Etymology
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reciprocity (n.)

"state or condition of free interchange, mutual responsiveness," 1766, from French réciprocité (18c.), from reciproque, from Latin reciprocus, past participle of reciprocare "rise and fall, move back and forth; reverse the motion of" (see reciprocal). Specifically as "equality of commercial privileges between the subjects of different governments" is by 1782. Related: Reciprocality (1650s).

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Definitions of reciprocity

reciprocity (n.)
a relation of mutual dependence or action or influence;
Synonyms: reciprocality
reciprocity (n.)
mutual exchange of commercial or other privileges;
From wordnet.princeton.edu