3.6 The Method of Sealed Bids

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3.6 The Method of Sealed Bids
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 1 (Bidding). Each player (in this case
Martin, Bart, Millhouse and Ralph) makes a bid
for each item, giving his honest assessment of
the value of each.
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 1 (Bidding). Each player (in this case
Martin, Bart, Millhouse and Ralph) makes a bid
for each item, giving his honest assessment of
the value of each. The bids appear below
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 2 (Allocation). Each item goes to the
highest bidder for that item. In this case,
Radioactive Man 1 goes to Martin, Fallout Boy
Annual 3 goes to Ralph and Millhouse gets Itchy
Scratchy. Bart gets nothing.
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 3 (Payments). Depending on what item a
player gets in Step 2, he/she will owe money or
be owed money. First we must calculate each
players fair share (under his/her value system)

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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 3 (Payments). Contd Martin Under his
own value system Martins fair share is 31, but
he got a comic a comic worth 100. This means
Martin must pay (100 - 31) 69 into a
pot. Bart Since Bart gets none of the comics
he is instead awarded his fair share in cash - he
gets 31.25 Millhouse Millhouse gets a comic
worth 48, but his fair share is 30.75 - he must
pay (48 - 30.75) 17.25 Ralph Ralph gets a
comic he values at 56 and his fair share is 20.
He must pay (56 - 20) 36.
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 3 (Payments). Contd Now we need to
consider how much money is in the pot. 69 -
31.25 17.25 36 91
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Example Martin, Bart, Millhouse and Ralph
stumble upon a box containing three comics
Radioactive Man 1, Fallout Boy Annual 3 and
Itchy Scratchy Comics 5. The kids have
decided to split up the loot using the Method of
Sealed Bids.
Step 4 (Dividing the Surplus). The surplus money
is divided equally amongst all the
participants. In this case each kid gets91/4
22.75 as a bonus. The final results are as
followsMartin gets Radioactive Boy 1 and pays
(69 - 22.75) 46.25Bart receives 31.25 22.75
54.Millhouse gets Itchy Scratchy and (22.75
- 17.25) 5.50Ralph gets Fallout Boy and must
pay (36 - 22.75) 13.25
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Notes The Method of Sealed Bids

• Each player must have enough money to play the
  game.
• Each player must be willing to accept money in
  place of any item.

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Example (exercise 39, pg 124) Three Sisters
(Ana, Belle and Chloe) wish to use the method of
sealed bids to divide up 4 pieces of furniture
they shared as children. Their bids on each of
the items are given in the following table.
Describe the final outcome of this
fair-division game.