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Dual Reduction and Elementary Games

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  • Roger B. Myerson

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.

Suggested Citation

  • Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • 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.
    2. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 133-154.
    3. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    4. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    5. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
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    Cited by:

    1. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    2. Ichiro Obara, "undated". "Approximate Implementability with Ex Post Budget Balance (Joint with D. Rahman)," UCLA Economics Online Papers 399, UCLA Department of Economics.
    3. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    4. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    5. David Rahman, 2012. "But Who Will Monitor the Monitor?," American Economic Review, American Economic Association, vol. 102(6), pages 2767-2797, October.
    6. Itai Arieli, 2008. "Towards a Characterization of Rational Expectations," Discussion Paper Series dp475, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    8. repec:dau:papers:123456789/3048 is not listed on IDEAS
    9. R.J., AUMANN & Jacques-Henri, DREZE, 2005. "When All is Said and Done, How Should You Play and What Should You Expect ?," Discussion Papers (ECON - Département des Sciences Economiques) 2005021, Université catholique de Louvain, Département des Sciences Economiques.
    10. repec:dau:papers:123456789/882 is not listed on IDEAS
    11. Robert Nau & Sabrina G Canovas & Pierre Hansen, 2005. "On the Geometry of Nash Equilibria and Correlated Equilibria," Levine's Bibliography 618897000000000961, UCLA Department of Economics.
    12. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    13. Itai Arieli, 2008. "Towards a Characterization of Rational," Levine's Working Paper Archive 122247000000002431, David K. Levine.
    14. Itai Arieli, 2008. "Towards a Characterization of Rational Expectations," Levine's Bibliography 122247000000001891, UCLA Department of Economics.
    15. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
    16. Jiang, Albert Xin & Leyton-Brown, Kevin, 2015. "Polynomial-time computation of exact correlated equilibrium in compact games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 347-359.
    17. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953, HAL.
    18. Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," SSE/EFI Working Paper Series in Economics and Finance 641, Stockholm School of Economics.
    19. Du, Songzi, 2009. "Correlated Equilibrium via Hierarchies of Beliefs," MPRA Paper 16926, University Library of Munich, Germany.
    20. repec:dau:papers:123456789/5219 is not listed on IDEAS
    21. Ichiro Obara & David Rahman, 2006. "Approximate Implementability with Ex Post Budget Balance," Levine's Bibliography 321307000000000280, UCLA Department of Economics.
    22. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    23. Hwang, Sung-Ha & Rey-Bellet, Luc, 2020. "Strategic decompositions of normal form games: Zero-sum games and potential games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 370-390.

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