MA 111 Agenda Monday 12 5 2011 Notes from Elizabeth Weaver 12 5 1 The Method of Sealed Bids The method of sealed bids can be used in fair division problems with any number of players where the set S is discrete The Method of Sealed Bids 1 Bidding Each player makes a bid in dollars for each of the items in the set S and places it in a sealed envelope to maintain the privacy condition 2 Allocation Each item will go to the highest bidder for that item Ties can be broken with a coin flip 3 First Settlement First calculate each player s fair share of the estate If the items a player received in step 2 total more than his fair share he must pay the difference in cash If the items a player received in step 2 total less than his fair share he receives the difference in cash 4 Division of the Surplus Calculate the difference between the amount the players paid and the amount the players received in step 3 This amount is the surplus and it is to be divided among all of the players equally 5 Final Settlement This is obtained by adding each player s share of the surplus money to the first settlement obtained in step 3 Example In her last will and testament Granny leaves her estate to Jed Elly May Jethro and Mr Drysdale with the stipulation that it must be divided equally and remain with them not be sold to outsiders Below is a listing of each player s bids on the items Jed Elly May Jethro Mr Drysdale Cabin 220 000 250 000 211 000 198 000 Rolls Royce 40 000 30 000 47 000 52 000 Picasso 280 000 240 000 234 000 190 000 Total Fair Share a Who won which items b How much should each person receive from or pay to the estate c How much surplus is there How much does each person receive of the surplus d Describe which players get what items and how much money they pay or receive in the final settlement What are the disadvantages of the method of sealed bids Example Chuck and Sarah are getting a divorce The only joint property of value they own is their house They decide to use the method of sealed bids Chuck bids 140 000 on the house Sarah bids 164 000 Sarah bid higher and therefore wins the house She pays her fair share into the estate while Chuck receives his in cash a How much is each person s fair share b How much is the surplus c Describe the final settlement Example Elmo Grover and Bert are dividing four pieces of furniture using the method of sealed bids Their bids on each of the items are given in the following table Dresser Desk Vanity Table Elmo 150 180 170 400 Grover 300 150 200 250 Bert 275 165 260 500 a What is the value of each person s fair share b How much should each person receive from or pay to the estate c How much surplus is there How much does each person receive of the surplus d Describe which players get what items and how much money they pay or receive in the final settlement Example Jack Janet and Chrissy jointly own a house They no longer want to be roommates and decide to use the method of sealed bids with the understanding that one of them will get the house and the other two will get cash Jack bids 180 000 Janet bids 120 000 and Chrissy bids 150 000 After the final settlement how much money do Janet and Chrissy get from Jack for their one third share of the house 12 5 2 After this lecture you should be able to carry out the method of sealed bids
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