IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v5y2015i1p120-135.html
   My bibliography  Save this article

Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs

Author

Listed:
  • Ayala Mashiah-Yaakovi

Abstract

An autonomous correlation device in a multistage game is a device that, before every stage, chooses for each player a private signal, possibly in a correlated way, and reveals to each player the signal chosen for him. The chosen signals depend only on previous signals, and not on the actions of the players. An extensive-form correlated $$\varepsilon $$ ε -equilibrium in a multistage game is an $$\varepsilon $$ ε -equilibrium in an extended game that includes an autonomous correlation device. In this paper we prove that every stochastic game with Borel measurable bounded payoffs has an extensive-form correlated $$\varepsilon $$ ε -equilibrium, for every $$\varepsilon >0$$ ε > 0 . Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:1:p:120-135
    DOI: 10.1007/s13235-014-0122-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-014-0122-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-014-0122-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. Maitra & W. Sudderth, 1998. "Finitely additive stochastic games with Borel measurable payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 257-267.
    2. MERTENS, Jean-François, 1987. "Repeated games. Proceedings of the International Congress of Mathematicians," LIDAM Reprints CORE 788, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    6. Eilon Solan, 2001. "Characterization of correlated equilibria in stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 259-277.
    7. repec:dau:papers:123456789/6019 is not listed on IDEAS
    8. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Eilon Solan, 1999. "Three-Player Absorbing Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 669-698, August.
    10. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    11. repec:dau:papers:123456789/6017 is not listed on IDEAS
    12. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    13. FORGES, Françoise, 1988. "Communication equilibria in repeated games with incomplete information," LIDAM Reprints CORE 809, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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..
    15. 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..
    16. Françoise Forges, 1988. "Communication Equilibria in Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 191-231, May.
    17. Mertens, J.-F., 1994. "Correlated- and communication equilibria," LIDAM Reprints CORE 1103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
    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. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2021. "Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels," Dynamic Games and Applications, Springer, vol. 11(4), pages 704-737, December.
    2. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.

    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. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    2. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    3. Bernhard von Stengel & Françoise Forges, 2008. "Extensive-Form Correlated Equilibrium: Definition and Computational Complexity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 1002-1022, November.
    4. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    5. Ray, Indrajit, 1996. "Efficiency in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 32(3), pages 157-178, December.
    6. Heng Liu, 2017. "Correlation and unmediated cheap talk in repeated games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1037-1069, November.
    7. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.
    8. Pavlo Prokopovych & Lones Smith, 2004. "Subgame Perfect Correlated Equilibria in Repeated Games," Econometric Society 2004 North American Summer Meetings 287, Econometric Society.
    9. Forgó, Ferenc, 2010. "A generalization of correlated equilibrium: A new protocol," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 186-190, November.
    10. Chirantan Ganguly & Indrajit Ray, 2023. "Simple Mediation in a Cheap-Talk Game," Games, MDPI, vol. 14(3), pages 1-14, June.
    11. 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..
    12. John Duffy & Ernest K. Lai & Wooyoung Lim, 2017. "Coordination via correlation: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 265-304, August.
    13. Rabah Amir & Sergei Belkov & Igor V. Evstigneev, 2017. "Correlated equilibrium in a nutshell," Theory and Decision, Springer, vol. 83(4), pages 457-468, December.
    14. Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).
    15. Ricardo Gonçalves, 2008. "A communication equilibrium in English auctions with discrete bidding," Working Papers de Economia (Economics Working Papers) 042008, Católica Porto Business School, Universidade Católica Portuguesa.
    16. Ferenc Forgó, 2011. "Generalized correlated equilibrium for two-person games in extensive form with perfect information," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 201-213, June.
    17. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
    18. Arce M. D. G., 1996. "The economic consequences of the peace: Keynes and correlation," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 50-50, February.
    19. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    20. Ramsey, David M. & Szajowski, Krzysztof, 2004. "Correlated equilibria in competitive staff selection problem," MPRA Paper 19870, University Library of Munich, Germany, revised 2006.

    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:spr:dyngam:v:5:y:2015:i:1:p:120-135. See general information about how to correct material in RePEc.

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.