Why not find something similar and price close to it with a small premium for features or a discount for the lack of a brand name?
Each customer experience is unique. Even though Starbucks was brewing coffee which was a relatively simple and arguably undifferentiated product in 1971, they could charge a different price. In 1971, this was because they could create a novel experience. Today Starbucks earns a premium for familiarity.
The uniqueness of customer experience and product justifies a price differential.
Even the most competitive environment like online retail justifies different prices for different retailers.
Pricing competitively is probably a good strategy in the absence of customer demand information such as when a store starts business.
Flying blind is comparable to ignoring customer data from actual purchases in the longer run.
Only an optimal pricing strategy can avoid the loss relative an informed pricing strategy.