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Dual Reduction and Elementary Games

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Author Info
Roger B. Myerson

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Abstract

Consider the linear incentive constraints that define the correlated equilibria of a game. The duals of these constraints generate Markov chains on the players' strategy sets. The stationary distributions for these Markov chains can be interpreted as the strategies in a reduced game, which is called a dual reduction. Any equilibrium of a dual reduction is an equilibrium of the original game. We say that a game is elementary if all incentive constraints can be satisfied as strict inequalities in a correlated equilibrium. Any game can be reduced to an elementary game by iterative dual reduction.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1133.

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Date of creation: Jun 1995
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Handle: RePEc:nwu:cmsems:1133

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References listed on IDEAS
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  1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  2. DHILLON, Amrita & MERTENS, Jean-Franois, 1992. "Perfect correlated equilibria," CORE Discussion Papers 1992039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  3. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer, vol. 15(3), pages 133-54.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997. [Downloadable!]
    Other versions:
  2. AUMANN, Robert J. & DREZE, Jacques H., 2005. "When all is said and done, how should you play and what should you expect ?," CORE Discussion Papers 2005021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  3. Itai Arieli, 2008. "Towards a Characterization of Rational Expectations," Levine's Bibliography 122247000000001891, UCLA Department of Economics. [Downloadable!]
  4. Ichiro Obara, . "Approximate Implementability with Ex Post Budget Balance (Joint with D. Rahman)," UCLA Economics Online Papers 399, UCLA Department of Economics. [Downloadable!]
  5. Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," Working Paper Series in Economics and Finance 641, Stockholm School of Economics. [Downloadable!]
  6. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953_v1, HAL. [Downloadable!]
  7. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993_v1, HAL. [Downloadable!]
  8. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991_v1, HAL. [Downloadable!]
  9. Du, Songzi, 2009. "Correlated Equilibrium via Hierarchies of Beliefs," MPRA Paper 16926, University Library of Munich, Germany. [Downloadable!]
  10. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992_v1, HAL. [Downloadable!]
  11. Ichiro Obara & David Rahman, 2006. "Approximate Implementability with Ex Post Budget Balance," Levine's Bibliography 321307000000000280, UCLA Department of Economics. [Downloadable!]
  12. Itai Arieli, 2008. "Towards a Characterization of Rational Expectations," Discussion Paper Series dp475, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  13. Itai Arieli, 2008. "Towards a Characterization of Rational," Levine's Working Paper Archive 122247000000002431, David K. Levine. [Downloadable!]
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