IDEAS home Printed from https://ideas.repec.org/p/pri/metric/wp008.pdf.html
   My bibliography  Save this paper

Interdependent Preferences and Strategic Distinguishability

Author

Listed:
  • Dirk Bergemann

    (Yale University)

  • Stephen Morris

    (Princeton University)

  • Satoru Takahashi

    (Princeton University)

Abstract

A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types.

Suggested Citation

  • Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2010. "Interdependent Preferences and Strategic Distinguishability," Working Papers 1267, Princeton University, Department of Economics, Econometric Research Program..
  • Handle: RePEc:pri:metric:wp008.pdf
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d17/d1772.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    2. Ledyard, John O., 1986. "The scope of the hypothesis of Bayesian equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 59-82, June.
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    4. , & , & ,, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
    5. Jörgen W. Weibull, 2004. "Testing Game Theory," Palgrave Macmillan Books, in: Steffen Huck (ed.), Advances in Understanding Strategic Behaviour, chapter 6, pages 85-104, Palgrave Macmillan.
    6. Chambers, Christopher P. & Lambert, Nicolas S., 2014. "Dynamically Eliciting Unobservable Information," Research Papers 3036, Stanford University, Graduate School of Business.
    7. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2012. "The Strategic Impact of Higher-Order Beliefs," Cowles Foundation Discussion Papers 1875, Cowles Foundation for Research in Economics, Yale University.
    8. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-691, June.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    10. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-1373, November.
    11. 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.
    12. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    13. ,, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
    14. Chambers, Christopher P., 2008. "Proper scoring rules for general decision models," Games and Economic Behavior, Elsevier, vol. 63(1), pages 32-40, May.
    15. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    16. Ziv Hellman, 2012. "A Game with No Bayesian Approximate Equilibria," Discussion Paper Series dp615, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    17. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
    18. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    19. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    20. 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.
    21. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    22. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    23. Harry J. Paarsch & Han Hong, 2006. "An Introduction to the Structural Econometrics of Auction Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262162350, February.
    24. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
    25. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
    26. David K. Levine, 1998. "Modeling Altruism and Spitefulness in Experiment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 593-622, July.
    27. Stephen Morris & Satoru Takahashi, 2011. "Common Certainty of Rationality Revisited," Working Papers 1301, Princeton University, Department of Economics, Econometric Research Program..
    28. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    29. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    30. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    31. Hellman, Ziv, 2014. "A game with no Bayesian approximate equilibria," Journal of Economic Theory, Elsevier, vol. 153(C), pages 138-151.
    32. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    33. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    34. repec:esx:essedp:722 is not listed on IDEAS
    35. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    36. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    37. Stephen Morris & Satoru Takahashi, 2012. "Games in Preference Form and Preference Rationalizability," Working Papers 1420, Princeton University, Department of Economics, Econometric Research Program..
    38. 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.
    39. Gul, Faruk & Pesendorfer, Wolfgang, 2016. "Interdependent preference models as a theory of intentions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 179-208.
    40. 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).
    41. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    42. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    43. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
    44. Wolfgang Pesendorfer & Faruk Gul, 2007. "The Canonical Space for Behavioral Types," Levine's Bibliography 843644000000000345, UCLA Department of Economics.
    45. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    2. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    3. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers 151501, University of Queensland, School of Economics.
    4. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    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. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2012. "Efficient Auctions and Interdependent Types," American Economic Review, American Economic Association, vol. 102(3), pages 319-324, May.
    7. Daley, Brendan & Sadowski, Philipp, 2017. "Magical thinking: A representation result," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Stephen Morris & Satoru Takahashi, 2011. "Common Certainty of Rationality Revisited," Working Papers 1301, Princeton University, Department of Economics, Econometric Research Program..
    9. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    10. Gul, Faruk & Pesendorfer, Wolfgang, 2016. "Interdependent preference models as a theory of intentions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 179-208.
    11. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    12. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    13. Tsakas, Elias, 2018. "Robust scoring rules," Research Memorandum 023, Maastricht University, Graduate School of Business and Economics (GSBE).
    14. repec:pri:metric:wp023_2011_bergemann_morris.pdf is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. 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.
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    4. Gul, Faruk & Pesendorfer, Wolfgang, 2016. "Interdependent preference models as a theory of intentions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 179-208.
    5. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    6. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Jain, Ritesh & Lombardi, Michele, 2022. "Continuous virtual implementation: Complete information," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    8. 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.
    9. 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.
    10. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    11. Aviad Heifetz & Willemien Kets, 2013. "Robust Multiplicity with a Grain of Naiveté," Discussion Papers 1573, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Working Papers 2020-23, Brown University, Department of Economics.
    13. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    14. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    15. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    16. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    17. Pintér, Miklós, 2011. "Invariance under type morphisms: the bayesian Nash equilibrium," MPRA Paper 38499, University Library of Munich, Germany.
    18. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, vol. 7(4), pages 1-17, October.
    19. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    20. Kunimoto, Takashi, 2020. "Robust virtual implementation with almost complete information," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 62-73.

    More about this item

    Keywords

    independent preferences; higher order preference hierarchy; universal type space; strategic distinguishability;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pri:metric:wp008.pdf. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/exprius.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bobray Bordelon (email available below). General contact details of provider: https://edirc.repec.org/data/exprius.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.