贝叶斯观点交换网络中的推理是PSPACE困难的
Reasoning in Bayesian Opinion Exchange Networks Is PSPACE-Hard
摘要：
我们研究了网络上完全理性的代理人的意见交换的贝叶斯模型。在这个模型中，代理接收私人信号，这些信号表明世界的未知状态。然后，他们反复向邻居宣布他们认为最有可能的世界状态，同时根据邻居的公告更新他们的信念。自Aumann（1976）和Geanakoplos和Polemarchakis（1982）的工作以来，这个模型在经济学中得到了广泛的研究。众所周知，在任何网络上，代理最终都有很高的概率同意。人们经常认为，在这个模型中的代理所需的计算是困难的，但在我们的结果之前，没有严格的工作显示这种硬度。我们表明，这是PSPACE-硬的代理计算他们的行动在这个模型中。此外，我们表明，它是同样困难的，甚至近似代理的后：这是PSPACE-难以区分后几乎完全集中在一个国家的世界或另一个。
英文摘要：
We study the Bayesian model of opinion exchange of fully rational agents arranged on a network. In this model, the agents receive private signals that are indicative of an unkown state of the world. Then, they repeatedly announce the state of the world they consider most likely to their neighbors, at the same time updating their beliefs based on their neighbors' announcements. This model is extensively studied in economics since the work of Aumann (1976) and Geanakoplos and Polemarchakis (1982). It is known that the agents eventually agree with high probability on any network. It is often argued that the computations needed by agents in this model are difficult, but prior to our results there was no rigorous work showing this hardness. We show that it is PSPACE-hard for the agents to compute their actions in this model. Furthermore, we show that it is equally difficult even to approximate an agent's posterior: It is PSPACE-hard to distinguish between the posterior being almost entirely concentrated on one state of the world or another.
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。
