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A Strategic Topology on Information Structures

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  • Dirk Bergemann
  • Stephen Morris
  • Rafael Veiel

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.

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  • Dirk Bergemann & Stephen Morris & Rafael Veiel, 2024. "A Strategic Topology on Information Structures," Papers 2411.09149, arXiv.org.
    • Handle: RePEc:arx:papers:2411.09149
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    1. Van Zandt, Timothy, 2010. "Interim Bayesian Nash equilibrium on universal type spaces for supermodular games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 249-263, January.
    2. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    3. Hellman, Ziv, 2014. "A game with no Bayesian approximate equilibria," Journal of Economic Theory, Elsevier, vol. 153(C), pages 138-151.
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