(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v42y2010i1p237-253.html
   My bibliography  Save this article

Computing uniformly optimal strategies in two-player stochastic games

Author

Listed:
  • Eilon Solan
  • Nicolas Vieille
Abstract
We provide a computable algorithm to calculate uniform ε-optimal strategies in two-player zero-sum stochastic games. Our approach can be used to construct algorithms that calculate uniform ε-equilibria and uniform correlated ε-equilibria in various classes of multi-player non-zero-sum stochastic games.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    • Handle: RePEc:spr:joecth:v:42:y:2010:i:1:p:237-253
    DOI: 10.1007/s00199-009-0437-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-009-0437-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-009-0437-1?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. Krishnendu Chatterjee & Rupak Majumdar & Thomas Henzinger, 2008. "Stochastic limit-average games are in EXPTIME," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 219-234, June.
    2. Herings, P. J. J. & Polemarchakis, H., 2002. "Equilibrium and arbitrage in incomplete asset markets with fixed prices," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 133-155, April.
    3. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    4. Eitan Altman & Konstantin E. Avrachenkov & Jerzy A. Filar, 1999. "Asymptotic linear programming and policy improvement for singularly perturbed Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 97-109, March.
    5. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, October.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
    6. repec:dau:papers:123456789/6017 is not listed on IDEAS
    7. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    8. 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.
    9. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Stochastic games on a product state space: the periodic case," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. 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.
    12. VIEILLE, Nicolas & SOLAN, Eilon, 2002. "Perturbed Markov Chains," HEC Research Papers Series 757, HEC Paris.
    13. repec:dau:papers:123456789/6019 is not listed on IDEAS
    14. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2008. "Stochastic Games on a Product State Space," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 403-420, May.
    15. Vrieze, O.J. & Tijs, S.H., 1982. "Fictitious play applied to sequences of games and discounted stochastic games," Other publications TiSEM da21d287-bc00-4a8e-a18f-0, Tilburg University, School of Economics and Management.
    16. 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.
    17. 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.
    18. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    19. Eilon Solan & Rakesh V. Vohra, 2002. "Correlated equilibrium payoffs and public signalling in absorbing games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 91-121.
    20. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
    21. B. Curtis Eaves & Uriel G. Rothblum, 1989. "A Theory on Extending Algorithms for Parametric Problems," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 502-533, 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. Cheng, Jianqiang & Leung, Janny & Lisser, Abdel, 2016. "Random-payoff two-person zero-sum game with joint chance constraints," European Journal of Operational Research, Elsevier, vol. 252(1), pages 213-219.
    2. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 1-7, January.
    3. Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.
    4. Miquel Oliu-Barton, 2014. "The Asymptotic Value in Finite Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 712-721, August.
    5. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    6. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    7. Miquel Oliu-Barton, 2012. "The asymptotic value in finite stochastic games," Working Papers halshs-00772631, HAL.

    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. Eilon Solan, 2018. "The modified stochastic game," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1287-1327, November.
    2. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2009. "Stochastic games on a product state space: the periodic case," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 263-289, June.
    3. 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.
    4. 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.
    5. Eilon Solan, 2002. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Discussion Papers 1356, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.
    7. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Stochastic games on a product state space: the periodic case," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Laraki, Rida & Renault, Jérôme, 2017. "Acyclic Gambling Games," TSE Working Papers 17-768, Toulouse School of Economics (TSE).
    9. Eilon Solan & Omri N. Solan, 2021. "Sunspot equilibrium in positive recursive general quitting games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 891-909, December.
    10. Eilon Solan, 2000. "The Dynamics of the Nash Equilibrium Correspondence and n-Player Stochastic Games," Discussion Papers 1311, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. 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.
    12. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
    13. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    14. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    15. Solan, Eilon & Solan, Omri N. & Solan, Ron, 2020. "Jointly controlled lotteries with biased coins," Games and Economic Behavior, Elsevier, vol. 119(C), pages 383-391.
    16. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2008. "Subgame-perfection in stochastic games with perfect information and recursive payoffs," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    17. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.
    18. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Johannes Horner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2009. "Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem," Cowles Foundation Discussion Papers 1742, Cowles Foundation for Research in Economics, Yale University, revised Aug 2010.
    20. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.

    More about this item

    Keywords

    Optimal strategies; Stochastic games; Computation; C63; C73;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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:joecth:v:42:y:2010:i:1:p:237-253. 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.