Game Theory and Mathematical Economics Research Seminar
Lecturer:
Prof. Yannai Gonczarowski (Harvard University)
Title:
Common Knowledge, Regained
Abstract:
For common knowledge to arise in dynamic settings, allplayers must simultaneously come to know it has arisen. Consequently, commonknowledge cannot arise in many realistic settings with timing frictions. This counterintuitive observation of Halpern and Moses (1990) was discussed by Arrowet al. (1987) and 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 is more permissive 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 à la Aumann (1976), showing it arises in the setting of Geanakoplos and Polemarchakis (1982) with timing frictions added, and applying it to characterize equilibrium behavior in a dynamic coordination game.
Joint work with Yoram Moses.
Location:
Eilan Hall, Feldman Building, Second Floor, Edmond Safra Campus.