The Method of Sealed Bids

Transcription

1 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, / 31

2 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, / 31

3 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, / 31

4 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, / 31

5 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, / 31

6 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, / 31

7 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, / 31

8 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, / 31

9 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, / 31

10 Example (3 Players, 2 Assets) Total Fair House Yacht Value Share John Joe Jim 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, / 31

11 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, / 31

12 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, / 31

13 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, / 31

14 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, / 31

15 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, / 31

16 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, / 31

17 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, / 31

18 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, / 31

19 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, / 31

20 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, / 31

21 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, / 31

22 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, / 31

23 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, / 31

24 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, / 31

25 Example (The Bidding) Summer Total Fair House Home Lamborghini Value Share John Joe Jim Jack Jeff The Bids Robb T. Koether (Hampden-Sydney College) The Method of Sealed Bids Mon, Feb 16, / 31

26 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, / 31

27 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, / 31

28 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, / 31

29 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, / 31

30 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, / 31

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, / 31