up to $500 for either room. Any solution where A takes the expensive room for $500-$750 and B takes the cheap room for $250-$500 will leave both content with their choice. B could do better by being strategic and switching his preference to only taking the cheap room for no more than $300, however.
Thanks, I think that's what I was misunderstanding.