Well it depends on a ton of different data and things. In short:
1. If a competitor comes into the same sector as you it could effect the CPA you are having, but not necessarily always. There are tons of factors with what they are selling, their targeting and all. Just because someone is in the same niche doesnt mean they are selling or targeting the same thing.
2. Depending on your budget you might not see a drastic change. Obviously you cant see who they are targeting so this is a straight shot in the dark–but if you have say a budget of $200 a day and they are also spending a budget of $200 a day. You are competing for CPM and budget strategy but with $200 a day say you both only can reach 4,000 a day but the target audience is 30 Million. You wont being competing for the same target customer. Eventually you might run into that but only if you have a large budget and they are targeting the exact same audience with the same or more budget. But there is no way to see this.
3. Next there are TONS of things to look at which would be way to long to go into like bid strategy and others. If you are targeting the exact same but with different TOF strategies with different budget targeting and optimization, you might never run into your competitor if they are only bidding $.30 for LPV and you are targeting $.50 for Clicks. Just depends on what you set up.
Having said that, which is very generalized, yes you could potentially see a slight increase in CPA depending on HOW NICHE you are. Someone selling sunglasses vs you selling cat shoes that are made of bamboo, yes you will see an increase depending on product and how narrow you are.
Once you get to LLA and leveraging past customer data it wont matter. When you get to scaling and using your audience data, its specifically targeted to customer behavior and no matter what he is selling or targeting, your ads will show to the best possible people and it wont matter if they are showing as well to the same audience or not because that audience is being selected by FB and Google.
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Hope that helps, sorry if its surface level ?