In the Coke - Pepsi game commitment to a strategy is a way to deliberately elicit particular behaviors. The same idea can be used to model social structures. Consider interpersonal relations.
Sally has a significant other. His name is Ted. They have been dating for some months without making any sort of formal commitment. The implication is that they could date others at their own discretion. Ted wonders "Shall I give my class ring to Sally and make a commitment". In offering the ring Ted is making a commitment. Does Sally have a way to enforce it? Is Ted's commitment to be 'true' credible? As the game unfolds Sally must then decide whether or not she will accept the ring.
In offering the ring Ted is making an implicit commitment, a promise, to not date, and expects a reciprocal commitment from Sally. Should one of them break the implicit covenant then the ring will not be returned and there will be some histrionics, embarrassment, and perhaps the opprobrium of friends. Ted is out at least the cost of the ring if he breaks his commitment. The leverage that Ted has to enforce Sally's commitment is her 'reputation' in the aftermath of a break-up.
You could continue the story through two more stages, an engagement and then marriage. The engagement announces the intention to continue the monogamous relationship to the alter. The marriage vows articulate the details of a commitment to a strategic plan.
You should be able to model the relationship between Ted and Sally as an extensive form game. First think of the names for nodes that represent the point at which decisions have to be made. Enumerate the branches coming off each node. Think about the notion of commitment and how each makes it credibly. Before you label it, the game tree might look something like:
Now ask yourself whether the 'commitment' discussed in this dating game is the same as the usage of commitment in game theory.
For a rather more twisted look at credible promises, read about the Corleone family in Mario Puzo's The Godfather.