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.

翻译：概率设定（例如，可忽略误差信道编码）与非概率设定（例如，零误差信道编码与对抗信道）历来被视为信息论中虽相关但彼此独立的分支，二者无法相互涵盖。我们提出一种基于博弈论与动态对冲的统一非概率信息理论，该理论既涵盖了经典的概率信道编码定理（可忽略误差，含或不含反馈）与无损信源编码定理，也适用于对抗性场景。在该框架中，编码被建模为编码器与对手之间的确定性博弈，编码器可购买收益取决于信道输出的保险。本文基于Ville、Dawid、Shafer与Vovk等人关于概率概念博弈论形式化的工作进行推广，将凸定价锥放宽为非凸下闭锥——这正是信息传输建模所需的精确松弛。下闭定价锥作为非概率编码结果的通用工具，既能涵盖对应的概率版本，也为概率信道、对抗信道与任意变信道提供了规范形式。