Consider the case of four heirs Ethel, Frank, Gertrude, and Howard who have equal claim to an estate consisting of a house, a car, and a boat. Their bids for the items are in the following table:

heir | house bid | car bid | boat bid |

Ethel | $180,000 | $12,000 | $25,000 |

Frank | $225,000 | $8,000 | $20,000 |

Gertrude | $250,000 | $10,000 | $24,000 |

Howard | $200,000 | $15,000 | $22,000 |

Gertrude pays $250,000 for the house, of which $180,000/4 = $45,000 is given to Ethel, $225,000/4 = $56,250 is given to Frank, $250,000/4 = $62,500 is returned to her, and $200,000/4 = $50,000 is given to Howard; that leaves $250,000 - ($45,000 + $56,250 + $62,500 + $50,000) = $36,250 in the pool. Similarly, Howard pays $15,000 for the car, of which $3000 is paid to Ethel, $2000 is paid to Frank, $2500 is paid to Gertrude, and $3750 is returned to Howard; and $3750 is added to the pool. Ethel pays $25,000 for the boat, of which she gets $6250 back, $5000 is paid to Frank, $6000 is paid to Gertrude, and $5500 is paid to Howard; leaving $2250 to be added to the pool. The pool contains $36,250 + $3750 + $2250 = $42,250; that is divided by four so that each receives $10,562.50. The $10,562.50 is a bonus above what each perceives as his share of the estate. The net result is that Ethel receives the boat and an additional $39,812.5 in cash; Frank gets $73,812.50; Gertrude gets the house, but pays $168437.50; and Howard gets the car and $54,812.50 in cash.

Exercise: What would be the effect on this procedure if each heir had to allocate a total of
$100 to the various assets?

What would be the effect of dividing all the funds equally, instead of according to the amount
bid?

Similarly, Gertrude could have reduced her outlay if she had only bid $225,000.01 for the house. She would have paid $25,000 less, but received $25,000/4 less back from the pool, so her net saving would have been $18,750. Of course, she could have gotten more money back if she had raised her bids on the items she did not receive.

Of course not everyone can win by knowing everyone else's bids. The advantages described are when three bids have been submitted, and the fourth person has access to them before he submits his bid. Bidding and modifying bids with total information is a different problem.

**Competencies:** If Archibald, Barthowlemew, Cassandra, and Daphne value the teapot,
umbrella, and Victrola in an estate as as A:5,7,10; B:6,4,12; C:5,8,11; and D:7,7,7
respectively, what is the result of the Knaster inheritance procedure?

What would the result be if Daphne knew the other bids before she entered hers, and modified her
bid to her best advantage?

**Reflection:**

**Challenge:** What would the result of the procedure be if everyone knew everyone else's
bids, and could keep modifying their bids?

May 2003