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 be- tween a pair of types as the di¤erence between the smallest " for which the action is " 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 " does not jump either up or down in the limit. As applied to sequences, the upper-semicontinuity prop- erty 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 Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number
1417.
Length: Date of creation: Jan 2006 Date of revision: Handle: RePEc:nwu:cmsems:1417
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Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006.
"Topologies on types,"
Theoretical Economics,
Society for Economic Theory, vol. 1(3), pages 275-309, September.
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Paper
Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005.
"Topologies on Types,"
Levine's Bibliography
784828000000000061, UCLA Department of Economics.
[Downloadable!]
Find related papers by JEL classification: C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Eddie Dekel & Drew Fudenberg & David K. Levine, 2000.
"Learning to Play Bayesian Games,"
Discussion Papers
1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
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Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005.
"Interim Rationalizability,"
Levine's Bibliography
666156000000000526, UCLA Department of Economics.
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