Topologies on types

Eddie Dekel, Drew Fudenberg, Stephen Morris

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)275-309
JournalTheoretical Economics
Issue number3
StatePublished - 2006


Dive into the research topics of 'Topologies on types'. Together they form a unique fingerprint.

Cite this