编码游戏：超越诚实多数假设
Game of Coding: Beyond Honest-Majority Assumptions
AI总结：
本文提出编码游戏理论，通过博弈论方法解决去中心化系统中编码安全问题，探讨对手与解码器的博弈动态及均衡条件。
摘要：
编码理论围绕将冗余纳入传输符号、计算任务和存储数据中，以抵御对抗性篡改。然而，编码理论中的错误校正依赖于严格的信任假设。在计算和存储领域，要求诚实节点数量必须多于对抗性节点一定数量。然而，在多个新兴现实案例中，特别是去中心化区块链应用中，这种假设往往不现实。因此，尽管编码在解决去中心化系统中的重要挑战中起着重要作用，其应用却受到限制。然而，在去中心化平台上，一个独特的特征出现，为安全编码提供了新的途径，超越传统方法的限制。在这些场景中，对手受益于合法解码器恢复数据，且更希望有较高的估计误差。这种激励促使他们理性行事，试图最大化自身收益。在本文中，我们提出了一种称为“编码游戏”的博弈论编码方法，捕捉这种独特的动态，其中每个对手和数据收集器（解码器）都有各自的目标函数以优化。目标函数反映了数据收集器和对手都希望增加数据被解码器恢复的可能性。此外，目标函数表达了数据收集器希望以更低的估计误差来估计输入，但对手则相反。作为第一步，仍然高度非平凡的步骤，我们为重复因子为2的重复码，在广泛类别的目标函数中，以最少的假设条件下，刻画了游戏的均衡。
英文摘要：
Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict trust assumption. In the context of computation and storage, it is required that honest nodes outnumber adversarial ones by a certain margin. However, in several emerging real-world cases, particularly, in decentralized blockchain-oriented applications, such assumptions are often unrealistic. Consequently, despite the important role of coding in addressing significant challenges within decentralized systems, its applications become constrained. Still, in decentralized platforms, a distinctive characteristic emerges, offering new avenues for secure coding beyond the constraints of conventional methods. In these scenarios, the adversary benefits when the legitimate decoder recovers the data, and preferably with a high estimation error. This incentive motivates them to act rationally, trying to maximize their gains. In this paper, we propose a game theoretic formulation for coding, called the game of coding, that captures this unique dynamic where each of the adversaries and the data collector (decoder) have respective utility functions to optimize. The utility functions reflect the fact that both the data collector and the adversary are interested in increasing the chance of data being recoverable by the data collector. Moreover, the utility functions express the interest of the data collector to estimate the input with lower estimation error, but the opposite interest of the adversary. As a first, still highly non-trivial step, we characterize the equilibrium of the game for the repetition code with a repetition factor of 2 for a wide class of utility functions with minimal assumptions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
