Northwestern University and Tel Aviv University

We de\u85ne 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 \u85xed game and action de\u85ne the distance be-tween a pair of types as the di¤erence between the smallest " for which the action is " interim correlated rationalizable. We de\u85ne 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 "\u85 nite types " (types describable by \u85nite type spaces) is dense but the set of \u85nite common-prior types is not