Topologies on types

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,: Northwestern University and Tel Aviv University
,: Harvard University
,: Princeton University
Authors registered in the RePEc Author Service: Eddie Dekel, Stephen Morris and Drew Fudenberg

Theoretical Economics, 2006, vol. 1, issue 3, 275-309

Abstract: 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.

Keywords: Rationalizability; incomplete information; common knowledge; universal type space; strategic topology (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Date: 2006-09-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (49)

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Related works:
Working Paper: Topologies on Types (2006)
Working Paper: Topologies on Type (2006)
Working Paper: Topologies on Types (2005)
Working Paper: Topologies on Types (2005)
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