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Topologies on Types

  • Dekel, Eddie
  • Fudenberg, Drew
  • Morris, Stephen

We define and analyze a "strategic topology'' on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference between the smallest epsilon for which the action is epsilon interim correlated rationalizable. We define a strategic topology in which a sequence of types converges if and only if this distance tends to zero for any action and game. Thus a sequence of types converges in the strategic topology if that smallest epsilon does not jump either up or down in the limit. As applied to sequences, the upper-semicontinuity property is equivalent to convergence in the product topology, but the lower-semicontinuity property is a strictly stronger requirement, as shown by the electronic mail game. In the strategic topology, the set of "finite types'' (types describable by finite type spaces) is dense but the set of finite common-prior types is not.

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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3160489.

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Date of creation: 2006
Date of revision:
Publication status: Published in Theoretical Economics
Handle: RePEc:hrv:faseco:3160489
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  1. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  2. Jehiel, Phillipe & Moldovanu, Benny, 1999. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 99-74, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  3. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  4. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
  5. Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
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  8. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics.
  9. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
  10. Fudenberg, Drew & Levine, David, 1986. "Limit Games and Limit Equilibria," Scholarly Articles 3350443, Harvard University Department of Economics.
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  17. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
  18. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
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  22. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
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