The Method of Sealed Bids
Lecture 13
Section 3.4
Robb T. Koether
Hampden-Sydney College
Mon, Feb 16, 2015
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
1 / 31
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
2 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
3 / 31
The Method of Sealed Bids
The method of sealed bids is used to divide assets that cannot be
subdivided.
For example, if there are 2 assets to be divided 3 ways, then either
Two players get the two assets and the third player is compensated
in cash, or
One player gets both assets and the other two players are
compensated in cash.
The first step is for each player to submit a sealed bid for each
asset.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
4 / 31
The Method of Sealed Bids
The five steps (to be explained) are
The bidding
The allocation of assets
The first settlement
Dividing the surplus
The final settlement
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
5 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
6 / 31
The Method of Sealed Bids
Example (3 Players, 2 Assets)
Three children, John, Joe, and Jim, are dividing two assets of their
parents’ estate.
The assets are
The house
The yacht.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
7 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
8 / 31
The Method of Sealed Bids
The Bidding
Each player submits a bid on each asset.
No player knows any other player’s bids.
The bids determine each player’s fair share.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
9 / 31
The Method of Sealed Bids
Example (3 Players, 2 Assets)
John
Joe
Jim
House
100
180
150
Yacht
200
150
90
Total
Value
300
330
240
Fair
Share
100
110
80
Each player bids on each asset.
The table shows their bids (in $1000s) and their fair shares.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
10 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
11 / 31
The Method of Sealed Bids
Allocation of Assets
Each asset goes to the highest bidder for that asset.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
12 / 31
The Method of Sealed Bids
Example (3 Players, 2 Assets)
Joe gets the house, worth $180 (to him).
John gets the yacht, worth $200 (to him).
Jim gets nothing, yet.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
13 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
14 / 31
The Method of Sealed Bids
The First Settlement
If the assets won by a player exceed his fair share, then he pays
the difference in cash to “the kitty.”
If the assets won (if any) by a player fall short of his fair share,
then he receives the difference in cash from the kitty.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
15 / 31
The Method of Sealed Bids
Example (3 Players, 2 Assets)
We use cash to even things up.
Joe’s fair share is $110 and he got the house (worth $180), so he
pays $70.
John’s fair share is $100 and he got the yacht (worth $200), so he
pays $100.
Jim’s fair share is $80 and he got nothing, so he receives 80.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
16 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
17 / 31
The Method of Sealed Bids
Dividing the Surplus
Whatever is left in the kitty is the surplus.
The surplus is divided equally among all the players.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (3 Players, 2 Assets)
If Joe paid $70 and John paid $100, for a total of $170.
Then Jim received $80, leaving $90.
So the surplus is $90.
We will divide it equally among the players, with each receiving
$30.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
19 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
20 / 31
The Method of Sealed Bids
The Final Settlement
The final settlement is a summary that describes for each player
Which assets he won (if any).
The net amount of cash that he paid or received.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (3 Players, 2 Assets)
The final settlement is as follows:
John receives the yacht (worth $200) and pays $70 in cash, for a
net value of 130.
Joe receives the house (worth $180) and pays $40 in cash, for a
net value of 140.
Jim receives $110 in cash.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
22 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
23 / 31
The Method of Sealed Bids
Example (3 Players, 2 Assets)
Five children, John, Joe, Jim, Jack, and Jeff are dividing three
assets of their parents’ estate.
The assets are
The house
The summer home
The Lamborghini
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
24 / 31
The Method of Sealed Bids
Example (The Bidding)
John
Joe
Jim
Jack
Jeff
House
200
250
300
200
250
Summer
Home
300
250
200
175
350
Lamborghini
150
200
150
250
150
Total
Value
650
700
650
625
750
Fair
Share
130
140
130
125
150
The Bids
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (The Allocation of Assets)
Jim gets the house, worth $300.
Jeff gets the summer home, worth $350.
Jack gets the Lamborghini, worth $250.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (The First Settlement)
Jim pays $170 in cash.
Jeff pays $200 in cash.
Jack pays $125 in cash.
John receives $130 in cash.
Joe receives $140 in cash.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (Dividing the Surplus)
The surplus is $225, to be divided 5 ways.
So, each player gets $45.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
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The Method of Sealed Bids
Example (The Final Settlement)
The final settlement is
John receives $175 in cash.
Joe receives $185 in cash.
Jim wins the house and pays $125.
Jack wins the Lamborghini and pays $80.
Jeff wins the summer home and pays $155.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
29 / 31
Outline
1
The Method of Sealed Bids
2
An Example – 3 Players, 2 Assets
The Bidding
The Allocation
The First Settlement
The Division of the Surplus
The Final Settlement
3
Another Example – 5 Players, 3 Assets
4
Assignment
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
30 / 31
Assignment
Assignment
Chapter 3: Exercises 43, 44, 46, 47, 48.
Robb T. Koether (Hampden-Sydney College)
The Method of Sealed Bids
Mon, Feb 16, 2015
31 / 31