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Worldpay and Tsys are small fry, akin to Chase Paymentech or Elavon. First Data is the big monster in the room, with 70% of the market, and all the other processing networks I just mentioned and more make up the remainder.

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True, but the big guys like First Data are out of reach to the size of shops that generally use square. (They can use them, but the fees don't get appreciably more competitive until you clear a certain scale.) I'd say Tsys and Worldpay are appropriate alternatives if you're the size of business who's considering square.

Wiki lists First Data as 45% of the market, which comes directly from this 2014 article:

http://www.crainsnewyork.com/article/20141201/TECHNOLOGY/141...

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