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Topologies on Types

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  • 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.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000061.

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Date of creation: 31 Aug 2005
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Handle: RePEc:cla:levrem:784828000000000061

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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. Atsushi Kajii & Stephen Morris, 1997. "Payoff Continuity in Incomplete Information Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1193R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics.
  4. Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers, Boston University - Industry Studies Programme 0093, Boston University - Industry Studies Programme.
  5. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
  6. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(2), pages 324-341, October.
  7. Philippe Jehiel & Benny Moldovanu, 1998. "Efficient Design with Interdependent Valuations," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1244, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
  9. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1421R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2004.
  10. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  11. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, Econometric Society, vol. 74(1), pages 213-233, 01.
  12. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, Elsevier, vol. 28(1), pages 192-200, October.
  13. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, American Economic Association, vol. 85(3), pages 291-303, June.
  14. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 345-61, March.
  15. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 395-421, March.
  16. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics.
  17. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  18. Barton L. Lipman, 1997. "Finite Order Implications of Common Priors," Game Theory and Information, EconWPA 9703005, EconWPA.
  19. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, American Economic Association, vol. 79(3), pages 385-91, June.
  20. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 189-198, February.
  22. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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