Editing Zero-sum game (section)

=== Zero-sum three-person games ===
[[File:The zero-sum three-person game.png|right|526x526px|Zero-sum three-person game]]
It is clear that there are manifold relationships between players in a zero-sum three-person game, in a zero-sum two-person game, anything one player wins is necessarily lost by the other and vice versa; therefore, there is always an absolute antagonism of interests, and that is similar in the three-person game.<ref name=":0">{{Cite book|last=Von Neumann|first=John |title=Theory of games and economic behavior|date=2007|publisher=Princeton University Press|author2=Oskar Morgenstern|isbn=978-1-4008-2946-0|edition=60th anniversary |location=Princeton|pages=220–223|oclc=830323721}}</ref> A particular move of a player in a zero-sum three-person game would be assumed to be clearly beneficial to him and may disbenefits to both other players, or benefits to one and disbenefits to the other opponent.<ref name=":0" /> Particularly, parallelism of interests between two players makes a cooperation desirable; it may happen that a player has a choice among various policies: Get into a parallelism interest with another player by adjusting his conduct, or the opposite; that he can choose with which of other two players he prefers to build such parallelism, and to what extent.<ref name=":0" /> The picture on the left shows that a typical example of a zero-sum three-person game. If Player 1 chooses to defence, but Player 2 & 3 chooses to offence, both of them will gain one point. At the same time, Player 1 will lose two-point because points are taken away by other players, and it is evident that Player 2 & 3 has parallelism of interests.