Siblings may engage in them

• They may be between schools
• Conference teams often have them
• What schools in the same district have, often

Wiktionary Word definitions in Wiktionary
n. (plural of rivalry English)

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
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. Syn: Emulation; competition. See Emulation .