Topologies on Type

Eddie Dekel and Drew Fudenberg

No 1417, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

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 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.

Keywords: rationalizability; incomplete informa- tion; common knowledge; universal type space; strategic topology. (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Date: 2006-01
New Economics Papers: this item is included in nep-gth and nep-knm
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Related works:
Journal Article: Topologies on types (2006)
Working Paper: Topologies on Types (2006)
Working Paper: Topologies on Types (2005)
Working Paper: Topologies on Types (2005)
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