Common Knowledge Regained: Overcoming the Tyranny of the Clock

Core Concepts

The traditional definition of common knowledge is too restrictive, as it requires simultaneity in dynamic settings. This paper proposes a new, more permissive definition of common knowledge that overcomes the Halpern-Moses Paradox, allowing common knowledge to arise without simultaneity, particularly in canonical examples exhibiting this paradox.

Abstract

The paper addresses the Halpern-Moses Paradox, which shows that in dynamic settings with timing frictions, common knowledge cannot arise due to the requirement of simultaneity in the traditional definition. The authors propose a new definition of common knowledge that is more permissive and can overcome this paradox.
Key highlights:

The traditional definition of common knowledge requires a strong form of mutuality between the epistemic states of players, which implies that common knowledge must become known simultaneously by all players.
The authors introduce a new definition of common knowledge that reasons about each player's knowledge as a certain local event occurs, rather than requiring simultaneity. This allows common knowledge to arise in the absence of simultaneity.
The authors provide an Induction Rule that can be used to establish when common knowledge holds under their new definition.
They demonstrate the usefulness of their definition by deriving an agreement theorem, showing it arises in the Geanakoplos and Polemarchakis (1982) setting with timing frictions, and applying it to characterize equilibrium behavior in a dynamic coordination game.

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Key Insights Distilled From

Common Knowledge, Regained

by Yannai A. Go... at arxiv.org 04-24-2024

https://arxiv.org/pdf/2311.04374.pdf

Deeper Inquiries

How can the authors' notion of common knowledge be extended or generalized to settings with more than two players?

The authors' notion of common knowledge can be extended to settings with more than two players by considering the interactions and knowledge sharing among all players in the group. In a multi-player setting, common knowledge would involve each player knowing that every other player knows a certain fact, and so on recursively. This extension would involve defining common knowledge events for each possible combination of players in the group, ensuring that the knowledge is shared and understood by all members simultaneously. By incorporating the unique interactions and communication channels between multiple players, the notion of common knowledge can be generalized to encompass larger groups and more complex dynamics.

How might the authors' definition of common knowledge be applied to analyze the emergence of social norms or conventions in dynamic settings with timing frictions?

The authors' definition of common knowledge can be applied to analyze the emergence of social norms or conventions in dynamic settings with timing frictions by examining how shared beliefs and understandings evolve among individuals over time. In the context of social norms, common knowledge plays a crucial role in establishing mutual expectations and behaviors within a community. By applying the authors' framework, researchers can track the development of common knowledge regarding specific norms or conventions, considering the impact of timing frictions on the dissemination of information and the synchronization of beliefs among individuals. This analysis can provide insights into how social norms are established, reinforced, and potentially challenged in dynamic environments where timing uncertainties exist.

What are some potential applications of the authors' framework for common knowledge in fields outside of economics and computer science, such as cognitive science or philosophy of language?

The authors' framework for common knowledge has potential applications in fields outside of economics and computer science, such as cognitive science or philosophy of language. In cognitive science, the notion of common knowledge can be utilized to study how individuals perceive and interpret shared information, leading to a better understanding of collaborative decision-making, social cognition, and group dynamics. By applying the authors' framework, researchers in cognitive science can investigate how common knowledge influences cognitive processes, memory formation, and social interactions among individuals.
In the philosophy of language, the authors' definition of common knowledge can be employed to explore the role of shared beliefs and linguistic conventions in communication and meaning-making. By analyzing how common knowledge shapes language use, interpretation, and understanding, philosophers can delve into the foundations of language as a social and communicative tool. This framework can shed light on how language evolves, adapts, and influences collective knowledge within linguistic communities, offering valuable insights into the nature of language and its relationship to shared beliefs and concepts.