The payment processing market is a bit more complicated:
When you make a transaction:
1) Your bank charges Visa/Mastercard an interchange fee (this is the bit capped at 0.2%/0.3%)
2) Visa/Mastercard charge a payments acquirer a processing fee
3) The payments acquirer charges the merchant a fee - this final fee is likely to be a blend of percentage and fixed fee per transaction. There's no cap imposed here.
EU-domestic debit cards 0.31% (max 0.75€), EU-domestic consumer credit cards 0.90%, EU-domestic company credit cards 1.10%, foreign consumer debit cards 1.25%, foreign company credit cards 1.45%, foreign credit cards 1.65%.
No per-transaction fees, but card readers have a monthly fee (39-53 EUR/mo).
Finnish source: https://www.yrittajat.fi/uutiset/572780-maksupaatteet-hintav...
So let's say that you swipe your card at a retailer, perhaps an IKEA.
IKEA has a card payments processor (ie: the vendor that the little terminal you sign on / stick the card into is from). This processor deals with a network (usually Visa or MasterCard, although there are smaller vendors such as Amex, Discover, etc) who ultimately connects the payment processors to the banks.
Now, for each transaction, your bank charges a fee to the network (the interchange fee, limited in the EU to like 0.3% I think) as a percentage of the total transaction. The network then charges some fees to the payment processor, which includes the fee that the bank charged. Finally the payment processor adds in their own fees and charges some unified fee schedule to the merchant (in our case, IKEA).
The payment processor doesn’t belong to any of the credit card companies if they are tied to any institution they will be part of the acquiring bank but these days most of them aren’t, all they do is facilitate the transaction and there could be more than one in the chain.
The issuing bank as in the institution that issued the card charges a fee, as well as the acquiring bank the bank that actually receives the payment also charges a fee.
There are fees that are levied on multiple parties across the chain by multiple parties however at the end these tend to be mostly be then baked into the fees that are levied on the merchant.
Each of them charges a fee, and can be charged a fee. A credit card transaction is a multiparty transaction with a lot of small fees.
The payments acquirer will then send on some of this fee from the merchant to Visa or Mastercard (again the exact rate depends on the transaction type). Visa or Mastercard will then send on an interchange fee to the bank that issued the card the customer paid with - this is the bit capped at 0.2% for consumer debit cards and 0.3% for consumer credit cards.
So essentially, card payments is a 3 sided market. The merchant chooses which payments acquirer they want to use. The issuing banks choose which card company they want to use. Customers choose which banks they want to bank with.
The interesting thing is that the EU has capped the banks' interchange fee, but not capped the fees elsewhere. When the interchange fee was reduced, this was passed on as a cost saving to the payments acquirer. This saving might have been passed onto the merchant (especially if the merchant is big and sophisticated enough to shop around), but it was equally possible that the payments acquirer could just enjoy the higher profit margin, or that Visa and Mastercard could raise their processing fee.
It goes unnoticed to the consumer because it didn't go unnoticed to the lawmakers. The EU caped the fees those companies can charge to merchants to 0.3% for credit card and 0.2% for debit card back in 2015 [1]. In the US it's less ignored because those fees to merchants are on average 10x bigger! (2% on average [2])
[1] http://europa.eu/rapid/press-release_IP-15-4585_en.htm
[2] https://www.hostmerchantservices.com/current-us-interchange-...