Consider a bimatrix game \((A,B)\). This game is a competition game if the best reply structures of \((A,B)\) and \((-B, -A)\) are such that the Nash equilibria of the two coincide. For competition games, the set of Nash equilibria is convex, and all Nash equilibria pay the same, thus generalizing properties of zero-sum games. Rivalry games are a subset of competition games, which are included in almost strictly competitive games. Finally, protective strategy profiles of competition games correspond exactly to proper equilibria.