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. Spatial boundaries are evident in every finite conflict, from the simplest board and court games to world wars.
The opponents in World War II agreed not to bomb Heidelberg and Paris and declared Switzerland outside the boundaries of conflict. When unnecessary and excessive damage is inflicted by one of the sides in warfare, a question arises as to the legitimacy of the victory that side may claim, even whether it has been a war at all and not simply gratuitous unwarranted violence. When Sherman burned his way from Atlanta to the sea, he so ignored the sense of spatial limitation that for many persons the war was not legitimately won by the Union Army, and has in fact never been concluded.
Numerical boundaries take many forms but are always applied in finite games. Persons are selected for finite play. It is the case that we cannot play if we must play, but it is also the case that we cannot play alone.
Thus, in every case, we must find an opponent, and in most cases teammates, who are willing to join in play with us. Not everyone who wishes to do so may play for, or against, the New York Yankees. Neither may they be electricians or agronomists by individual choice, without the approval of their potential colleagues and competitors.
Because finite players cannot select themselves for play, there is never a time when they cannot be removed from the game, or when the other contestants cannot refuse to play with them. The license never belongs to the licensed, nor the commission to the officer.
What is preserved by the constancy of numerical boundaries, of course, is the possibility that all contestants can agree on an eventual winner. Whenever persons may walk on or off the field of play as they wish, there is such a confusion of participants that none can emerge as a clear victor. Who, for example, won the French Revolution?James Carse – Finite and Infinite Games