Maybe the previous weeks have an effect on the next, for example a low price point brings more new users that will bias the result of the next week and so forth

Maybe the previous weeks have an effect on the next, for example a low price point brings more new users that will bias the result of the next week and so forth. It's hard to make a controlled experiment... but at least it is possible to do multiple experiments over time shuffling the order in which the prices are tried.