In game theory, a zero-sum or constant-sum game is a game in which there is a single constant payoff that will be divided equally between the players; in order for one player to get a better result, one or more other players have to get worse results. For instance, in many games, there can be one winner and everyone else loses; there is a single "win" available. In others, you might have draws, but a draw could be considered as all of the given players splitting the win equally; for instance, in chess, a win is 1 point, a loss 0, and a draw 0.5 for each player. In some games, like poker, that constant payoff to split is 0; in order for one player to make money, another has to lose money.
A cooperative game is not be zero-sum. There are two possible outcomes; either everyone wins, or everyone loses. Thus, from the perspective of game theory, there is one outcome in which the total payoff for the players is greater than in another outcome. However, this is somewhat trivially non-zero sum; there aren't any interesting decisions that affect how much the total payoff is. Poker played at a casino, likewise, is non-zero sum as you are always losing the rake to the casino; but again, it's not in an interesting way as you don't make any interesting decisions that affect the total value of the game.
Note that all of these non-zero sum games could be made zero-sum if you consider the game itself or the house as a player; then there is one "win" split between the players and the game, or one pool of money split between the players and the casino. This is true of any non-zero-sum game; you can always posit an extra hypothetical player, or consider the interests of the house, whose gain or loss is the negative of the gain or loss of the players of the game. But it's still interesting to consider games as non-zero sum from the perspective of the players themselves.
So, are there any games which are non-zero sum in an interesting way? That is, in which players have to make interesting decisions during the game, that affect the total payoff of the game. For instance, a game in which, depending on the action of the players, the outcome could be that one player gets 10 points, or two players each get 8, or three players all get 7 points would be non-zero sum game; the total value of the game depends on decisions that the players make within the game. A game like Shadows over Camelot, which will randomly be zero-sum or non-zero sum depending on whether there's a traitor, isn't really interesting as the actions of the players don't affect what the possible payoffs are, only a random card chosen at the beginning affects this.
I am only interested in actual fun playable games, not hypothetical mathematical examples, and only interested in how games are actually played in practice, not hypothetical tournament setups that you could play; in almost any game with a variable score, you could institute a system in which your absolute score in the game was used in the tournament results, but that's not the way that most tournaments I've seen are played. I want to know about games or tournament structures that people actually play.
Note that in order for this question to even make sense, there may need to be some kind of external value associated with the game; some metagame that the game is played within, such as a tournament or ranking system, or a gambling game in which the players in an individual game may wind up with more or less money than they started with. If so, please describe how this metagame works, and interacts with the outcome of individual games.