In a board or video game where there are n-players and only one winner, a common intuitive strategy is for people to generally sabotage the person in the lead. Once a person in the lead gets to a certain point where it's hard to catch up to, you have to start forming alliances to bring down the person in the lead to bring them back down to the same level as everyone else, so that at least someone else has a chance at winning.
In reality, it can get much more complicated, especially when the player advantages / disadvantages are not symmetrical, but I thought this was such an intuitive concept that I, not being well-versed in game theory, maybe falsely remembered reading a game theory article about a simple, abstract version of this sort of game (about how players would sabotage the person most likely to win), but now I can't find an article or proof on any.
Is the intuition wrong, am I searching for the wrong thing, or is it just a much more complicated problem than I had thought?
Edit: I also realize that the game I described is kind of vague; I'm not necessarily looking for a specific example, but I guess any formal analysis on a game that is similar.
The game you explain is a non-cooperative game, because players are trying to use strategies that maximize their payoff (i.e. win).
A cooperative game can also be applied this situation if you consider each fixed time instant. When there is a single person that is far ahead of others, and there is an incentive for other players to team up to "attack" the current winner. In the case that players would benefit from forming teams, the (cooperative) game would be called cohesive. Going back to your situation, the case when there is a winner far ahead of others and when players can team up to bring the winner down, the game is cohesive. When there is no "winner" that is far ahead of others, the core of the cooperative game is empty, and hence you just have a non-cooperative game.