We investigate how a blockchain can distill the collective belief of its nodes regarding the trustworthiness of a (sub)set of nodes into a {\em reputation system} that reflects the probability of correctly performing a task. To address this question, we introduce a framework that breaks it down into two sub-problems: 1. (Information Extraction): How can the system distill trust information from a function of the nodes' true beliefs? 2. (Incentive Design): How can we incentivize nodes to truthfully report such information? To tackle the first sub-problem, we adapt, in a non-trivial manner, the well-known PageRank algorithm to our problem. For the second, we define a new class of games, called Trustworthy Reputation games (TRep games), which aim to extract the collective beliefs on trust from the actions of rational participants. We then propose a concrete TRep game whose utility function leverages Personalized PageRank and can be instantiated through a straightforward blockchain rewards mechanism. Building on this, we show how the TRep game enables the design of a reputation system. Such systems can enhance the robustness, scalability, and efficiency of blockchain and DeFi solutions. For instance, we demonstrate how such a system can be used within a Proof-of-Reputation blockchain.

翻译：我们研究区块链如何将其节点对（子）节点集合可信度的集体信念提炼为反映正确执行任务概率的声誉系统。为解决该问题，我们引入一个框架，将其分解为两个子问题：1.（信息提取）：系统如何从节点真实信念的函数中提取信任信息？2.（激励设计）：如何激励节点如实报告此类信息？针对第一个子问题，我们以非平凡的方式将著名的PageRank算法适配至本问题。对于第二个问题，我们定义了一类称为可信声誉博弈的新博弈，其目标是从理性参与者的行为中提取关于信任的集体信念。随后我们提出一个具体的可信声誉博弈，其效用函数利用个性化PageRank算法，并可通过简单的区块链奖励机制实例化。在此基础上，我们展示了可信声誉博弈如何支持声誉系统的设计。此类系统能提升区块链与去中心化金融解决方案的鲁棒性、可扩展性与效率。例如，我们演示了此类系统如何在声誉证明区块链中应用。