IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v3y2013i2p162-171.html
   My bibliography  Save this article

Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff

Author

Listed:
  • R. Laraki
  • A. Maitra
  • W. Sudderth

Abstract

Consider a two-person, zero-sum stochastic game with Borel state space S, finite action sets A,B, and Borel measurable law of motion q. Suppose the payoff is a bounded function f of the infinite history of states and actions that is measurable for the product of the Borel σ-field for S and the σ-fields of all subsets for A and B, and is lower semicontinuous for the product of the discrete topologies on the coordinate spaces. Then the game has a value and player II has a subgame perfect optimal strategy. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • R. Laraki & A. Maitra & W. Sudderth, 2013. "Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff," Dynamic Games and Applications, Springer, vol. 3(2), pages 162-171, June.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:162-171
    DOI: 10.1007/s13235-012-0054-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-012-0054-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-012-0054-7?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. Ashok P. Maitra & William D. Sudderth, 2007. "Subgame-Perfect Equilibria for Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 711-722, August.
    2. A. Maitra & W. Sudderth, 2003. "Borel stay-in-a-set games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 97-108, December.
    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. J'anos Flesch & Arkadi Predtetchinski & Ville Suomala, 2021. "Random perfect information games," Papers 2104.10528, arXiv.org.
    2. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    3. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. 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.
    5. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.

    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. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eilon Solan & Koos Vrieze, 2010. "Perfect-Information Games with Lower-Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 742-755, November.
    2. Mitri Kitti, 2013. "Conditional Markov equilibria in discounted dynamic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 77-100, August.
    3. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    4. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    5. Flesch, Janos & Herings, P. Jean-Jacques & Maes, Jasmine & Predtetchinski, Arkadi, 2019. "Individual upper semicontinuity and subgame perfect ϵ-equilibria in games with almost perfect information," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Yehuda Levy, 2015. "Existence of SPE in Discounted Stochastic Games; Revisited and Simplified," Economics Series Working Papers 739, University of Oxford, Department of Economics.
    7. Barelli, Paulo & Duggan, John, 2014. "A note on semi-Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 151(C), pages 596-604.
    8. Qingda Wei & Xian Chen, 2021. "Nonzero-sum Risk-Sensitive Average Stochastic Games: The Case of Unbounded Costs," Dynamic Games and Applications, Springer, vol. 11(4), pages 835-862, December.
    9. Vartika Singh & Veeraruna Kavitha, 2024. "Stochastic Vaccination Game Among Influencers, Leader and Public," Dynamic Games and Applications, Springer, vol. 14(5), pages 1268-1316, November.
    10. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    11. Gong, Rui & Page, Frank & Wooders, Myrna, 2015. "Endogenous correlated network dynamics," LSE Research Online Documents on Economics 65098, London School of Economics and Political Science, LSE Library.
    12. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    13. Mitri Kitti, 2013. "Subgame Perfect Equilibria in Discounted Stochastic Games," Discussion Papers 87, Aboa Centre for Economics.
    14. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    15. Ashok P. Maitra & William D. Sudderth, 2007. "Subgame-Perfect Equilibria for Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 711-722, August.
    16. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    17. Anna Jaśkiewicz & Andrzej S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.
    18. Roger A. Purves & William D. Sudderth, 2011. "Perfect Information Games with Upper Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 468-473, August.
    19. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    20. Page, Frank, 2016. "Stationary Markov equilibria for approximable discounted stochastic games," LSE Research Online Documents on Economics 67808, London School of Economics and Political Science, LSE Library.

    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:3:y:2013:i:2:p:162-171. 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.