Fair, Equitable Compensation Arrangements

A's bid

3

B's bid

2.5

C's bid

1.5

winner:

A

B

C

winner's bid:

3 (A's bid)

mean bid:

7

3

fair arrangements:

1

2

≤c<

7

6

and

5

6

≤b≤2-c||c

7

6

and b

5

6

fair and envy-free arrangements:

5

6

≤c≤1 and bc

equitable arrangement:

c

9

14

and b

15

14

Suppose you and two siblings jointly inherit an object that cannot be physically divided. You must decide who will get to keep the object and how much that sibling will compensate the others. This Demonstration finds and graphs all possible fair, equitable, and envy-free compensation arrangements for such a situation.

A fair arrangement is one in which each sibling feels he or she is getting at least

1

3

of the value of the object.An equitable arrangement is one in which each sibling feels he or she is getting the same fraction of the value.An envy-free arrangement is one in which no sibling thinks some other sibling is getting more value than he or she is.

Start by specifying each sibling's bid (aka valuation/utility) for the jointly owned object. You then specify who is to get the object and see what, if any, are the possible fair, equitable, and envy-free arrangements.