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There are many more variants of the secretary problem that modify its other assumptions

perhaps bringing it more in line with the real-world challenges of finding love
(or a secretary]. But the lessons to be learned from optimal
stopping aren’t limited to dating or hiring. In fact, trying to
make the best choice when options only present
themselves one by one is also the basic structure of selling
a house, parking a car, and quitting when you’re ahead.
And they’re all, to some degree or other, solved problems.

If we alter two more aspects of the classical secretary
problem, we find ourselves catapulted from the realm of
dating to the realm of real estate. Earlier we talked about
the process of renting an apartment as an optimal
stopping problem, but owning a home has no shortage of
optimal stopping either.

Imagine selling a house, for instance. After consulting
with several real estate agents, you put your place on the
market; a new coat of paint, some landscaping, and then
it’s just a matter of waiting for the offers to come in. As
each offer arrives, you typically have to decide whether to
accept it or turn it down. But turning down an offer comes
at a cost—another week (or month) of mortgage payments
while you wait for the next offer, which isn’t guaranteed to
be any better.

Selling a house is similar to the full-information game.
We know the objective dollar value of the offers, telling us
not only which ones are better than which, but also by how
much. V\7hat’s more, we have information about the
broader state of the market, which enables us to at least
roughly predict the range of offers to expect. (This gives us
the same “percentile” information about each offer that we
had with the typing exam above.) The difference here,
however, is that our goal isn’t actually to secure the single
best offer—it’s to make the most money through the
process overall. Given that waiting has a cost measured in
dollars, a good offer today beats a slightly better one
several months from now.




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About Unknown

ZAKARIA AL BAZZAR, 19 yo, university student. love everything about new tech, and I'm sharing it with you :)
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