Play with null sum
A play of null sum is a play where the sum of the profits of all the players is equal to 0.
For example if one defines profit of part of failures as 1 if one gains, 0 if the part is null and -1 if one loses, the set of failures is a play with null sum.
In economy, this simplifying concept is important: the plays with null sum correspond to the absence of production or destruction of products.
In 1944, John von Neumann and Oskar Morgenstern showed that any play with null sum for N people is in fact only one generalized form of plays to null sum for two people, and that any play with nonnull nap for N people can be brought back to a play to null sum for N + 1 people, the n+1-ième person representing the profit or the total loss.
So the plays with null sum for two people or two entities constitute the essential part of the mathematical theory of the plays.
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