Settling costs when three roommates divide shared household goods

[hkBattousai]

I'm a collage student, I rented an apartment flat with my 2 friends. We bought all house things by each of us paying 1/3 of their price.

An now we are to break apart, I decided to make a drawing (like lottery) to decide who take which house hold.

Assume that,
A, B, C: Names of three people
T: Total cost of all household goods
N: Total number of all all household goods
a_i: Cost of element of set of the household goods that A takes as a result of the drawing
b_i: Cost of element of set of the household goods that B takes as a result of the drawing
c_i: Cost of element of set of the household goods that C takes as a result of the drawing
m: Number of household goods that A takes as a result of the drawing
n: Number of household goods that B takes as a result of the drawing
k: Number of household goods that C takes as a result of the drawing

Can you give me the function f defined as,
f(person₁, person₂): Amount of money that person₁ pays to person₂
in terms of the parameters listed above.

 

[CompuChip]

It only depends on what each person ends up taking, since everyone has already paid 1/3, doesn't it?

So suppose A takes 1/2 of all the goods, B takes 3/8 and C takes 1/8.
Then A will have to deposit (1/2 - 1/3)T in the common bank account and B should pay (3/8 - 1/3)T, while C gets to withdraw (1/3 - 1/8)T.

If you want, you can skip the bank account and settle it directly by making A pay (1/2-1/3)T to C directly, and let B pay (3/8-1/3)T to C.