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<strong>Method</strong> <strong>of</strong> <strong>Sealed</strong> <strong>Bids</strong>Unit 3 – Fair Division
NEWS FLASH! GRANDMA DIESAND LEAVES ESTATE TO 4GRANDCHILDREN!Alice, grandmother <strong>of</strong> four, died yesterday fromcomplications arising from a quiz on fair division.Alice, age 68, suffered a heart attack afterreceiving her quiz grade on fair division. To hergrandchildren's surprise, she left behind anestate worth a lot <strong>of</strong> Benjamins. The onlyproblem, she left behind a mountain cabin,Maserati car, and a Picasso painting to bedivided fairly among her four grandchildren. It isyour job as her grandchildren to grant Alice’sfinal wish; divide her estate evenly among thefour <strong>of</strong> you.
How can we divide the estate sincethe objects are discrete?I am now passing out an envelope to eachgroup.Inside each envelope are the bids that each<strong>of</strong> you made on the estate.Open your envelopes and place the bids onyour paper.
How can we divide the estate sincethe objects are discrete?Now that you have placed your bids on yourpaper. Assign the objects to the highestbidder.Raise your hand if youdid not win an object.
You must determine each person’s fairdollarshare.To do this: Add each person’s bids and thendivide by the total number <strong>of</strong> players.The fair-dollar share is the baseline for thesettlements.
Over or Under?Look at each player.If the total value <strong>of</strong> the items for a player is more thanhis/her fair-dollar share, then the player pays the estatethe difference.If the total value <strong>of</strong> items that the player receives is lessthan his/her fair-dollar share, then the player gets thedifference in cash.Find out how much money each player will owe or receiveand give or pay that much. This is your first settlement.
Surplus?Is there a surplus? Is there anymoney leftover after each playerhas received his/her fair share?If yes, then divide the surplus (extra money)by the number <strong>of</strong> players. Distribute thismoney to each player.
Final SettlementTo find the final settlement:Add the surplus money to the firstsettlement.
What did everyone get?One player gets the Picasso and owes theestate $124,000.00.Another player gets the cabin and pays theestate $99,000.00.Another player gets $144,000.00 in cash.The last player gets the Maserati plus$79,000.00.
For <strong>Sealed</strong> <strong>Bids</strong> to work…You must satisfy two conditions:1. _______________________________________________________________.2. _______________________________________________________________________________________________________
<strong>Method</strong> <strong>of</strong> <strong>Sealed</strong> <strong>Bids</strong>Step 1: (____________) Each player makes abid in dollars for each item in the estate. (<strong>Bids</strong>are done independently and are very secretive)Step 2: (____________) Each item goes to thehighest bidder. (If there is a tie, flip a coin)Step 3: (________________) Calculate the fairdollarshare. Determine how much money eachplayer owes or is owed.Step 4: (___________________) Divide thesurplus evenly among the players.Step 5: (__________________________) Addthe surplus money to the first settlement.
p. 114 (54, 55, 56)Homework
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