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Topologies on Types

Author

Listed:
  • Eddie Dekel
  • Drew Fudenberg
  • Stephen Morris
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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Levine's Bibliography 784828000000000061, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:784828000000000061
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    File URL: http://www.princeton.edu/%7Esmorris/pdfs/tot.pdf
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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