  We study a game for recognising formal languages, in which two players with
imperfect information need to coordinate on a common decision, given private
input words correlated by a finite graph. The players have a joint objective to
avoid an inadmissible decision, in spite of the uncertainty induced by the
input.
  We show that the acceptor model based on consensus games characterises
context-sensitive languages. Further, we describe the expressiveness of these
games in terms of iterated synchronous transductions and identify a subclass
that characterises context-free languages.
