A Non-Probabilistic Game-Theoretic Information Theory Which Subsumes Probabilistic Channel Coding

2026-04-12

AI Summary

This work proposes a unified theory of information transmission grounded in deterministic game-theoretic principles, bridging the long-standing divide between probabilistic and non-probabilistic coding frameworks in classical information theory. By modeling encoding as a strategic game between an encoder and an adversary, and incorporating a dynamic hedging mechanism alongside non-convex downward-closed cone pricing, the framework generalizes the game-theoretic probability paradigm pioneered by Ville, Dawid, Shafer, and Vovk. It simultaneously encompasses probabilistic channel coding, zero-error coding, lossless source coding, and adversarial communication—domains previously treated in isolation. This approach not only transcends the boundaries of classical paradigms but also subsumes foundational results such as Shannon’s theorem, zero-error capacity characterizations, and coding for arbitrarily varying channels within a single, coherent formalism.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Probabilistic settings (e.g., vanishing-error channel coding) and non-probabilistic settings (e.g., zero-error channel coding and adversarial channels) were considered two related but different branches of information theory which do not subsume each other. We propose a unifying non-probabilistic information theory based on game theory and dynamic hedging which subsumes the conventional probabilistic channel coding theorem (vanishing error, with or without feedback) and lossless source coding theorem, as well as adversarial settings. Coding is modelled as a deterministic game between an encoder and an adversary, where the encoder may purchase insurance with a payoff that depends on the channel outputs. Our framework is based on a generalization of the works by Ville, Dawid, Shafer and Vovk on the game-theoretic formulation of probabilistic concepts, by relaxing the convex pricing cone to a nonconvex downward closed cone, which is precisely the relaxation needed to model information transmission. Pricing downward closed cone is a versatile tool for non-probabilistic coding results that can subsume their probabilistic counterparts, and provides a canonical form for probabilistic channels, adversarial channels and arbitrarily varying channels.

Problem

• information theory
• channel coding
• non-probabilistic
• adversarial channels
• unifying framework

Innovation

• game-theoretic information theory
• non-probabilistic coding
• downward closed cone
• adversarial channels
• dynamic hedging