IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9809003.html
   My bibliography  Save this paper

Asynchronous Choice and Markov Equilibria:Theoretical Foundations and Applications

Author

Listed:
  • V. Bhaskar

    (University of Essex)

  • Fernando Vega-Redondo

    (University of Alicante)

Abstract

This paper provides a theoretical foundation for Markov (perfect) equilibria in repeated games with asynchronous moves that is based on memory costs. We show that if players incur a ``complexity cost'' which depends on the memory length required by their strategies, then any rationalizable strategy is Markovian. Thus, every Nash or perfect equilibrium is Markovian as well. We also provide a dynamic learning rationale for this conclusion. Our result has interesting implications for repeated asynchronous choice games where the stage game is of common interest. If players are sufficiently patient, rationalizability ensures repeated play of the efficient stage-game equilibrium if this equilibrium satisfies a risk-related condition --- in 2x2 games risk- dominance is a sufficient condition.

Suggested Citation

  • V. Bhaskar & Fernando Vega-Redondo, 1998. "Asynchronous Choice and Markov Equilibria:Theoretical Foundations and Applications," Game Theory and Information 9809003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9809003
    Note: Type of Document - Tex; prepared on IBM PC ; to print on any;
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9809/9809003.dvi.gz
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9809/9809003.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9809/9809003.ps.gz
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
    3. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    4. James Dow, 1991. "Search Decisions with Limited Memory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 1-14.
    5. Kalai, E & Neme, A, 1992. "The Strength of a Little Perfection," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 335-355.
    6. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    7. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    9. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    10. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
    11. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
    12. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    13. Eaton, Jonathan & Engers, Maxim, 1990. "Intertemporal Price Competition," Econometrica, Econometric Society, vol. 58(3), pages 637-659, May.
    14. Lipman, Barton L. & Srivastava, Sanjay, 1990. "Informational requirements and strategic complexity in repeated games," Games and Economic Behavior, Elsevier, vol. 2(3), pages 273-290, September.
    15. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
    16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    17. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
    18. Haller, Hans & Lagunoff, Roger, 2010. "Markov Perfect equilibria in repeated asynchronous choice games," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1103-1114, November.
    19. Beggs, Alan W & Klemperer, Paul, 1992. "Multi-period Competition with Switching Costs," Econometrica, Econometric Society, vol. 60(3), pages 651-666, May.
    20. De Fraja, Giovanni, 1993. "Staggered vs. synchronised wage setting in oligopoly," European Economic Review, Elsevier, vol. 37(8), pages 1507-1522, December.
    21. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, 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. Dutta, Prajit K., 2012. "Coordination need not be a problem," Games and Economic Behavior, Elsevier, vol. 76(2), pages 519-534.

    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. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
    2. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    3. Victor Aguirregabiria & Jihye Jeon, 2020. "Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(2), pages 203-235, March.
    4. Ding, Zhanwen & Wang, Qiao & Cai, Chaoying & Jiang, Shumin, 2014. "Fictitious play with incomplete learning," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 1-8.
    5. Arthur Charpentier & Romuald Elie & Carl Remlinger, 2020. "Reinforcement Learning in Economics and Finance," Papers 2003.10014, arXiv.org.
    6. Christoph March, 2011. "Adaptive social learning," Working Papers halshs-00572528, HAL.
    7. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
    8. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.
    9. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    10. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    11. Takashi Kamihigashi & Taiji Furusawa, 2006. "Immediately Reactive Equilibria in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 199, Research Institute for Economics & Business Administration, Kobe University.
    12. Iskakov, A. & Iskakov, M., 2017. "In Search of a Generalized Concept of Rationality," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 181-189.
    13. Vives, Xavier & Jun, Byoung, 2001. "Incentives in Dynamic Duopoly," CEPR Discussion Papers 2899, C.E.P.R. Discussion Papers.
    14. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    15. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    16. Lupia, Arthur & Levine, Adam Seth & Zharinova, Natasha, 2010. "When Should Political Scientists Use the Self-Confirming Equilibrium Concept? Benefits, Costs, and an Application to Jury Theorems," Political Analysis, Cambridge University Press, vol. 18(1), pages 103-123, January.
    17. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    18. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    19. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    20. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.

    More about this item

    Keywords

    Markov Equilibrium; Bouded Memory;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpga:9809003. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.