Gamification is quite different from Game theory. Game theory is about strategic decision making especially in the context of choices available to the competitors. Prisoner's dilemma is a classic game theory situation.
Gamification is a completely different concept and it's about providing rich and engaging experience to customers/stakeholders. Gamification can be applied in many context in life. For example talk to a kid and ask what they like more: Games or Studies. Invariably the answer is games. Why? That's what gamification tries to answer and that's what it tries to do. The concept tries to provide notions which can be implemented to provide a game like experience.
The concept of gamification is applied by building the notion of user engagement and rewards. This is how many of the sites keep the user engaged by building a reward system. For example based on the number of answers a user has given in a question answer site, the user might be awarded different levels of batch.