Payment platforms are a classic multi-sided market. Visa and Mastercard are the two dominant payment platforms outside of cash. American Express is in third place in payment card market share.
Most dominant platforms in multi-sided markets either subsidize one side of the market or make it essentially free for that side of the market. You can get a huge selection of Visa and Mastercards for no annual fee. Unlike, Visa and Mastercard, American Express has taken a strategy of splitting their monetization between both merchants and consumers, and many of their cards carry an annual fee. In exchange for that, they tend to offer more attractive benefits and perks which attract a higher end customer, often business people.
For merchants, a consumer that uses an American Express card costs more since American Express takes a bigger commission on the transaction. The tradeoff that makes it worthwhile, from the merchants perspective, is the hope of bringing in that attractive high end customer.
This model breaks down in low-end Chinese restaurants, though. A rich and/or business person won't spend substantially more on Chinese food than any other customer of the restaurant since there's a limit to how much you can eat, and a cheap Chinese restaurant can fill you up for very little money. Most cheap Chinese restaurants don't even have any single high end dish or alcoholic drink that they can use for price discrimination to siphon off extra profit from that high end customer.
So many low-end Chinese restaurants don't accept American Express. Some don't even accept credit cards at all.
I thought of this yesterday because for the first time in a long time, I had to do a walk of shame to the ATM to pull out cash to pay for a meal. When I go running, I usually throw my Mastercard in my running shorts so I can grab groceries on the way back. Since my refrigerator is broken right now, I'm also eating out for every meal. I forgot to grab my Mastercard out of my running shorts yesterday after my morning run, and after dinner at a low-end Asian restaurant my American Express was summarily waved off. I had no Mastercard and not enough cash.
I had to endure the stink-eye from the restaurant manager as I sheepishly left an Amex and driver's license as collateral and schlepped a few blocks to the nearest ATM. I would have offered to wash dishes, but given what I suspect was the meager hourly wage of a dishwasher at that restaurant it might have cost me a few hours of my life.