In part I of this paper [see ibid. 8, 111-139 (1984; Zbl 0552.90099)] we introduced extensive games with a non-atomic continuum of players. It was shown that the Nash plays (outcomes) are invariant of the information patterns on the game, provided that no player’s unilateral change in moves can be observed by others. This led to an enormous reduction in the Nash plays of these games, as exemplified in the anti-folk theorem. Our concern in this sequel is to develop a finite version of these results.