If the second person knew of the existence of the first, he could buy the glass of water and sell it to the first, pocketing any difference. Their perceived values should be similar.
No, the perceived value wouldn't be similar. If the first person is about to die of dehydration and only the water can save him, he very likely would be willing to pay more / sacrifice more to get the water. The second person will match the price only up to a point. If he had to cut his finger off to pay for the water, he wouldn't do it. But the first person might, to save his life. They value the water differently.
No, there should be an equilibrium market price in dollars thst they both pay if they are participants in a shared market. That doesn't mean the value to each is the same.
Of course, the fact that they have access to that shared market also changes the value to each of them from that in the original hypothetical.
I think we have a difference in vocabulary. I would say value and equilibrium market price refer to the same thing, but you are saying it is the particular use it has to the individual which is of course not quantifiable. Assuming the person who's had no water has access to a functioning market they will only pay market price. Arguing about them perceiving it to have a higher value seems like a pointless philosophical argument.
