As far as I understand it a contract is made when there is an offer and an acceptance of that offer. If you are Ebay/Amazon I don't think that you can show one price and then just happen to change it as the user accepts it. The price charged should be the one offered. If the product page shows a price and user puts it in their basket and orders in within a reasonable time (5-10 minutes) the offered price should be honoured even if the price changed in the 5-10 minutes and all customers going to the product page at that point see the new price.
Note: This is not the behaviour I expect to see of share trading platforms but it is the way consumer goods sales should behave.
With the advent of electronic price labeling in retail stores we will soon live in a world where the price can change after you've picked up an item of the shelf and before you check out at the front of the store.
I don't think that this would be legal in the UK unless on upwards changes the labels changed a reasonable[0] time before the prices. Unfair Commercial Practices Directive and probably some other laws would probably cover it.
[0] A small shop could probably do it much quicker than a large supermarket which might have to allow for people being in there for an hour.
Note: This is not the behaviour I expect to see of share trading platforms but it is the way consumer goods sales should behave.