Document Type
Discussion Paper
Publication Date
11-7-2024
CFDP Number
2413
CFDP Pages
65
Journal of Economic Literature (JEL) Code(s)
C72
Abstract
Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an “almost common knowledge topology” reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. An information structure is said to be simple if each player has a finite set of types and each type has a distinct first-order belief about payoff states. We show that simple information structures are dense in the almost common knowledge topology and thus it is without loss to restrict attention to simple information structures in information design problems.
Recommended Citation
Bergemann, Dirk; Morris, Stephen; and Veiel, Rafael, "A Strategic Topology on Information Structures" (2024). Cowles Foundation Discussion Papers. 2821.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2821