Wikipedia:Reference desk/Archives/Mathematics/2014 October 16

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October 16

Algorithm

I am searching for an algorithm to break down the acquisition cost of a 100.000$ house to a number of people. The goal of the algorithm is to get people into it at the early stage. I want to convince other people to pay a part of the cost. So I thought of an incentive. The prize when a person joins should go down fast at the start for every addition person to speed up the seed phase in which I am willing to take a greater share. At the start there are mostly enthusiast who are willing to pay a higher price at the start to get the collection running.

When I am buying the house I would pay the total 100.000$.

I convince a person to pay for it together, I pay 2/3 (-> 66.666$) and the other person 1/3 (-> 33.333$). Perfect, my percentage dropped to 66% and the other person had the incentive to pay lesser than I and also lesser than the "normal distribution" (100.000$/2= 50.000$).

A next (third) person joins to lower the cost for us and the person should pay lower than the previous person (me and the second person with whom I shared cost initially).

Every addition person should lower the price for all the others already in and pay less than the previous ones.

The last step repeats until 40 people are in. Now enough people are in and the threshold is low enough to share the costs equally (-> Prize/People = 100.000/40 = 2.500) without the initially prohibitive high cost which were chilling finding other people than enthusiast.

Is there a name for that algorithm? 87.78.103.137 (talk) 21:59, 16 October 2014 (UTC)

Don't know a name, but if after the first person joins you reduce every additional payment to 93.6% of the previous one, you end up down around the $2500 you want:

$33,333.33 x 0.93639 = $2527.18

But to me it looks like the incentive is to wait, as the early birds risk more money and get no more benefit. Also, this sounds close to a pyramid scheme. Just what is the benefit to owning 1/40th of a house, anyway ? Will they be set up as time shares ?  :StuRat (talk) 14:25, 17 October 2014 (UTC)