On comparisons of information structures with infinite states

• 成果类型: Article
• 署名作者: Khan, M. Ali; Yu, Haomiao; Zhang, Zhixiang
• 署名单位: Johns Hopkins University; The New School; Toronto Metropolitan University; Central University of Finance & Economics
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2024.105841
• 发表日期: 2024
• 关键词: Information structure; sufficiency; Informativeness; Bayesian-better-than; Convex domination; Mean-preserving spread/dilation

摘要

Blackwell's theorem on the comparison of information structures is by now sufficiently wellunderstood for a finite state space, but important gaps remain in the infinite case. While the equivalence of (i) sufficiency and (ii) more -informativeness is known, we present a comprehensive theory that establishes equivalences between these two orders (in both their original and almost all versions) and three additional prior -dependent criteria on general (Polish) state spaces. We consider (iii) Bayesian preference, (iv) convex dominance, and (v) mean -preserving -spread (dilation) for all priors as well as for a given full -support prior. We provide counterexamples to underscore the necessity of the assumptions underlying some of our findings, and offer a generalization of the Hirschleifer-Schlee theorem as an application.