To understand how groups coordinate, we study infinitely repeated N-pl
ayer coordination games in the context of strategic uncertainty. In a
situation where players share no common language or culture, ambiguity
is always present. However, finding an adequate principle for a commo
n language is not easy: a tradeoff between simplicity and efficiency h
as to be made. All these points are illustrated on repeated N-player c
oordination games on m loci. In particular, we demonstrate how a commo
n principle can accelerate coordination. We present very simple rules
that are optimal in the space of all languages for m (number of coordi
nation loci) from 2 to 5 and for all N, the number of players. We also
show that when more memory is used in the language (strategies), play
ers may not coordinate, whereas this is never the case when players re
member only the previous period.