Topologies on Types

37 Pages Posted: 8 Sep 2005

See all articles by Eddie Dekel

Eddie Dekel

Northwestern University - Department of Economics; Tel Aviv University - Eitan Berglas School of Economics

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Stephen Morris

Princeton University - Department of Economics

Date Written: September 2005


We define and analyze strategic topologies on types, under which two types are close if their strategic behavior will be similar in all strategic situations. To operationalize this idea, we adopt interim rationalizability as our solution concept, and define a metric topology on types in the Harsanyi-Mertens-Zamir universal type space. This topology is the coarsest metric topology generating upper and lower hemicontinuity of rationalizable outcomes. While upper strategic convergence is equivalent to convergence in the product topology, lower strategic convergence is a strictly stronger requirement, as shown by the electronic mail game. Nonetheless, we show that the set of finite types (types describable by finite type spaces) are dense in the lower strategic topology.

Keywords: rationalizability, incomplete information, common knowledge, universal type space, strategic topology

JEL Classification: C70, C72

Suggested Citation

Dekel-Tabak, Eddie and Fudenberg, Drew and Morris, Stephen Edward, Topologies on Types (September 2005). Harvard Institute of Economic Research Discussion Paper No. 2093. Available at SSRN: or

Eddie Dekel-Tabak

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

Tel Aviv University - Eitan Berglas School of Economics ( email )

P.O. Box 39040
Ramat Aviv, Tel Aviv, 69978
(972) 3-6409715 (Phone)
(972) 3-6409908 (Fax)

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Stephen Edward Morris

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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