Which behavior does head-butting in bighorn sheep illustrate?

Head-butting in bighorn sheep illustrates intrasexual selection.

Intrasexual selection is a type of intraspecific competition between members of the same species and same sex (commonly males) contending enormously for potential mates of the opposite sex. During the mating season, the bighorn rams can be seen butting heads and wondering through the bands of females in order to determine dominance and to compete for access to potential mates.