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On the complexity of coordination

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  • 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.
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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
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    References listed on IDEAS

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    1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    2. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
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    6. 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).
    7. Amparo Urbano & Penélope Hernández, 2001. "Pseudorandom Processes: Entropy And Automata," Working Papers. Serie AD 2001-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. 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.
    9. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    10. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
    11. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
    12. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    13. Amparo Urbano & Penélope Hernández, 2001. "Communication And Automata," Working Papers. Serie AD 2001-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
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    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.
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    4. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
    5. Fernando Oliveira, 2010. "Bottom-up design of strategic options as finite automata," Computational Management Science, Springer, vol. 7(4), pages 355-375, October.
    6. Bavly, Gilad & Peretz, Ron, 2019. "Limits of correlation in repeated games with bounded memory," Games and Economic Behavior, Elsevier, vol. 115(C), pages 131-145.
    7. 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.
    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 & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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