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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 141 (2008)
Issue (Month): 1 (July)
Pages: 28-67

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Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:28-67

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
  5. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Leslie M. Marx & Jeroen M. Swinkels, 1996. "Order Independence for Iterated Weak Dominance," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1066R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  8. 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.
  9. Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, Econometric Society, vol. 1(1), pages 19-65, March.
  10. 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.
  11. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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Citations

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Cited by:
  1. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner’s Dilemma," Working Papers, University of California, Davis, Department of Economics 137, University of California, Davis, Department of Economics.
  2. Kamada, Yuichiro & Fudenberg, Drew, 0. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, Econometric Society.
  3. Pelosse, Yohan, 2011. "Ontological foundation of Nash Equilibrium," MPRA Paper 39934, University Library of Munich, Germany.
  4. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
  5. Du, Songzi, 2009. "Correlated Equilibrium via Hierarchies of Beliefs," MPRA Paper 16926, University Library of Munich, Germany.
  6. Adam Brandenburger, 2008. "The Relationship Between Classical and Quantum Correlation in Games," Levine's Working Paper Archive 122247000000002312, David K. Levine.
  7. Du, Songzi, 2008. "A Note on Intrinsic Correlation," MPRA Paper 12698, University Library of Munich, Germany, revised 12 Jan 2009.
  8. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(5), pages 2115-2145, September.
  9. 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, MDPI, Open Access Journal, vol. 2(1), pages 52-86, February.
  10. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.
  11. Pelosse, Yohan, 2009. "Mediated Contests and Strategic Foundations for Contest Success Functions," MPRA Paper 18664, University Library of Munich, Germany.
  12. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
  13. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer, Springer, vol. 46(3), pages 377-399, April.
  14. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
  15. Du, Songzi, 2012. "Correlated equilibrium and higher order beliefs about play," Games and Economic Behavior, Elsevier, vol. 76(1), pages 74-87.

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