Exploration vs exploitation tradeoff to find a price that maximizes revenue
Without making any underlying assumptions you will not get anywhere. That said, there are multi-arm bandit strategies that try to optimize the rewards, there is a ton of research on this field. It comes down to sampling from a distribution of your options (in your case two) and adapting this distribution based on the rewards.

https://en.wikipedia.org/wiki/Multi-armed_bandit

Once you know that the reward distribution from each bandit comes from a specific distribution, you can deduce optimal sampling strategies. Once you have at least some prior information you can do fairly well although not always optimal. Regardless, most strategies will do better than normal A/B testing if the strategy is not super greedy.