Asymmetric method of sealed bids . Suppose that an estate consisting of M indivisible items is to be divided among N heirs ( P 1 , P 2 , ... , P N ) using the method of sealed bids. Suppose that Grandma’s will stipulates that P 1 is entitled to x 1 % of the estate, P 2 is entitled to x 2 % of the estate,…, P N is entitled to x N % of the estate. The percentages add up to 100%, but they are not all equal (Grandma loved some grandchildren more than others). Describe a variation of the method of sealed bids that ensures that each player receives a “fair share” (i.e., P 1 receives a share that she considers to be worth at least x 1 % of the estate, P 2 receives a share that he considers to be worth at least x 2 % of the estate, etc.).
Asymmetric method of sealed bids . Suppose that an estate consisting of M indivisible items is to be divided among N heirs ( P 1 , P 2 , ... , P N ) using the method of sealed bids. Suppose that Grandma’s will stipulates that P 1 is entitled to x 1 % of the estate, P 2 is entitled to x 2 % of the estate,…, P N is entitled to x N % of the estate. The percentages add up to 100%, but they are not all equal (Grandma loved some grandchildren more than others). Describe a variation of the method of sealed bids that ensures that each player receives a “fair share” (i.e., P 1 receives a share that she considers to be worth at least x 1 % of the estate, P 2 receives a share that he considers to be worth at least x 2 % of the estate, etc.).
Solution Summary: The author explains the method of sealed bids, which ensures that each player receives a fair share of the estate.
Asymmetric method of sealed bids. Suppose that an estate consisting of M indivisible items is to be divided among N heirs
(
P
1
,
P
2
,
...
,
P
N
)
using the method of sealed bids. Suppose that Grandma’s will stipulates that
P
1
is entitled to
x
1
%
of the estate,
P
2
is entitled to
x
2
%
of the estate,…,
P
N
is entitled to
x
N
%
of the estate. The percentages add up to 100%, but they are not all equal (Grandma loved some grandchildren more than others). Describe a variation of the method of sealed bids that ensures that each player receives a “fair share” (i.e.,
P
1
receives a share that she considers to be worth at least
x
1
%
of the estate,
P
2
receives a share that he considers to be worth at least
x
2
%
of the estate, etc.).
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