[madrox]

I was surprised that there was no mention of the secretary problem [1]. Optimal stopping has a whole host of problems and means of evaluating them [2]. I'm curious how this solution compares to just using the 1/e rule.

Generally, the 1/e rule in this situation implies you should evaluate prices until Wednesday afternoon for the max sell price up to that point, and then sell the next time you see a price higher than that max (or Saturday afternoon whichever comes first). You won't always get the best price this way, but you'll perform better than any other know strategy. This strategy works with friends, too, as you can account for their prices in this strategy.

The only reason this may not be the best strategy here is that there are ways of having some information about future prices.

[1] https://en.wikipedia.org/wiki/Secretary_problem [2] https://en.wikipedia.org/wiki/Optimal_stopping

[underanalyzer]

Afaik the 1/e solution is only optimal when you don't know anything about the distribution being draw from (but also why it's amazing). Since the author knows the probability distribution the prices are being draw from you can do much better with a little dynamic programming.

[dmurray]

It's also solving a different problem: it maximises the when probability that you get the absolute best match, rather than maximising the expected value of your choice.

[ISL]

Furthermore, I suspect it requires that each measurement is independent and identically-distributed.

If your measurements are correlated (as prices generally are -- if they were lower than average yesterday, they are more likely to be lower than average today), the secretary-problem approach will not work.

[scast]

Yes, exactly. I was looking to solve the second problem, not the former. Following the secretary rule is good strategy for a lot of things, but I think we actually have more information here.

[scast]

Hey there, author here.

I am not super well versed on the secretary problem but I think some people have already looked into it for AC [1].

In general, what I was looking was to associate a risk profile to a series of decisions of either HOLD or SELL(amount) given the current probability distribution.

[1]: https://www.reddit.com/r/GAMETHEORY/comments/fn2grx/optimizi...

[palmerlao]

I think something like backward induction could be used here to find a lower-regret but probably more complicated strategy: https://en.wikipedia.org/wiki/Backward_induction