Common Knowledge, Regained.

Formally, for common knowledge to arise in a dynamic setting, knowledge that it has arisen must be simultaneously attained by all players. As a result, new common knowledge is unattainable in many realistic settings, due to timing frictions. This unintuitive phenomenon, observed by Halpern and Moses (1990), was discussed by Arrow et al. (1987) and by Aumann (1989), was called a paradox by Morris (2014), and has evaded satisfactory resolution for four decades. We resolve this paradox by proposing a new definition for common knowledge, which coincides with the traditional one in static settings but generalizes it in dynamic settings. Under our definition, common knowledge can arise without simultaneity, particularly in canonical examples of the Haplern-Moses paradox. We demonstrate its usefulness by deriving for it an agreement theorem \`a la Aumann (1976), and showing that it arises in the setting of Geanakoplos and Polemarchakis (1982) with timing frictions added.