John Nash game hex

Mathmatician John Nash created this board game. Hex.

In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, you and I are in Nash equilibrium if I am making the best decision I can, taking into account your decision, and you are making the best decision you can, taking into account my decision. Likewise, many players are in Nash equilibrium if each one is making the best decision (s)he can, taking into account the decisions of the others.