Consider a Bayesian binary decision-making problem in star networks, where local agents make selfish decisions independently, and a fusion agent makes a final decision based on aggregated decisions and its own private signal. In particular, we assume all agents have private beliefs for the true prior probability, based on which they perform Bayesian decision making. We focus on the Bayes risk of the fusion agent and counterintuitively find that incorrect beliefs could achieve a smaller risk than that when agents know the true prior. It is of independent interest for sociotechnical system design that the optimal beliefs of local agents resemble human probability reweighting models from cumulative prospect theory. We also consider asymptotic characterization of the optimal beliefs and fusion agent's risk in the number of local agents. We find that the optimal risk of the fusion agent converges to zero exponentially fast as the number of local agents grows. Furthermore, having an identical constant belief is asymptotically optimal in the sense of the risk exponent. For additive Gaussian noise, the optimal belief turns out to be a simple function of only error costs and the risk exponent can be explicitly characterized.

中文翻译：

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星形网络中基于错误信念的决策


考虑星形网络中的贝叶斯二元决策问题，其中本地代理独立做出自私决策，融合代理根据聚合决策和自己的私有信号做出最终决策。特别是，我们假设所有代理都对真实先验概率有私人信念，并据此执行贝叶斯决策。我们关注融合代理的贝叶斯风险，并违反直觉地发现，与代理知道真实先验时相比，不正确的信念可以获得更小的风险。对于社会技术系统设计来说，局部代理的最优信念类似于累积前景理论中的人类概率重新加权模型，这对于社会技术系统设计具有独立的意义。我们还考虑了最优信念的渐近特征和本地代理数量中融合代理的风险。我们发现，随着本地智能体数量的增长，融合智能体的最优风险以指数速度快速收敛到零。此外，从风险指数的意义上来说，拥有相同的恒定信念是渐近最优的。对于加性高斯噪声，最佳置信结果是仅包含误差成本的简单函数，并且可以明确表征风险指数。