The advice you will find is that price parity builds trust and channel conflict destroys it. That is true and it is not an answer, because it skips the arithmetic that makes the question hard.
Here is the arithmetic. On your own site you keep the price minus payment fees and whatever the traffic cost you. On a marketplace you keep the price minus commission, which on most platforms lands somewhere between the middle teens and a quarter of the order value, and that commission comes out of the same number on the same label. So identical prices do not mean identical outcomes. They mean the marketplace order is materially less profitable, every time, by design.
Most brands respond by doing nothing, and absorb it. That is a defensible choice if the marketplace is bringing you customers you could not otherwise reach, which for a lot of categories it genuinely is. What is not defensible is absorbing it without ever having worked out how much you are absorbing.
The second thing people miss is that you often cannot price up freely even if you want to. Amazon dropped its explicit price parity clause and replaced it with a fair pricing policy that still lets it act against sellers whose prices look wrong next to the rest of the market, and plenty of other platforms have terms in the same spirit. Read yours before you build a plan on top of it. A strategy that breaches a contract you signed is not a strategy.
So the workable position is usually this. Hold the headline price at parity, because the customer really does check and being caught out is worse than the margin. Then make your own site the better place to buy for reasons that are not the number on the label. Bundles that do not exist on the marketplace. A longer guarantee. Faster delivery. The colour they cannot get elsewhere. A returning-customer offer the marketplace never sees because it never gave you the customer.
That way the marketplace does the job it is good at, which is putting you in front of people who have never heard of you, and your own site does the job it is good at, which is keeping them.
Parity is not a price. It is a promise about the label, and everything that happens after the label is still yours to compete on.
If this is the exact wall you are staring at, tell me what you are seeing: mail@sandeepkv.com, or message me on LinkedIn.