The use of a "rival" in literature is a common theme. A lot of the time, a strong rival inspires the protagonist to become better, and does so for the rival as well. They both feed off of being competitive with one another. Thus, a good rivalry is good for the rivals (more on that, and when it is bad, below).
Defining the Troll: Emotional Schadenfreude and Personal Responsibility
A troll is someone that gains value from the act of causing others to lose value.
Okay, that was a bit dry sounding. How is this: a troll is someone that takes pride and joy at causing misery, anger, and distress in others; a troll derives pleasure by actively creating displeasure in others. However, a troll isn’t just schadenfreude; a troll gains value by being the direct cause of that schadenfreude. Thus, a troll is comprised of two major parts: emotional schadenfreude and personal responsibility.