IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v32y2003i1p133-150.html
   My bibliography  Save this article

The MaxMin value of stochastic games with imperfect monitoring

Author

Listed:
  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

Abstract

We study finite zero-sum stochastic games in which players do not observe the actions of their opponent. Rather, at each stage, each player observes a stochastic signal that may depend on the current state and on the pair of actions chosen by the players. We assume that each player observes the state and his/her own action. We prove that the uniform max-min value always exists. Moreover, the uniform max-min value is independent of the information structure of player 2. Symmetric results hold for the uniform min-max value. Copyright Springer-Verlag 2003

Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "The MaxMin value of stochastic games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 133-150, December.
    • Handle: RePEc:spr:jogath:v:32:y:2003:i:1:p:133-150
    DOI: 10.1007/s001820300150
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001820300150
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001820300150?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Radner, Roy, 1981. "Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship," Econometrica, Econometric Society, vol. 49(5), pages 1127-1148, September.
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    3. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
    4. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 43, pages 1665-1686, Elsevier.
    5. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    6. Coulomb, Jean-Michel, 1992. "Repeated Games with Absorbing States and No Signals," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 161-174.
    7. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 57-89.
    8. Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 191-217.
    10. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 211-226.
    11. Ehud Lehrer, 1992. "Correlated Equilibria in Two-Player Repeated Games with Nonobservable Actions," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 175-199, February.
    12. Rubinstein, Ariel & Yaari, Menahem E., 1983. "Repeated insurance contracts and moral hazard," Journal of Economic Theory, Elsevier, vol. 30(1), pages 74-97, June.
    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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
    4. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    5. Levy, Yehuda, 2012. "Stochastic games with information lag," Games and Economic Behavior, Elsevier, vol. 74(1), pages 243-256.
    6. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    7. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    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. Renault, Jerome & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 49(2), pages 313-344, November.
    2. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
    3. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    4. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2008. "Discounted and finitely repeated minority games with public signals," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 44-74, July.
    5. Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Deb, Joyee & González-Díaz, Julio & Renault, Jérôme, 2016. "Uniform folk theorems in repeated anonymous random matching games," Games and Economic Behavior, Elsevier, vol. 100(C), pages 1-23.
    7. repec:dau:papers:123456789/2347 is not listed on IDEAS
    8. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "What you get is what you see: Cooperation in repeated games with observable payoffs," Journal of Economic Theory, Elsevier, vol. 181(C), pages 197-237.
    9. Vieille, Nicolas, 2002. "Stochastic games: Recent results," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 48, pages 1833-1850, Elsevier.
    10. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    11. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," HEC Research Papers Series 754, HEC Paris.
    13. Drew Fudenberg & David K. Levine, 2008. "An Approximate Folk Theorem with Imperfect Private Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 14, pages 309-330, World Scientific Publishing Co. Pte. Ltd..
    14. Shmaya, Eran & Solan, Eilon, 2004. "Zero-sum dynamic games and a stochastic variation of Ramsey's theorem," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 319-329, August.
    15. Gilli, Mario, 1999. "On Non-Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 27(2), pages 184-203, May.
    16. 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.
    17. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    18. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    19. repec:dau:papers:123456789/6223 is not listed on IDEAS
    20. Dionne, G. & Doherty, N., 1991. "Adverse Selection In Insurance Markets: A Selective Survey," Cahiers de recherche 9105, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    21. Miyagawa, Eiichi & Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2008. "The folk theorem for repeated games with observation costs," Journal of Economic Theory, Elsevier, vol. 139(1), pages 192-221, March.
    22. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.

    More about this item

    Keywords

    Stochastic games; Imperfect monitoring; Maxmin value; Minmax value;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    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:jogath:v:32:y:2003:i:1:p:133-150. 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.