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

Consensus Game Acceptors and Iterated Transductions