THERE ARE at least two kinds of games. One could be called finite, the other infinite.
至少有两种游戏。一种可称为有限游戏，另一种为无限游戏。
A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.
有限游戏为了取胜的目的而玩，而无限游戏则是为了继续玩的目的。
If a finite game is to be won by someone it must come to a definitive end. It will come to an end when someone has won.
如果有限游戏会被某个人所赢得，那么游戏必须走到明确的终结。有人取胜，游戏便终结了。
We know that someone has won the game when all the players have agreed who among them is the winner. No other condition than the agreement of the players is absolutely required in determining who has won the game.
我们知道，如果所有玩家都同意其中某个人是赢家，那么这个人就赢得了游戏。要确定谁赢得游戏，除了玩家的同意，不需要其他任何条件是绝对必要的。
It may appear that the approval of the spectators, or the referees, is also required in the determination of the winner. However, it is simply the case that if the players do not agree on a winner, the game has not come to a decisive conclusion—and the players have not satisfied the original purpose of playing. Even if they are carried from the field and forcibly blocked from further play, they will not consider the game ended.
观众或裁判的认可看似也是决定赢家的必要条件。但是，只有在参与者对于谁是赢家没有达成共识、游戏没有达成决定性的结果且参与者未履行参与的初衷时，这种情况才成立。否则，即使被逐出赛场并被强行禁止进一步参与，他们也不会认为游戏结束了。
Suppose the players all agree, but the spectators and the referees do not. Unless the players can be persuaded that their agreement was mistaken, they will not resume the play—indeed, they cannot resume the play. We cannot imagine players returning to the field and truly playing if they are convinced the game is over.
假设参与者就谁是赢家达成了共识，但观众和裁判没有，那么除非参与者能够被说服他们的共识有误，否则他们不会继续将游戏进行下去，他们也不能继续下去。我们无法想象，如果参与者确信游戏已经结束，他们还会重回赛场并真正地参与游戏。
There is no finite game unless the players freely choose to play it. No one can play who is forced to play.
除非参与者自愿选择参与，否则不存在有限游戏。谁也无法同被迫参与的人进行游戏。
It is an invariable principle of all play, finite and infinite, that whoever plays, plays freely. Whoever must play, cannot play.
这是所有游戏不变的原则，有限游戏和无限游戏均是如此，无论谁参与，都是自愿参与。被迫参与便失去了参与的意义。
Just as it is essential for a finite game to have a definitive ending, it must also have a precise beginning. Therefore, we can speak of finite games as having temporal boundaries—to which, of course, all players must agree. But players must agree to the establishment of spatial and numerical boundaries as well. That is, the game must be played within a marked area, and with specified players.