The Method of Sealed Bids - Hampden-Sydney Collegepeople.hsc.edu/faculty-staff/robbk/Math111/Lectures/Spring 2015/Lecture 13 - The Method...Outline 1 The Method of Sealed Bids 2 An

The Method of Sealed BidsLecture 13Section 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 AssetsThe BiddingThe AllocationThe First SettlementThe Division of the SurplusThe Final Settlement

3 Another Example – 5 Players, 3 Assets

4 Assignment


Outline




4 Assignment


The Method of Sealed Bids

The method of sealed bids is used to divide assets that cannot besubdivided.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 compensatedin cash, orOne player gets both assets and the other two players arecompensated in cash.

The first step is for each player to submit a sealed bid for eachasset.



The five steps (to be explained) areThe biddingThe allocation of assetsThe first settlementDividing the surplusThe final settlement


Outline




4 Assignment



Example (3 Players, 2 Assets)Three children, John, Joe, and Jim, are dividing two assets of theirparents’ estate.The assets are

The houseThe yacht.


Outline




4 Assignment



The BiddingEach player submits a bid on each asset.No player knows any other player’s bids.The bids determine each player’s fair share.



Example (3 Players, 2 Assets)

Total FairHouse Yacht Value Share

John 100 200 300 100Joe 180 150 330 110Jim 150 90 240 80

Each player bids on each asset.The table shows their bids (in $1000s) and their fair shares.


Outline




4 Assignment



Allocation of AssetsEach asset goes to the highest bidder for that asset.



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.


Outline




4 Assignment



The First SettlementIf the assets won by a player exceed his fair share, then he paysthe 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.



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 hepays $70.John’s fair share is $100 and he got the yacht (worth $200), so hepays $100.Jim’s fair share is $80 and he got nothing, so he receives 80.


Outline




4 Assignment



Dividing the SurplusWhatever is left in the kitty is the surplus.The surplus is divided equally among all the players.



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.


Outline




4 Assignment



The Final SettlementThe 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.



Example (3 Players, 2 Assets)The final settlement is as follows:

John receives the yacht (worth $200) and pays $70 in cash, for anet value of 130.Joe receives the house (worth $180) and pays $40 in cash, for anet value of 140.Jim receives $110 in cash.


Outline




4 Assignment



Example (3 Players, 2 Assets)Five children, John, Joe, Jim, Jack, and Jeff are dividing threeassets of their parents’ estate.The assets are

The houseThe summer homeThe Lamborghini



Example (The Bidding)

Summer Total FairHouse Home Lamborghini Value Share

John 200 300 150 650 130Joe 250 250 200 700 140Jim 300 200 150 650 130Jack 200 175 250 625 125Jeff 250 350 150 750 150

The 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.



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.



Example (Dividing the Surplus)The surplus is $225, to be divided 5 ways.So, each player gets $45.



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.


Outline




4 Assignment


Assignment

AssignmentChapter 3: Exercises 43, 44, 46, 47, 48.


Documents

The Method of Sealed Bids - Hampden-Sydney Collegepeople.hsc.edu/faculty-staff/robbk/Math111/Lectures/Spring 2015/Lecture 13 - The Method...Outline 1 The Method of Sealed Bids 2 An