The traditional definition of a nonlocal game is restricted to having two players and one round (e.g., here), but it is natural to consider a more general class of games that may have more than two players and more than one round of questions. While there has been a lot of work dealing with games with more than two players, I have found very little on multi-round games. For instance, there is a recent preprent of Crépeau and Yang that gives a definition of a multi-party, multi-round non-signaling distribution and seems to describe a multi-round game (although the paper is written in the language of commitment schemes rather than games, so I'm not entirely sure my interpretation is correct).
Has there been any other work dealing with multi-round games? And is there a reason so much of the literature has focused on single-round games? Are multi-round games inherently "no more interesting" than single-round games from the perspective of understanding nonlocality?