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Topologies on Types: Connections

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  • Yi-Chun Chen
  • Siyang Xiong

Abstract

For different purposes, economists may use different topologies on types. We char- acterize the relationship among these various topologies. First, we show that for any general types, convergence in the uniform-weak topology implies convergence in both the strategic topology and the uniform strategic topology. Second, we explicitly con- struct a type which is not the limit of any finite types under the uniform strategic topology, showing that the uniform strategic topology is strictly fi ner than the strategic topology. With these results, we can linearly rank various topologies on the universal type space, which gives a clear picture of the relationship between the implication of types for beliefs and their implication for behaviors.

Suggested Citation

  • Yi-Chun Chen & Siyang Xiong, 2008. "Topologies on Types: Connections," Discussion Papers 1470, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1470
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    References listed on IDEAS

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    1. James Heckman & Flavio Cunha, 2007. "The Technology of Skill Formation," American Economic Review, American Economic Association, vol. 97(2), pages 31-47, May.
    2. Angrist, Joshua D. & Guryan, Jonathan, 2008. "Does teacher testing raise teacher quality? Evidence from state certification requirements," Economics of Education Review, Elsevier, vol. 27(5), pages 483-503, October.
    3. Betts, Julian R, 1998. "The Impact of Educational Standards on the Level and Distribution of Earnings," American Economic Review, American Economic Association, vol. 88(1), pages 266-275, March.
    4. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    5. Kane, Thomas J. & Rockoff, Jonah E. & Staiger, Douglas O., 2008. "What does certification tell us about teacher effectiveness? Evidence from New York City," Economics of Education Review, Elsevier, vol. 27(6), pages 615-631, December.
    6. Julian R. Betts & Robert M. Costrell, 2000. "Incentives and Equity Under Standards-Based Reform," UMASS Amherst Economics Working Papers 2000-08, University of Massachusetts Amherst, Department of Economics.
    7. Carl Shapiro, 1986. "Investment, Moral Hazard, and Occupational Licensing," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 843-862.
    8. Costrell, Robert M, 1994. "A Simple Model of Educational Standards," American Economic Review, American Economic Association, vol. 84(4), pages 956-971, September.
    9. Morris M. Kleiner, 2000. "Occupational Licensing," Journal of Economic Perspectives, American Economic Association, vol. 14(4), pages 189-202, Fall.
    10. James J. Heckman & John Eric Humphries & Paul A. LaFontaine & Pedro L. Rodríguez, 2012. "Taking the Easy Way Out: How the GED Testing Program Induces Students to Drop Out," Journal of Labor Economics, University of Chicago Press, vol. 30(3), pages 495-520.
    11. Derek Neal, 2002. "How Vouchers Could Change the Market for Education," Journal of Economic Perspectives, American Economic Association, vol. 16(4), pages 25-44, Fall.
    12. Hanushek, Eric A. & Rivkin, Steven G., 2006. "Teacher Quality," Handbook of the Economics of Education, Elsevier.
    13. Gottlieb, Daniel & Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de, 2004. "A model of mixed signals with applications to countersignaling an the GED," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 553, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    14. Thomas S. Dee & Brian A. Jacob, 2006. "Do High School Exit Exams Influence Educational Attainment or Labor Market Performance?," NBER Working Papers 12199, National Bureau of Economic Research, Inc.
    15. Roger Klein & Richard Spady & Andrew Weiss, 1991. "Factors Affecting the Output and Quit Propensities of Production Workers," Review of Economic Studies, Oxford University Press, vol. 58(5), pages 929-953.
    16. Yona Rubinstein & James J. Heckman, 2001. "The Importance of Noncognitive Skills: Lessons from the GED Testing Program," American Economic Review, American Economic Association, vol. 91(2), pages 145-149, May.
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    More about this item

    Keywords

    the universal type space; the strategic topology; the uniform strategic topology; the uniform-weak topology; interim correlated rationalizable actions;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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