 Given the importance of common knowledge in social interactions, it is remarkable that only quite recently have philosophers and social scientists attempted to analyze the concept. David Hume (1740) was perhaps the first to make explicit reference to the role of mutual knowledge in coordination. In his account of convention in A Treatise of Human Nature, Hume argued that a necessary condition for coordinated activity was that agents all know what behavior to expect from one another. Without the requisite mutual knowledge, Hume maintained, mutually beneficial social conventions would disappear. Much later, J. E. Littlewood (1953) presented some examples of common-knowledge-type reasoning, and Thomas Schelling (1960) and John Harsanyi (1967–1968) argued that something like common knowledge is needed to explain certain inferences people make about each other. The philosopher Robert Nozick describes, but does not develop, the notion in his doctoral dissertation (Nozick 1963), while the first mathematical analysis and application of the notion of common knowledge is found in the technical report by Friedell (1967), then published as (Friedell  1969).[1]  The first full-fledged philosophical analysis of common knowledge was offered by David Lewis (1969) in the monograph Convention. Stephen Schiffer (1972), Robert Aumann (1976), and Gilbert Harman (1977) independently gave alternate definitions of common knowledge. Jon Barwise (1988, 1989) gave a precise formulation of Harman’s intuitive account. Throughout the 1980s a number of epistemic logicians, both from philosophy and from computer science, studied the logical structure of common knowledge, and the interested reader should consult the relevant portions of the two important monographs (Fagin et al. 1995) and (Meyer and Van der Hoek 1995). Margaret Gilbert (1989) proposed a somewhat different account of common knowledge which she argues is preferable to the standard account. Others have developed accounts of mutual knowledge, approximate common knowledge, and common belief which require less stringent assumptions than the standard account, and which serve as more plausible models of what agents know in cases where strict common knowledge seems impossible (Brandenburger and Dekel 1987,  Monderer and Samet 1989, Rubinstein 1992). The analysis and applications of common knowledge and related multi-agent knowledge concepts has become a lively field of research.