Cores of Cooperative Games in Information Theory

TL;DR

This paper explores the role of core concepts in cooperative game theory within information theory, highlighting their application in characterizing limits in multi-user scenarios like network coding and distributed estimation.

Contribution

It unifies various information theory problems through cooperative game core analysis, revealing fundamental dualities between information inequalities and resource allocation.

Findings

Identifies core structures in multiple information theory scenarios.

Establishes dualities between information inequalities and resource regions.

Provides a unifying framework for multi-user information problems.

Abstract

Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network information theory such as Slepian-Wolf source coding and multiple access channels, classical settings in statistics such as robust hypothesis testing, and new settings at the intersection of networking and statistics such as distributed estimation problems for sensor networks. Cooperative game theory allows one to understand aspects of all of these problems from a fresh and unifying perspective that treats users as players in a game, sometimes leading to new insights. At the heart of these analyses are fundamental dualities that have been long studied in the context of cooperative games; for information theoretic purposes, these are dualities between information inequalities on the one hand and properties of rate, capacity or other resource allocation regions on the other.