IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2001-21.html
   My bibliography  Save this paper

On the complexity of coordination

Author

Listed:
  • O. Gossner
  • P. Hernandez

Abstract

Many results on repeated games played by finite automata rely on the complexity of the exact implementation of a coordinated play of length n. For a large proportion of sequences, this complexity appears to be no less than n. We study the complexity of a coordinated play when allowing for a few mismatches. We prove the existence of a constant C such that if (m log m /n) >= C, almost all sequences of length n can be predicted by an automaton of size m with a coordination rate close to 1. This contrasts with Neyman [6] that shows that when (m log m/n) is close to 0, almost no sequence can be predicted with a coordination ratio significantly larger than the minimal one.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • O. Gossner & P. Hernandez, 2001. "On the complexity of coordination," THEMA Working Papers 2001-21, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2001-21
    as

    Download full text from publisher

    File URL: http://www.u-cergy.fr/IMG/documents//2001-21Gossner.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Abraham Neyman, 1998. "Finitely Repeated Games with Finite Automata," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 513-552, August.
    2. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    3. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    4. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
    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. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    2. Michele Piccione & Ariel Rubinstein, 2003. "Modeling the Economic Interaction of Agents With Diverse Abilities to Recognize Equilibrium Patterns," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 212-223, March.
    3. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.
    4. Yair Goldberg, 2003. "On the Minmax of Repeated Games with Imperfect Monitoring: A Computational Example," Discussion Paper Series dp345, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. repec:dau:papers:123456789/6127 is not listed on IDEAS
    6. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
    7. Fernando Oliveira, 2010. "Bottom-up design of strategic options as finite automata," Computational Management Science, Springer, vol. 7(4), pages 355-375, October.
    8. Olivier Gossner & Penélope Hernández, 2005. "Coordination Through De Bruijn Sequences," Working Papers. Serie AD 2005-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Olivier Gossner & Jöhannes Horner, 2006. "When is the individually rational payoff in a repeated game equal to the minmax payoff?," Discussion Papers 1440, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Olivier Gossner & Penélope Hernández & Ron Peretz, 2016. "The complexity of interacting automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 461-496, March.

    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. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    2. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
    3. Ueda, Masahiko, 2023. "Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners’ dilemma game," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    4. Compte, Olivier & Postlewaite, Andrew, 2015. "Plausible cooperation," Games and Economic Behavior, Elsevier, vol. 91(C), pages 45-59.
    5. Oliver Compte & Andrew Postlewaite, 2010. "Plausible Cooperation, Fourth Version," PIER Working Paper Archive 15-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Jan 2015.
    6. Olivier Gossner & Penélope Hernández & Ron Peretz, 2016. "The complexity of interacting automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 461-496, March.
    7. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.
    8. Jérôme Renault & Marco Scarsini & Tristan Tomala, 2007. "A Minority Game with Bounded Recall," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 873-889, November.
    9. Olivier Gossner & Penélope Hernández, 2003. "On the Complexity of Coordination," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 127-140, February.
    10. David Baron & Ehud Kalai, 1990. "Dividing a Cake by Majority: The Simplest Equilibria," Discussion Papers 919, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Beal, Sylvain & Querou, Nicolas, 2007. "Bounded rationality and repeated network formation," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 71-89, July.
    12. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 593-611, August.
    13. Hernández, Penélope & Solan, Eilon, 2016. "Bounded computational capacity equilibrium," Journal of Economic Theory, Elsevier, vol. 163(C), pages 342-364.
    14. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
    16. René Levínský & Abraham Neyman & Miroslav Zelený, 2020. "Should I remember more than you? Best responses to factored strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1105-1124, December.
    17. Sylvain Béal, 2010. "Perceptron versus automaton in the finitely repeated prisoner’s dilemma," Theory and Decision, Springer, vol. 69(2), pages 183-204, August.
    18. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
    19. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    20. GOSSNER, Olivier, 1998. "Repeated games played by cryptographically sophisticated players," LIDAM Discussion Papers CORE 1998035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    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:ema:worpap:2001-21. 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: Stefania Marcassa (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.html .

    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.