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Quotient spaces of boundedly rational types

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Abstract

By identifying types whose low-order beliefs – up to level li – about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash (li; l-i)-equilibria capture players’ inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustrate the constructions.

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  • Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient spaces of boundedly rational types," Economics Working Papers 1287, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1287
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    1. Camille Cornand & Frank Heinemann, 2014. "Measuring agents’ reaction to private and public information in games with strategic complementarities," Experimental Economics, Springer;Economic Science Association, vol. 17(1), pages 61-77, March.
    2. Jehiel, Philippe & Koessler, Frédéric, 2008. "Revisiting games of incomplete information with analogy-based expectations," Games and Economic Behavior, Elsevier, vol. 62(2), pages 533-557, March.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, April.
    5. Tyran, Jean-Robert, 2003. "Behavioral Game Theory. Experiments in Strategic Interaction: Colin F. Camerer, Princeton University Press, Princeton, New Jersey, 2003, p. 550, Price $65.00/[UK pound]42.95, ISBN 0-691-09039-4," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 32(6), pages 717-720, December.
    6. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    7. 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.
    8. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    10. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    11. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    13. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    14. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    15. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    16. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    17. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
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    Cited by:

    1. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.

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    More about this item

    Keywords

    Incomplete-information games; high-order reasoning; type space; quotient space; hierarchies of beliefs; bounded rationality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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