IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i3d10.1007_s10957-011-9974-4.html
   My bibliography  Save this article

Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

Author

Listed:
  • Beatris Escobedo-Trujillo

    (CINVESTAV-IPN)

  • Daniel López-Barrientos

    (CINVESTAV-IPN)

  • Onésimo Hernández-Lerma

    (CINVESTAV-IPN)

Abstract

This paper deals with zero-sum stochastic differential games with long-run average payoffs. Our main objective is to give conditions for existence and characterization of bias and overtaking optimal equilibria. To this end, first we characterize the family of optimal average payoff strategies. Then, within this family, we impose suitable conditions to determine the subfamilies of bias and overtaking equilibria. A key step to obtain these facts is to show the existence of solutions to the average payoff optimality equations. This is done by the usual “vanishing discount” approach. Finally, a zero-sum game associated to a certain manufacturing process illustrates our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9974-4
    DOI: 10.1007/s10957-011-9974-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9974-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-011-9974-4?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. 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.
    2. 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.
    3. 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.
    4. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2005. "Bias and overtaking equilibria for zero-sum continuous-time Markov games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 437-454, July.
    5. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    6. Hiroshi Atsumi, 1965. "Neoclassical Growth and the Efficient Program of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 127-136.
    Full references (including those not matched with items on IDEAS)

    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. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    2. 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.
    3. 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.
    4. Asheim, Geir B. & d'Aspremont, Claude & Banerjee, Kuntal, 2010. "Generalized time-invariant overtaking," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 519-533, July.
    5. Goeschl, Timo & Jarke, Johannes, 2014. "Trust, but verify? When trustworthiness is observable only through (costly) monitoring," WiSo-HH Working Paper Series 20, University of Hamburg, Faculty of Business, Economics and Social Sciences, WISO Research Laboratory.
    6. Nitin Agarwal & Merlyna Lim & Rolf Wigand, 2012. "Raising and Rising Voices in Social Media," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 4(3), pages 113-126, June.
    7. Andriy Zapechelnyuk & Ro'i Zultan, 2008. "Altruism, Partner Choice, and Fixed-Cost Signalling," Levine's Working Paper Archive 122247000000002199, David K. Levine.
    8. Vogt, Carsten, 2000. "The evolution of cooperation in Prisoners' Dilemma with an endogenous learning mutant," Journal of Economic Behavior & Organization, Elsevier, vol. 42(3), pages 347-373, July.
    9. Spagnolo, Giancarlo, 2005. "Managerial incentives and collusive behavior," European Economic Review, Elsevier, vol. 49(6), pages 1501-1523, August.
    10. Chaim Fershtman & Ariel Pakes, 2000. "A Dynamic Oligopoly with Collusion and Price Wars," RAND Journal of Economics, The RAND Corporation, vol. 31(2), pages 207-236, Summer.
    11. Basu, Kaushik, 2010. "A marketing scheme for making money off innocent people: A user's manual," Economics Letters, Elsevier, vol. 107(2), pages 122-124, May.
    12. Davidson Cheng, 2022. "Asymmetric Equilibria in Symmetric Multiplayer Prisoners Dilemma Supergames," Papers 2205.13772, arXiv.org.
    13. David G. Pearce, 1991. "Repeated Games: Cooperation and Rationality," Cowles Foundation Discussion Papers 983, Cowles Foundation for Research in Economics, Yale University.
    14. Torsten Heinrich & Henning Schwardt, 2013. "Institutional Inertia and Institutional Change in an Expanding Normal-Form Game," Games, MDPI, vol. 4(3), pages 1-28, August.
    15. Jochen Haller, 2002. "The Impact of Electronic Markets on B2B-Relationships," Industrial Organization 0204004, University Library of Munich, Germany, revised 05 Feb 2004.
    16. Murray, Timothy & Garg, Jugal & Nagi, Rakesh, 2021. "Limited-trust equilibria," European Journal of Operational Research, Elsevier, vol. 289(1), pages 364-380.
    17. Fikret Adaman & Yahya M. Madra, 2012. "Understanding Neoliberalism as Economization: The Case of the Ecology," Working Papers 2012/04, Bogazici University, Department of Economics.
    18. Richard McLean & Ichiro Obara & Andrew Postlewaite, 2001. "Informational Smallness and Private Monitoring in Repeated Games," PIER Working Paper Archive 05-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Jul 2005.
    19. Douglas Davis & Asen Ivanov & Oleg Korenok, 2014. "Aspects of Behavior in Repeated Games: An Experimental Study," Working Papers 727, Queen Mary University of London, School of Economics and Finance.
    20. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.

    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:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9974-4. 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.