Game of Coding for Vector-Valued Computations

2026-02-04

AI Summary

This work addresses the limitations of traditional coding theory, which relies on an honest majority assumption and thus fails in permissionless decentralized settings where adversaries may dominate. While existing game-theoretic coding approaches support only scalar computations, this paper presents the first extension of the game-theoretic coding framework to N-dimensional Euclidean space. By integrating game theory, coding theory, and high-dimensional vector analysis, we develop an economically incentivized fault-tolerant mechanism along with a method for solving equilibrium strategies. We establish a rigorous mathematical model for vector-valued game-theoretic coding, fully characterize its equilibrium strategies, and prove that it preserves robustness and decodability even when adversaries constitute a majority. This provides a theoretical foundation for large-scale decentralized applications such as machine learning in permissionless environments.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

The game of coding is a new framework at the intersection of game theory and coding theory; designed to transcend the fundamental limitations of classical coding theory. While traditional coding theoretic schemes rely on a strict trust assumption, that honest nodes must outnumber adversarial ones to guarantee valid decoding, the game of coding leverages the economic rationality of actors to guarantee correctness and reliable decodability, even in the presence of an adversarial majority. This capability is paramount for emerging permissionless applications, particularly decentralized machine learning (DeML). However, prior investigations into the game of coding have been strictly confined to scalar computations, limiting their applicability to real world tasks where high dimensional data is the norm. In this paper, we bridge this gap by extending the framework to the general $N$-dimensional Euclidean space. We provide a rigorous problem formulation for vector valued computations and fully characterize the equilibrium strategies of the resulting high dimensional game. Our analysis demonstrates that the resilience properties established in the scalar setting are preserved in the vector regime, establishing a theoretical foundation for secure, large scale decentralized computing without honest majority assumptions.

Problem

• game of coding
• vector-valued computations
• decentralized machine learning
• high-dimensional data
• adversarial majority

Innovation

• Game of Coding
• vector-valued computation
• decentralized machine learning
• adversarial majority resilience
• economic rationality