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Topologies on Types

Author

Listed:
  • Eddie Dekel
  • Drew Fudenberg
  • Stephen Morris

Abstract

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 oper- ationalize 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 hemiconti- nuity 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.

Suggested Citation

  • Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Harvard Institute of Economic Research Working Papers 2093, Harvard - Institute of Economic Research.
  • Handle: RePEc:fth:harver:2093
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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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