  The naming game (NG) describes the agreement dynamics of a population of
agents that interact locally in a pairwise fashion, and in recent years
statistical physics tools and techniques have greatly contributed to shed light
on its rich phenomenology. Here we investigate in details the role played by
the way in which the two agents update their states after an interaction. We
show that slightly modifying the NG rules in terms of which agent performs the
update in given circumstances (i.e. after a success) can either alter
dramatically the overall dynamics or leave it qualitatively unchanged. We
understand analytically the first case by casting the model in the broader
framework of a generalized NG. As for the second case, on the other hand, we
note that the modified rule reproducing the main features of the usual NG
corresponds in fact to a simplification of it consisting in the elimination of
feedback between the agents. This allows us to introduce and study a very
natural broadcasting scheme on networks that can be potentially relevant for
different applications, such as the design and implementation of autonomous
sensor networks, as pointed out in the recent literature.
