Game of Coding: Coding Theory in the Presence of Rational Adversaries, Motivated by Decentralized Machine Learning

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.