The point that I would stress is that 2-player and n-player zero-sum games have very different properties. 2-player zero-sum games are interesting because it's

The point that I would stress is that 2-player and n-player zero-sum games have very different properties. 2-player zero-sum games are interesting because it's one of the few cases where game theory makes a unique prediction. In general 2-player games there can be multiple Nash equilibria, and the theory does not tell us which one will be chosen. In a zero-sum 2-player game, the only equilibrium strategies are the minimax-ones, which can be directly computed. Also, by inspecting the minimax strategies we can tell that there is no possibility of bargains, there is no role for cheap talk, etc etc. This is where the informal connotations of a "zero sum game" comes from: it's dog-eat-dog and cold hard randomness. But in n-player games, assuming that the payoffs sum to zero does not lead to any particularly interesting consequences. Any general n-player game can be encoded as a zero-sum (n+1)-player game[0], so all the general subtleties of game theory comes back into play. For example, consider n pirates that need to split a chest of gold. The sum of payoffs is fixed (it's the number of coins), but still there is a large rule for "politics", i.e. talk to form coalitions, etc. There are a lot of Nash equilibria of the "the three of us gang up on the two of them", and no way a priori to figure out which one will be chosen. [0] http://people.csail.mit.edu/costis/6853fa2011/lec3.pdf http://people.csail.mit.edu/costis/6853fa2011/lec3.pdf