Topologies on Types

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Topologies on Types

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Eddie Dekel
Drew Fudenberg
Stephen Morris

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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 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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Article
- Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on types," Theoretical Economics, Society for Economic Theory, vol. 1(3), pages 275-309, September. [Downloadable!]
Paper
- Eddie Dekel & Drew Fudenberg, 2006. "Topologies on Type," Discussion Papers 1417, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
- Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Levine's Bibliography 784828000000000061, UCLA Department of Economics. [Downloadable!]

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February. [Downloadable!] (restricted)
Other versions:
- Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001. [Downloadable!]
- Eddie Dekel & Drew Fudenberg & David K Levine, 2002. "Learning to Play Bayesian Games," Levine's Working Paper Archive 625018000000000151, David K. Levine. [Downloadable!]
- Eddie Dekel & Drew Fudenberg & David K. Levine, 2001. "Learning to Play Bayesian Games," Harvard Institute of Economic Research Working Papers 1926, Harvard - Institute of Economic Research. [Downloadable!]
Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April. [Downloadable!] (restricted)
Other versions:
- Drew Fudenberg & David K. Levine, 1986. "Limit Games and Limit Equilibria," Levine's Working Paper Archive 220, David K. Levine. [Downloadable!]
- Drew Fudenberg & David Levine, 1983. "Limit Games and Limit Equilibria," UCLA Economics Working Papers 289, UCLA Department of Economics. [Downloadable!]
Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October. [Downloadable!] (restricted)
Philippe Jehiel & Benny Moldovanu, 1998. "Efficient Design with Interdependent Valuations," Discussion Papers 1244, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Other versions:
- Jehiel, Phillipe & Moldovanu, Benny, 1998. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 98-22, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
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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. [Downloadable!] (restricted)
MERTENSÊ, Jean-Franois & SORINÊ, Sylvain & ZAMIRÊ, Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics. [Downloadable!]
Other versions:
- Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Harvard Institute of Economic Research Working Papers 2064, Harvard - Institute of Economic Research. [Downloadable!]
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. [Downloadable!] (restricted)
Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Society for Economic Theory, vol. 1(1), pages 19-65, March. [Downloadable!]
Other versions:
- Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics. [Downloadable!]
- 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. [Downloadable!]
Barton L. Lipman, 1997. "Finite Order Implications of Common Priors," Game Theory and Information 9703005, EconWPA. [Downloadable!]
Other versions:
- Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, 07. [Downloadable!] (restricted)
Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine. [Downloadable!]
Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," NajEcon Working Paper Reviews 666156000000000593, www.najecon.org. [Downloadable!]
Other versions:
- Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation, Yale University. [Downloadable!]
- Stephen Morris & Dirk Bergemann, 2004. "Robust Mechanism Design," Yale School of Management Working Papers ysm380, Yale School of Management. [Downloadable!]
- Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation, Yale University, revised Apr 2004. [Downloadable!]
- Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Levine's Bibliography 666156000000000035, UCLA Department of Economics. [Downloadable!]
- Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November. [Downloadable!] (restricted)
Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
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- Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee. [Downloadable!]
McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March. [Downloadable!] (restricted)
Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, 01. [Downloadable!] (restricted)
Other versions:
- Aviad Heifetz & Zvika Neeman, 2004. "On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design," Discussion Paper Series dp350, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
Pierpaolo Battigalli & Marciano Siniscalchi, 2003. "Rationalization and Incomplete Information," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 3(1), pages 1073-1073. [Downloadable!] (restricted)
Other versions:
- P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine. [Downloadable!]
Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July. [Downloadable!] (restricted)
Other versions:
- Neeman, Z., 1998. "The Relevance of Private Infromation in Mechanism Design," Papers 93, Boston University - Department of Economics.
- Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers 0093, Boston University - Industry Studies Programme.
Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
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. [Downloadable!]
Other versions:
- Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September. [Downloadable!] (restricted)
Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Levine's Bibliography 122247000000001569, UCLA Department of Economics. [Downloadable!]
Other versions:
- Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation, Yale University. [Downloadable!]
Wolfgang Pesendorfer & Faruk Gul, 2007. "The Canonical Space for Behavioral Types," Levine's Bibliography 843644000000000345, UCLA Department of Economics. [Downloadable!]
Pierpaolo Battigalli & Alfredo Di Tillio & Edoardo Grillo & Antonio Penta, 2008. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," Working Papers 340, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics. [Downloadable!]
Other versions:
- Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Society for Economic Theory, vol. 2(1), pages 15-40, March. [Downloadable!]

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