This isn't really a paradox - it's simply a statement that people can miscalculate. I bet if I bought it for $3.00 I could unload it on someone for $2.99, and so on... it might begin getting difficult around $0.05, just because it becomes harder for someone to miscalculate when the negative consequence is a lot closer.
So, if you're in a society of people who all think ahead all the way, no one will buy the bottle. Since most people in any other society aren't going to think ahead all the way, there is some point at which the consequence can be pushed far enough back that someone will think that someone else will buy it for less than they did. This person could very well be wrong, but if you manage to sell it to them, whatever price you picked was the right one.
Lastly, it is misleading to even think that there is anything to do with money really in this problem. Ariels msged me mentioning a "Fair Price". The problem might as well be phrased as "You can only give this bottle to someone who has climbed fewer mountains than you had when you got the bottle."... and the problem comes out the same (though a lot more tiring).
While I'm at it, there are a couple of silly ways around this (easily avoided by clarifications of the rule):
- Inflation One dollar keeps on dropping in value, so you could argue that selling it for the same numeric price will actually be a decrease in value. Note that if you hold onto it for a fairly extended period of time, this is a quite marked effect.
- Here, take this! Sell it to someone without explaining the disadvantages.
- Oooh, shiny! Sell it to someone who does not understand the consequences.
- Yeah, Right Sell it to someone who could understand the consequences but doesn't believe you. If necessary, give it to them.
- Abuse of wishes "I wish I paid $50.00 for this bottle" no one is ever REALLY screwed - they just need to sacrifice some amount of money and screw around with the timeline. Okay, this could cause problems.
- Let's get organized here As an extrapolation on the first idea, you could arrange to be inventing smaller and smaller units of currency to handle the accounting of the sale. Of course, then the IRS will come in, claim the bottle was sold for less than it was worth, which constitutes sales tax evasion, and impound the bottle. The last holder has bad things happen for eternity.
A creative person can continue at this for some time longer, I'm sure.