[Advice] Looking for tips on pricing.

Background: So we manufacture sports equipment for an animal-oriented sport, mostly common in the USA. We have over 15 years of experience in the industry and make excellent quality product. Some of the top-selling “brands” in this sport currently do or used to at some point outsource their manufaturing from us. Recently we decided to expand our business and sell directly to the customer via Amazon since wholesale margins are extremely low and company orders aren’t reliable enough. We have around 30 ASINs currently listed. We have priced our products competitively to market price. We aren’t looking to massively undersell and ruin the market since that would be unfair to the companies we currently manufacture for. We are looking to slowly and steadily build our brand and expand our customer base. Over the past month we have sold maybe 15 units, but still are a couple of hundred bucks out of pocket for advertising.

Issue: On Amazon, in this industry, one brand currently dominates all Amazon sales and has been doing so for a while. They have probably over 200 ASINs with a couple thousand clicks on each product and about 800 +- 200 units of each product being sold monthly. The problem we are facing is that for example they have a product listed at 35.99. We list it for 32.99. Next day, we see that their product is on a discount from an increased list price of 42 dollars, currently for 29.99. Are these prices adjusted automatically via some feature on Amazon? Is someone manually monitoring sales and adjusting pricing according to competitor products? Any insight on this and in general for a new brand would be appreciated.