Price discrimination is common in big box retail (location based) and the ideal pricing structure is perfect pricing where a product is sold at the maximum price each customer is willing to spend for the offer. So geographic location is used by the big box and the IP address that is incoming does show where the person is coming from to a degree.
Also many retailers online, use profiles to work toward perfect pricing where they profile of someone with heuristics to identify that this shopper will do x amount of product/price research and is estimated to be x elastic based on the profile of this shopper compared to others with similar characteristics.
So I'd really suggest that the black and white A/B test should be challenged because it depends on the characteristics of what it is being offered and the diversity of the site’s consumer.
Consider the characteristics of what is being offered. So if the offering requires a customer relationship of one time then this may be a much simpler price test that you could do. You could use Google ad words to land people on different prices with the same ad copy reaching different price points for different key words. Also testing could be done with Facebook advertisement, which is not search driven, but demographic driven and provide different price points to get an indication of demographic price elasticity. The whole consistency of price only matters if the customer behavior is to go back and forth to the website. If the customer normally buys or abandons on the first landing then putting in a cookie or profile method is unnecessary and a simple A/B is all that is needed. If the customer does research before pulling the trigger, which search engines have made to be easy, then having a cookie for price behaviors is needed. If the site is a diverse complex offer (Amazon like) where greater profiling and price determination could be done then the situation is far more than just a simple A/B test to maximize profits but customer profile testing to determine like customers and what is their price elasticity for different offerings.