Collaborative Research Updating Ambiguous Beliefs: Bayesian and Non-Bayesian Learning

不确定条件下决策的贝叶斯方法 规定决策者有唯一的先验概率 和效用函数，从而做出决策， 最大化期望效用。 这一范式的合理性在于 公理化的处理，但受到几类证据的挑战： 实验结果不符合相容性条件 贝叶斯方法所暗示的，人们在 指定先验概率和经济现象 与理论结果相矛盾。 在许多模型建议推广贝叶斯方法是 非加性概率模型和多重先验模型。 这些模型已经通过了一个重要的考验：它们已经被 公理化的 然而，这些一次性决策模型几乎没有 关于动态更新概率的问题， 收集信息。 那么自然的问题是： 经济主体更新信念的合理方式， 时间？ 本研究将公理化地处理这个问题，并建议 合理的更新规则，满足一些基本要求。 一系列伪贝叶斯规则，其中每一个都可以考虑 贝叶斯规则对于唯一的加性先验的推广，将 提出并研究。 一类经典的更新规则， 每一个都有一组给定的先验，可能是规则 他们中的一些人面对新的信息，并继续与 其余的贝叶斯更新，也将进行研究。 一个唯一的先验概率的假设显然是 不现实的 新的政治环境，技术进步， 新公司和新产品都是反例， 唯一先验的假设是不合理的。 因此，这 这些研究将为我们制定和实施 建立我们对经济行为主体适应新的 现象或新信息。

The Bayesian approach to decision making under uncertainty prescribes that a decision maker have a unique prior probability and a utility function such that decisions are made so as to maximize the expected utility. This paradigm was justified by axiomatic treatments but challenged by several classes of evidence: experimental results incompatible with the consistency condition implied by the Bayesian approach, difficulties people have in specifying a prior probability, and economic phenomena contradictory to the theoretical results. Among many models suggested to generalize the Bayesian approach are the nonadditive probabilities model and the multiple priors model. These models have passed an important test: they have been axiomatized. However, these one-shot decision models shed little light on the problem of dynamically updating probabilities as new information is gathered. The natural question then is: what are the reasonable ways for economic agents to update beliefs over time? This study will deal with this problem axiomatically and suggest plausible updating rules which satisfy some basic requirements. A family of pseudo-Bayesian rules, each of which may be considered a generalization of Bayes' rule for a unique additive prior, will be presented and studied. A family of classical updating rules, each of which starts out with a given set of priors, possibly rules some of them out in the face of new information, and continues with the Bayesian updates of the remaining ones, will also be studied. The assumption of a unique given prior probability is clearly unrealistic. New political circumstances, technological advances, new firms, and new products are all counter-examples in which the assumption of a unique prior is unreasonable. Consequently, this study will provide important theoretical foundation upon which we build our understanding of the adjustment of economic agents to new phenomena or new information.