IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v151y2014icp596-604.html
   My bibliography  Save this article

A note on semi-Markov perfect equilibria in discounted stochastic games

Author

Listed:
  • Barelli, Paulo
  • Duggan, John

Abstract

We establish that general discounted stochastic games with state transitions that are absolutely continuous with respect to a fixed, atomless measure admit stationary semi-Markov perfect equilibria, i.e., equilibria in which each player's action depends only on the current state and on the previous state and action profile. This resolves an open existence question stemming from an error in the proof of Theorem 4 of Chakrabarti [3]. Moreover, the result follows from “un-correlating” Nowak and Raghavan's [25] stationary correlated equilibrium, establishing that there is no need to resort to additional, unmodeled state variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:596-604
    DOI: 10.1016/j.jet.2014.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053114000271
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2014.03.001?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. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
    2. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    4. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    5. 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.
    6. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    7. Mertens, J.-F. & Parthasarathy, T., 1991. "Nonzero-sum stochastic games," LIDAM Reprints CORE 912, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
    9. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    10. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
    11. Maitra, A & Sudderth, W, 1993. "Finitely Additive and Measurable Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 201-223.
    12. 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.
    13. 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.
    14. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 121-132, 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. Subir K. Chakrabarti, 2021. "Stationary equilibrium in stochastic dynamic models: Semi-Markov strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 177-194, October.
    2. Duggan, John, 2017. "Existence of stationary bargaining equilibria," Games and Economic Behavior, Elsevier, vol. 102(C), pages 111-126.
    3. Eunmi Ko, 2024. "Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation," Games, MDPI, vol. 15(5), pages 1-17, September.
    4. Liu, Heng, 2018. "Efficient dynamic mechanisms in environments with interdependent valuations: the role of contingent transfers," Theoretical Economics, Econometric Society, vol. 13(2), May.
    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. 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 S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.
    2. 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.
    3. 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.
    4. 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.
    5. He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    6. Frank H. Page & Myrna H. Wooders, 2009. "Endogenous Network Dynamics," Working Papers 2009.28, Fondazione Eni Enrico Mattei.
    7. Page, Frank, 2016. "On K-Class discounted stochastic games," LSE Research Online Documents on Economics 67809, London School of Economics and Political Science, LSE Library.
    8. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
    9. Page, Frank, 2015. "Stationary Markov equilibria for K-class discounted stochastic games," LSE Research Online Documents on Economics 65103, London School of Economics and Political Science, LSE Library.
    10. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    11. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
    12. 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.
    13. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
    14. Subir K. Chakrabarti, 2021. "Stationary equilibrium in stochastic dynamic models: Semi-Markov strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 177-194, October.
    15. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 669-704, June.
    16. Qingda Wei & Xian Chen, 2022. "Discounted stochastic games for continuous-time jump processes with an uncountable state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 187-218, April.
    17. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    18. John Duggan, 2011. "Noisy Stochastic Games," RCER Working Papers 562, University of Rochester - Center for Economic Research (RCER).
    19. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    20. Yehuda Levy, 2015. "Existence of SPE in Discounted Stochastic Games; Revisited and Simplified," Economics Series Working Papers 739, University of Oxford, Department of Economics.

    More about this item

    Keywords

    Stochastic games; Existence; Stationary equilibrium; Semi-Markov perfect equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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:eee:jetheo:v:151:y:2014:i:c:p:596-604. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.