Knaster inheritance procedure

Knaster inheritance procedure

The Knaster inheritance procedure allows for more than two parties (heirs) and for assets which cannot be divided. The procedure is quite simple (let n be the number of bidders): each heir bids on each item in the estate, for each item the high bidder pays the price of that item into a pool, and each bidder (including the high bidder) then receives (1/n) of their bid from the pool. The money in the pool at the end is then divided equally among all the heirs. Thus each heir receives their perceived fare share of each item, and a cash bonus at the end. This may require the heirs to have more cash at their disposal than they can easily raise. The procedure is best illustrated by an example.

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?

If you know your opponents' pricings

Frank ended up with no assets, but $73,812.50 in cash. Could he have gotten more if he had known his siblings' bids before he entered his? For each item that he did not get, he received he got 1/4 of his bid, hence if bid more he would have received more (the money was reduced by another factor of 1/4 when it came to him from the pool). But if he had bid more than the top bid he would have received the item and had to pay for it. Hence he should have bid $.01 below the top bid for each item. For convenience I will assume he matched the winning bid, but did not get the item. Then he would have received $62,500 + $3750 + $6250 = $72,500 before the money from the pool. The money in the pool would have been reduced by $9250 to $33,000, so his total cash would be $72,500 + $33,000/4 = $80,750, almost a 10% increase.

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?


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

May 2003

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