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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.

Suggested Citation

  • 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.
  • Handle: RePEc:igi:igierp:340
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2014. "Informational Robustness and Solution Concepts," Cowles Foundation Discussion Papers 1973, Cowles Foundation for Research in Economics, Yale University.
    2. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    3. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society.
    4. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    5. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    6. Cappelletti Giuseppe, 2010. "A Note on Rationalizability and Restrictions on Beliefs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-13, September.
    7. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    8. Pierpaolo Battigalli & Gabriele Beneduci & Pietro Tebaldi, 2017. "Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies," Working Papers 602, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    9. Robles Jack & Shimoji Makoto, 2012. "On Rationalizability and Beliefs in Discrete Private-Value First-Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-21, May.
    10. repec:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0547-5 is not listed on IDEAS
    11. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    12. Willemien Kets, 2014. "Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information," Discussion Papers 1569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Astrid Gamba, 2011. "On the Evolution of Preferences," Jena Economic Research Papers 2011-032, Friedrich-Schiller-University Jena.
    14. Esponda, Ignacio, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
    15. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    16. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
    17. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    18. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    19. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    20. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.
    21. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.
    22. Du, Songzi, 2012. "Correlated equilibrium and higher order beliefs about play," Games and Economic Behavior, Elsevier, vol. 76(1), pages 74-87.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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