A Strategic Topology on Information Structures

Dirk Bergemann, Stephen Morris and Rafael Veiel

No 2413, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 Òalmost common knowledge topologyÓ 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.

Pages: 65 pages
Date: 2024-11
New Economics Papers: this item is included in nep-des, nep-gth and nep-mic
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Working Paper: A Strategic Topology on Information Structures (2024)
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