Because most games are made of other games, they typically have multiple goals running at the same time. One of the most effective ways to keep players engaged is to introduce verbs and goals that are in conflict or competition with each other. Even if one goal might be of a higher priority than the others, this tension forces players to make decisions from moment to moment.
Assigning different verbs and goals to individual players is an absolutely critical part of multiplayer design, and is the essence of the Roles (Design Pattern)
Practical Creativity by Raph Koster, GDC 2014 Game Design Patterns