Fair Division: Method of Sealed Bids

The method of sealed bids applies in the situation when a number of distinct items is to be shared by a comparable number of players. The method will only work provided participants are able and willing to trade the goods for cash.

Each player assigns a (subjective) value to each of the items at hand and submits the bids in a sealed envelope. (The average of the bids by a single player provides that player's estimate for the fair share of the goods.) Players are not aware about each other's estimates. Envelopes are open simultaneously, and items are assigned to the highest bidder. The goods received by a player may exceed or not add up to that player's subjective value of the fair share. Depending on the circumstances the player than agrees to pay the excess over or receive a cash payment to make up to the fair share.

The total of the payments and the receipts is never negative. If it's positive, it may be evenly divided between the participants.

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