Value-based distance between information structures

• 成果类型: Article
• 署名作者: Gensbittel, Fabien; Peski, Marcin; Renault, Jerome
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; University of Toronto
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4782
• 发表日期: 2022-07-01
• 页码: 1225-1267
• 关键词: Value of information; universal type space; c7

摘要

We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of information in games versus single-agent problems, the value of additional information, informational substitutes, complements, or joint information. The convergence to a countable information structure under value-based distance is equivalent to the weak convergence of belief hierarchies, implying, among other things, that for zero-sum games, approximate knowledge is equivalent to common knowledge. At the same time, the space of information structures under the value-based distance is large: there exists a sequence of information structures where players acquire increasingly more information, and epsilon > 0 such that any two elements of the sequence have distance of at least epsilon. This result answers by the negative the second (and last unsolved) of the three problems posed by Mertens in his paper Repeated Games (1986).