Not being a Tennis Fan, I might offer some side information as the term was used in Slot Racing. in a normal race, there were eight lanes or tracks- the Orange ( they were color coded) had the tactical advantage. to minimize this, the Round-Robin rules required racers change lanes after each qualifying heat- left to right, or something like that. It was time-consuming as one might guess. Anything involving a rotation of duty orders- or a similar practice where players exchange positions ( this is or was done in skeet shooting) might be given this name. Origins are obscure, but the Robin is a migratory bird!
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The modern use of the term dates from the 17th Century French ruban rond (round ribbon). This described the practice of signatories to petitions against authority (usually Government officials petitioning the Crown) appending their names on a document in a non-hierarchical circle or ribbon pattern (and so disguising the order in which they have signed) in order that none may be identified as a ring leader.
This practice was adopted by sailors petitioning officers in the Royal Navy (first recorded 1731).
The term round-robin is recorded in English much earlier, although not with the above meaning. It first appears in 1546 meaning someone who is round and called Robin, and appears later applied to a category of person with the precise meaning unknown: "These Wat Tylers and Round-Robins being driven or persuaded out of Whitehall abc" (1671).
It refers to a competition (or group or stage within a competition) where each team plays every other team