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Interactive Epistemology and Solution Concepts for Games with Asymmetric Information

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  • Pierpaolo Battigalli
  • Alfredo Di Tillio
  • Edoardo Grillo
  • Antonio Penta

Abstract

We use an interactive epistemology framework to provide a systematic analysis of some solu- tion concepts for games with asymmetric information. We characterize solution concepts using expressible epistemic assumptions, represented as events in the canonical space generated by primitive uncertainty about the payoff relevant state, payoff irrelevant information, and actions. In most of the paper we adopt an interim perspective, which is appropriate to analyze genuine incomplete information. We relate Delta-rationalizability (Battigalli and Siniscalchi, 2003) to interim correlated rationalizability (Dekel, Fudenberg, and Morris, 2007) and to rationalizability in the interim strategic form. We also consider the ex ante perspective, which is appropriate to ana- lyze asymmetric information about an initial chance move. We prove the equivalence between interim correlated rationalizability and an ex ante notion of correlated rationalizability.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 340.

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Date of creation: 2008
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Handle: RePEc:igi:igierp:340

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  1. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(2), pages 370-391, August.
  2. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1629, Cowles Foundation for Research in Economics, Yale University.
  3. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(2), pages 324-341, October.
  4. Carlsson, H. & Damme, E.E.C. van, 1990. "Global games and equilibrium selection," Discussion Paper, Tilburg University, Center for Economic Research 1990-52, Tilburg University, Center for Economic Research.
  5. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 3(1), pages 1-46, June.
  6. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics.
  7. John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
  8. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 2093, Harvard - Institute of Economic Research.
  9. Stephen Morris & Hyun Song Shin, 2007. "Common Belief Foundations of Global Games," Levine's Bibliography 122247000000001638, UCLA Department of Economics.
  10. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, Elsevier, vol. 57(1), pages 1-38, March.
  11. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1519, Cowles Foundation for Research in Economics, Yale University.
  12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262650401, December.
  13. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  14. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, Elsevier, vol. 61(4), pages 165-184, December.
  15. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262562006, December.
  16. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 74(1), pages 40-61, May.
  17. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, Elsevier, vol. 106(2), pages 356-391, October.
  18. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  19. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
  20. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, Econometric Society, vol. 75(2), pages 365-400, 03.
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Citations

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Cited by:
  1. Aviad Heifetz & Willemien Kets, 2013. "Robust Multiplicity with a Grain of Naiveté," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1573, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(2), May.
  3. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(2), pages 424-447.
  4. Astrid Gamba, 2011. "On the Evolution of Preferences," Jena Economic Research Papers, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics 2011-032, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  5. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2010. "Interdependent Preferences and Strategic Distinguishability," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1772RR, Cowles Foundation for Research in Economics, Yale University, revised Jul 2014.
  6. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, Elsevier, vol. 61(4), pages 165-184, December.
  7. Willemien Kets, 2013. "Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Du, Songzi, 2012. "Correlated equilibrium and higher order beliefs about play," Games and Economic Behavior, Elsevier, Elsevier, vol. 76(1), pages 74-87.
  9. Makoto Shimoji & Paul Schweinzer, 2012. "Implementation without Incentive Compatibility: Two Stories with Partially Informed Planners," Discussion Papers, Department of Economics, University of York 12/21, Department of Economics, University of York.
  10. Esponda, Ignacio, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(2), May.

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