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Topologies on Types

  • Eddie Dekel
  • Drew Fudenberg
  • Stephen Morris

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.

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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2093.

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Date of creation: 2005
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Handle: RePEc:fth:harver:2093
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  1. Drew Fudenberg & David K. Levine, 1986. "Limit Games and Limit Equilibria," Levine's Working Paper Archive 220, David K. Levine.
  2. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
  3. Eddie Dekel & Drew Fudenberg & David K Levine, 2002. "Learning to Play Bayesian Games," Levine's Working Paper Archive 625018000000000151, David K. Levine.
  4. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics.
  5. Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers 0093, Boston University - Industry Studies Programme.
  6. Aviad Heifetz & Zvika Neeman, 2004. "On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design," Discussion Paper Series dp350, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  7. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  8. Atsushi Kajii & Stephen Morris, 1997. "Payoff Continuity in Incomplete Information Games," Discussion Papers 1193R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
  10. Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-59, September.
  12. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, 07.
  13. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  14. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  15. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  16. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  17. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
  18. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  19. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  20. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  21. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
  22. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
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