פיקוס (![[info]](http://p-stat.livejournal.com/img/userinfo.gif){kind=small} shayel) wrote,@ 2007-02-06 13:37:00 |
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The Sugar-Daddy Problem
I had the following discussion with a colleague:
Me: …you start with a big fortune, and it turns into a small fortune by itself.Which made me think of the issue in game theoretic terms, as follows:
Him: This is usually accomplished by getting married, you know.
Me: For you it does. When I'll get married, I hope the other party will be the sugar daddy.
A young spender with a negligible amount of money, yet a steady spending rate of S1 in the first year of his marriage and Sn = γsSn-1 (γs>1) for each year thereafter, weds a rich sugar daddy, his money he plans on spending.
Assume the sugar daddy has an initial capital of M, doesn't work, and earns a constant yearly interest of γm>1 on his money. As they got married in a hurry (before the Governator annuls the marriage), they made no prenup agreement, and thus, upon divorce, the spender will receive exactly half of the sugar daddy's money. However, he will receive no further interest on her part of the money, as the banker is a good friend of his former husband. The sugar daddy will keep getting the interest, of course.
Each of them wants to have as much money as possible, either by keeping it in the bank or by spending it.
Assume they live a finite number of years, is there an equilibrium at a year t>0 when they should divorce? What if they are able to live forever?
