The Collaborative International Dictionary of English v.0.48:

Rivalry \Ri"val*ry\, n.; pl. Rivalries.
   The act of rivaling, or the state of being a rival; a
   competition. "Keen contention and eager rivalries."
   --Jeffrey.
   [1913 Webster]

   Syn: Emulation; competition. See Emulation.
        [1913 Webster]