The critical thing to note in this problem is that our threshold depends only on the cost of search

Since the chances of the next offer being a good one—and the cost of
finding out—never change, our stopping price has no
reason to ever get lower as the search goes on, regardless
of our luck. We set it once, before we even begin, and then
we quite simply hold fast.
The University of Wisconsin—Madison’s Laura Albert
McLay, an optimization expert, recalls turning to her
knowledge of optimal stopping problems when it came
time to sell her own house. “The first offer we got was
great,” she explains, “but it had this huge cost because they
wanted us to move out a month before we were ready.
There was another competitive offer  [but] we just kind
of held out until we got the right one.” For many sellers,
turning down a good offer or two can be a nerve-racking
proposition, especially if the ones that immediately follow
are no better. But McLay held her ground and stayed cool.
“That would have been really, really hard,” she admits, “if I
didn’t know the math was on my side.”
This principle applies to any situation where you get a
series of offers and pay a cost to seek or wait for the next.
As a consequence, it’s relevant to cases that go far beyonc
selling a house. For example, economists have used this
algorithm to model how people look for jobs, where ii
handily explains the otherwise seemingly paradoxical faci
of unemployed workers and unfilled vacancies existing at
the same time.
In fact, these variations on the optimal stopping
problem have another, even more surprising property. As
we saw, the ability to “recall” a past opportunity was vita
in Kepler’s quest for love. But in house selling and jol
hunting, even if it’s possible to reconsider an earlier offer
and even if that offer is guaranteed to still be on the table
you should nonetheless never do so. If it wasn’t above youi
threshold then, it won’t be above your threshold now
what you’ve paid to keep searching is a sunk cost. Don’t
compromise, don’t second-guess. And don’t look back.
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ZAKARIA AL BAZZAR, 19 yo, university student. love everything about new tech, and I'm sharing it with you :)
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