Unattainability of Common Knowledge in Asymmetric Games with Imperfect Information

TL;DR

This paper models asymmetric game interactions with imperfect information, showing that common knowledge of the game state cannot be achieved when agents have contrasting capabilities, highlighting strategic limitations in such environments.

Contribution

It introduces a conceptual model demonstrating the unattainability of common knowledge in asymmetric games with imperfect information using epistemic logic.

Findings

Common knowledge of the game state is unattainable under extreme asymmetry.

The model uses Kripke structures to analyze information dynamics.

Results highlight strategic limitations in environments with uneven information and action capabilities.

Abstract

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed.