When two individuals, groups or entities are pitted against each other with the intention of outdoing the other, it can be said that they are competing. Some other synonyms for "in rivalry" include "vying", "competing", "contending", "fighting", "arguing", "warring" and "racing". These verbs connote a healthy, forceful and aggressive desire to accomplish a goal that may or may not be mutually exclusive. At times, some synonyms for "in rivalry" like "competing" or "vying" might simply mean trying to be better than one's personal best. For others, "racing" might imply that the stakes are high, with a winner and a loser that everyone is eagerly waiting for.