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Two Strongly Truthful Mechanisms for Three Heterogeneous Agents Answering One Question

机译：三个异质代理回答一个问题的两种强真实机制

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摘要

Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents' reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting. Our Differential Peer Prediction mechanisms are strongly truthful: Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know (detail-free) in the single question setting. Moreover, they only require three agents, each of which submits a single item report: two report their signals (answers), and the other reports her forecast (prediction of one of the other agent's reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule's special properties. Moreover, we can recast the Bayesian Truth Serum mechanism 20 into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium.
机译：同行的预测机制激励利己主义的代理人如实报告他们即使没有信号验证通过比较代理的报告和同龄人。提出两个新的机制,源和目标微分同行预测,证明非常强有力的保证很一般设置。微分同行预测机制强烈的真实:真情流露的是严格的贝叶斯纳什均衡。支付严格高于其他平衡,不包括置换平衡,支付同样是真情流露。代理之间的不对称的先知先觉,不需要知道(detail-free)机制一个问题设置。需要三个代理,每个提交单项报告:两个报告他们的信号(答案),其他报告她的预测(预测的另一个代理的报告)。我们的技术是简单的证明,概念上的动机,并打开对数评分规则的特殊属性。此外,我们可以重塑贝叶斯真理血清机制[20]进入我们的框架。我们的研究结果扩展到连续的设置信号略弱的保证真实的最优平衡。

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