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Invariance under type morphisms: the bayesian Nash equilibrium

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  • Pintér, Miklós

Abstract

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38499.

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Date of creation: 2011
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Handle: RePEc:pra:mprapa:38499

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Keywords: Games with incomplete information; Bayesian Nash Equilibrium; Type space;

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  1. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on types," Theoretical Economics, Econometric Society, Econometric Society, vol. 1(3), pages 275-309, September.
  2. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 189-198, February.
  3. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
  5. Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December.
  7. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  8. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, INFORMS, vol. 14(3), pages 159-182, November.
  9. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer, Springer, vol. 46(3), pages 377-399, April.
  10. 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).
  11. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information, EconWPA 9609002, EconWPA, revised 17 Sep 1996.
  12. MERTENS, Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part C : Further Developments," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1994022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer, Springer, vol. 21(4), pages 329-338.
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