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Intrinsic correlation in games

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  • Brandenburger, Adam
  • Friedenberg, Amanda

Abstract

Correlations arise naturally in non-cooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the non-cooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? The epistemic view of games gives an answer. Under this view, the players' hierarchies of beliefs (beliefs, beliefs about beliefs, etc.) about the strategies played in the game are part of the description of a game. This gives a source of correlation: A player believes other players' strategy choices are correlated, because he believes their hierarchies of beliefs are correlated. We refer to this kind of correlation as "intrinsic," since it comes from variables--viz., the hierarchies of beliefs--that are part of the game. We compare the intrinsic route with the "extrinsic" route taken by Aumann [Subjectivity and correlation in randomized strategies, J. Math. Econ. 1 (1974) 76-96], which adds signals to the original game.

Suggested Citation

  • Brandenburger, Adam & Friedenberg, Amanda, 2008. "Intrinsic correlation in games," Journal of Economic Theory, Elsevier, vol. 141(1), pages 28-67, July.
  • Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:28-67
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    Citations

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    Cited by:

    1. Johan Van Benthem & Eric Pacuit & Olivier Roy, 2011. "Toward a Theory of Play: A Logical Perspective on Games and Interaction," Games, MDPI, Open Access Journal, vol. 2(1), pages 1-35, February.
    2. Dirk Bergemann & Stephen Morris, 2014. "Informational Robustness and Solution Concepts," Cowles Foundation Discussion Papers 1973, Cowles Foundation for Research in Economics, Yale University.
    3. Du, Songzi, 2008. "A Note on Intrinsic Correlation," MPRA Paper 12698, University Library of Munich, Germany, revised 12 Jan 2009.
    4. Adam Brandenburger, 2007. "A Connection Between Correlation in Game Theory and Quantum Mechanics," Levine's Working Paper Archive 122247000000001725, David K. Levine.
    5. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    6. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    7. Pelosse, Yohan, 2009. "Mediated Contests and Strategic Foundations for Contest Success Functions," MPRA Paper 18664, University Library of Munich, Germany.
    8. Pelosse, Yohan, 2011. "Ontological foundation of Nash Equilibrium," MPRA Paper 39934, University Library of Munich, Germany.
    9. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    10. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    11. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    12. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    13. Adam Brandenburger, 2008. "The Relationship Between Classical and Quantum Correlation in Games," Levine's Working Paper Archive 122247000000002312, David K. Levine.
    14. Du, Songzi, 2009. "Correlated Equilibrium via Hierarchies of Beliefs," MPRA Paper 16926, University Library of Munich, Germany.
    15. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.
    16. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    17. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    18. Perea Andrés, 2006. "Nash Equilibrium as an Expression of Self-Referential Reasoning," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    19. Kamada, Yuichiro & Fudenberg, Drew, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    20. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.
    21. 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:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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