IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v64y2006i3p481-494.html
   My bibliography  Save this article

Remarks on sensitive equilibria in stochastic games with additive reward and transition structure

Author

Listed:
  • Andrzej Nowak

Abstract

A class of stochastic games with additive reward and transition structure is studied. For zero-sum games under some ergodicity assumptions 1-equilibria are shown to exist. They correspond to so-called sensitive optimal policies in dynamic programming. For a class of nonzero-sum stochastic games with nonatomic transitions nonrandomized Nash equilibrium points with respect to the average payoff criterion are also obtained. Included examples show that the results of this paper can not be extented to more general payoff or transition structure. Copyright Springer-Verlag 2006

Suggested Citation

  • Andrzej Nowak, 2006. "Remarks on sensitive equilibria in stochastic games with additive reward and transition structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 481-494, December.
  • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:481-494
    DOI: 10.1007/s00186-006-0090-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0090-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00186-006-0090-4?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. Andrzej S. Nowak, 1999. "Sensitive equilibria for ergodic stochastic games with countable state spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(1), pages 65-76, August.
    2. Andrzej S. Nowak, 1999. "Optimal strategies in a class of zero-sum ergodic stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 399-419, December.
    3. Andrzej S. Nowak & Anna Jaśkiewicz, 2005. "Nonzero-sum semi-Markov games with the expected average payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 23-40, September.
    4. repec:ebl:ecbull:v:17:y:2006:i:2:p:1-10 is not listed on IDEAS
    5. Raghavan, T.E.S. & Tijs, S.H. & Vrieze, O.J., 1985. "On stochastic games with additive reward and transition structure," Other publications TiSEM 28f85a14-9a6e-4ed8-9a4b-a, Tilburg University, School of Economics and Management.
    6. 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.
    7. Andrzej Nowak, 2006. "A note on an equilibrium in the great fish war game," Economics Bulletin, AccessEcon, vol. 17(2), pages 1-10.
    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. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    2. Anna Jaśkiewicz & Andrzej Nowak, 2015. "On pure stationary almost Markov Nash equilibria in nonzero-sum ARAT stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 169-179, April.

    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. Anna Jaśkiewicz & Andrzej Nowak, 2015. "On pure stationary almost Markov Nash equilibria in nonzero-sum ARAT stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 169-179, April.
    2. A. Jaśkiewicz & A. S. Nowak, 2006. "Approximation of Noncooperative Semi-Markov Games," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 115-134, October.
    3. 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.
    4. Beatris Escobedo-Trujillo & Daniel López-Barrientos & Onésimo Hernández-Lerma, 2012. "Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 662-687, June.
    5. 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.
    6. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
    7. Frank H. Page & Myrna H. Wooders, 2009. "Endogenous Network Dynamics," Working Papers 2009.28, Fondazione Eni Enrico Mattei.
    8. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    9. Agnieszka Wiszniewska-Matyszkiel & Rajani Singh, 2020. "When Inaccuracies in Value Functions Do Not Propagate on Optima and Equilibria," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    10. Flesch, J. & Thuijsman, F. & Vrieze, O.J., 2007. "Stochastic games with additive transitions," European Journal of Operational Research, Elsevier, vol. 179(2), pages 483-497, June.
    11. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
    12. Bohren, J. Aislinn, 2024. "Persistence in a dynamic moral hazard game," Theoretical Economics, Econometric Society, vol. 19(1), January.
    13. Chakrabarti, Subir K., 2003. "Pure strategy Markov equilibrium in stochastic games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 693-724, September.
    14. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
    15. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    16. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 455-474, April.
    17. Yehuda Levy, 2015. "Existence of SPE in Discounted Stochastic Games; Revisited and Simplified," Economics Series Working Papers 739, University of Oxford, Department of Economics.
    18. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    19. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    20. Nowak, Andrzej S., 2008. "Equilibrium in a dynamic game of capital accumulation with the overtaking criterion," Economics Letters, Elsevier, vol. 99(2), pages 233-237, May.

    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:mathme:v:64:y:2006:i:3:p:481-494. 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.