AI 中文总结
研究具有输入相关对抗噪声的编码博弈，引入统一多节点、多维度公式，构造输入独立联合噪声分布，证明其保留接受概率和均方估计误差，使输入相关和独立模型有相同性能区域与均衡效用。
AI 中文摘要
编码博弈框架被引入以扩展编码理论恢复超出其传统限制，传统限制下诚实报告数量必须超过对抗或损坏报告数量。它通过利用对抗参与者的理性行为及其维持系统运行的动机来实现。然而，现有编码博弈公式假设对抗噪声分布与实际计算的真实值无关。当有信息的对手能使其报告适应所计算的值时，此假设可能具有局限性。本文研究具有输入相关对抗噪声的编码博弈。我们引入统一的多节点、多维度公式。对于每个条件对抗噪声分布族，我们构造一个输入独立的联合噪声分布，并证明这种简化精确地保留了接受概率和接受的均方估计误差。因此，输入相关和输入独立模型具有相同的可实现性能区域和相同的均衡效用。
英文摘要
The game of coding framework was introduced to extend coding-theoretic recovery beyond its traditional limit, under which the number of honest reports must exceed the number of adversarial or corrupted reports. It does so by exploiting the rational behavior of adversarial participants and their incentive to keep the system live. Existing game-of-coding formulations, however, assume that the adversarial-noise distribution is independent of the realized ground-truth computation. This assumption may be restrictive when an informed adversary can adapt its reports to the value being computed. In this paper, we study the game of coding with input-dependent adversarial noise. We introduce a unified multi-node, multidimensional formulation. For every family of conditional adversarial-noise distributions, we construct an input-independent joint noise distribution, and prove that this reduction exactly preserves the probability of acceptance and the accepted mean-squared estimation error. Consequently, the input-dependent and input-independent models have identical achievable performance regions, and the same equilibrium utilities.
