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Title:Topologies on types PDF Logo
Authors:Dekel, Eddie
Fudenberg, Drew
Morris, Stephen
Issue Date:2006
Series/Report no.:Discussion paper // Center for Mathematical Studies in Economics and Management Science 1417
Abstract:We de.ne 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 .xed game and action de.ne the distance be-tween a pair of types as the diĆ¾erence between the smallest for which the action is interim correlated rationalizable. We de.ne 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 .nite types (types describable by .nite type spaces) is dense but the set of .nite common-prior types is not.
Subjects:rationalizability
incomplete information
common knowledge
universal type space
strategic topology.
JEL:C70
C72
Document Type:Working Paper
Appears in Collections:Discussion Papers, Kellogg School of Management, Northwestern University

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