Coding theory plays a crucial role in enabling reliable communication, storage, and computation. Classical approaches assume a worst-case adversarial model and ensure error correction and data recovery only when the number of honest nodes exceeds the number of adversarial ones by some margin. However, in some emerging decentralized applications, particularly in decentralized machine learning (DeML), participating nodes are rewarded for accepted contributions. This incentive structure naturally gives rise to rational adversaries who act strategically rather than behaving in purely malicious ways. In this paper, we first motivate the need for coding in the presence of rational adversaries, particularly in the context of outsourced computation in decentralized systems. We contrast this need with existing approaches and highlight their limitations. We then introduce the game of coding, a novel game-theoretic framework that extends coding theory to trust-minimized settings where honest nodes are not in the majority. Focusing on repetition coding, we highlight two key features of this framework: (1) the ability to achieve a non-zero probability of data recovery even when adversarial nodes are in the majority, and (2) Sybil resistance, i.e., the equilibrium remains unchanged even as the number of adversarial nodes increases. Finally, we explore scenarios in which the adversary's strategy is unknown and outline several open problems for future research.

翻译：编码理论在实现可靠通信、存储与计算方面发挥着至关重要的作用。经典方法通常假设最坏情况下的对手模型，并仅在诚实节点数量以一定优势超过对手节点数量时，才能确保纠错与数据恢复。然而，在一些新兴的去中心化应用中，特别是在去中心化机器学习（DeML）中，参与节点会因贡献被采纳而获得奖励。这种激励结构自然催生了理性对手，他们采取策略性行为而非纯粹的恶意破坏。本文首先阐述了在理性对手存在下进行编码的必要性，特别是在去中心化系统的外包计算场景中。我们将这一需求与现有方法进行对比，并指出其局限性。随后，我们引入了编码博弈，这是一种新颖的博弈论框架，它将编码理论扩展到诚实节点不占多数的信任最小化环境中。以重复编码为例，我们重点阐述了该框架的两个关键特征：（1）即使在对手节点占多数的情况下，仍能以非零概率实现数据恢复；（2）具备女巫攻击抵抗能力，即即使对手节点数量增加，均衡状态仍保持不变。最后，我们探讨了对手策略未知的场景，并提出了若干有待未来研究的开放性问题。