rivalry

As a noun rivalry

is the relationship between two or more rivals who regularly compete with each other the term usually applies to two rivals.

As an adjective emulatory is

pertaining to emulation or rivalry.

As nouns the difference between rivalry and outshow

is that rivalry is the relationship between two or more rivals who regularly compete with each other the term usually applies to two rivals while outshow is that which is shown openly, evinced, or revealed.

As a verb outshow is

(archaic) to show or present publicly; exhibit openly.

As a noun rivalry

is the relationship between two or more rivals who regularly compete with each other the term usually applies to two rivals.

As an adjective rivalrous is

having a relationship of rivalry.