  Notably, Lewis introduces the concept of common knowledge. Roughly, \(p\) is common knowledge iff everyone knows \(p\), everyone knows that everyone knows \(p\), everyone knows that everyone knows that everyone knows that \(p\), etc. The subsequent game-theoretic and philosophical literature offers several different ways of formalizing this intuitive idea, due to researchers such as Robert Aumann (1976) and Stephen Schiffer (1972). Recently, some controversy has arisen concerning the precise relation between these later formalizations and Lewis’s own informal remarks. Robin Cubitt and Robert Sugden (2003) argue that Lewis’s conception of common knowledge is radically different from the later formalizations, while Peter Vanderschraaf (1998) and Giacomo Sillari (2005) downplay the differences.  See the entry on  common knowledge  for discussion of this controversy and of how common knowledge informs both game theory and the philosophical study of convention.