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Question

There are n children in a party. The organizer brought k gifts, with k > n. Each gift is different and each kids has a potentially different ranking over the different gifts. (a) The organizer decides to put the kids in a line and ask each kid sequentially to pick her most preferred gift. Is the allocation efficient? (b) Some parents complained that this mechanism was unfair, since the last kid in the queue was unhappy with his gift. Instead, they decided to make a lottery and give kids gifts at random. Is this fair? is it efficient? (c) Since every kid was crying after getting a gift they disliked, the organizer decided to allow kids to exchange their assigned gifts. Is the final allocation efficient? Is it fair?

          There are n children in a party. The organizer brought k gifts, with k > n. Each gift is different and each kids has a potentially different ranking over the different gifts.
(a) The organizer decides to put the kids in a line and ask each kid sequentially to pick her most preferred gift. Is the allocation efficient?
(b) Some parents complained that this mechanism was unfair, since the last kid in the queue was unhappy with his gift. Instead, they decided to make a lottery and give kids gifts at random. Is this fair? is it efficient?
(c) Since every kid was crying after getting a gift they disliked, the organizer decided to allow kids to exchange their assigned gifts. Is the final allocation efficient? Is it fair?

There are n children in a party. The organizer brought k gifts, with k > n. Each gift is different and each kids has a potentially different ranking over the different gifts.
(a) The organizer decides to put the kids in a line and ask each kid sequentially to pick her most preferred gift. Is the allocation efficient?
(b) Some parents complained that this mechanism was unfair, since the last kid in the queue was unhappy with his gift. Instead, they decided to make a lottery and give kids gifts at random. Is this fair? is it efficient?
(c) Since every kid was crying after getting a gift they disliked, the organizer decided to allow kids to exchange their assigned gifts. Is the final allocation efficient? Is it fair?

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