Value-Based Distance Between Information Structures

Fabien Gensbittel, Marcin Peski and Jérôme Renault
Additional contact information
Marcin Peski: University of Toronto

Post-Print from HAL

Abstract: 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 ε > 0 such that any two elements of the sequence have distance of at least ε. This result answers by the negative the second (and last unsolved) of the three problems posed by J.F. Mertens in his paper Repeated Games , ICM 1986.

Date: 2022
New Economics Papers: this item is included in nep-gth, nep-mic and nep-ure
Note: View the original document on HAL open archive server: https://hal.science/hal-01869139v3
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Theoretical Economics, 2022

Downloads: (external link)
https://hal.science/hal-01869139v3/document (application/pdf)

Related works:
Journal Article: Value-based distance between information structures (2022)
Working Paper: Value-based distance between information structures (2022)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01869139

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().