These strategies guarantee that the loser will not lose more than the
value of the game and that the winner will gain at least this value.
The solution is the "Saddle Point".
The distinction between zero-sum games (ZSG) and nonzero-sum games
(NZSG) is not trivial. A player playing a ZSG cannot gain if prohibited
to use certain strategies. This is not the case in NZSGs. In ZSG, the
player does not benefit from exposing his strategy to his rival and is
never harmed by having foreknowledge of his rival's strategy. Not so in
NZSGs: at times, a player stands to gain by revealing his plans to the
"enemy". A player can actually be harmed by NOT declaring his strategy
or by gaining acquaintance with the enemy's stratagems. The very
ability to communicate, the level of communication and the order of
communication - are important in cooperative cases. A Nash solution:
1. is not dependent upon any utility function;
2. it is impossible for two players to improve the Nash solution
(=their position) simultaneously (=the Paretto optimality);
3. is not influenced by the introduction of irrelevant (not very
gainful) alternatives; and
4. is symmetric (reversing the roles of the players does not affect the
solution).
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