ri·val·ry 
/ˈraɪvəlri/ noun
plural ri·val·ries /ˈraɪvəlri/ noun : a state or situation in which people or groups are competing with each other [count] ▪ There is a bitter/friendly rivalry between the two groups. [noncount] ▪ a strong sense of rivalry ▪ In our family there was plenty of sibling rivalry. [=competition or jealousy between sisters and brothers]
