概率公共信念的动态刻画

Dynamics for Probabilistic Common Belief

Robert Aumann的不一致的达成定理揭示了如果两个主体关于某事件E具有相同的先验概率,并且利用私人信息更新了他们关于事件的概率,那么,若事件的后验概率是他们之间的公共知识,则这个后验值一定是相同的。而Dov Monderer和Dov Samet考虑了包含有关于公共知识概率赋值的一种变体,推广了奥曼这个结论。在这篇文章中,笔者基于概率和动态认知逻辑,采用多种方法考察了关于他们结论的动态刻画。本文主要的目标是构建一个模型,可以描述随着主体彼此间的交互深入和环境变化,主体知识和信念所发生的变化。同时,笔者表明这种逻辑框架对于研究交互社会群体中主体信念改变的动态进程是富足和灵活的。

Robert Aumann＇s agreeing to disagree theorem shows that if two agents have the same prior probability and update their probability of an event E with private information by conditioning, then if the posterior probabilities of E are common knowledge, then the posteriors must be the same. Dov Monderer and Dov Samet prove a generalization of Aumann＇s result involving a probabilistic variant of common knowledge. In this paper, I use various methods from probabilistic and dynamic-epistemic logics to explore a dynamic characterization of the Monderer and Samet result. The main goal is to develop a model that describes the evolution of the agents＇ knowledge and （probabilistic） beliefs as they interact with each other and the environment. will show how the logical frameworks are rich and flexible tools that can be used to study many dynamic processes of interactive social belief change.