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On the Complexity of Coordination

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  • Olivier Gossner

    (THEMA, UMR CNRS 7536, Université Paris X-Nanterre, 200 avenue de la République, 92001 Nanterre, France, and CORE, 34 Voie du Roman Pays, Université Catholique de Louvain, Louvain, Belgique)

  • Penélope Hernández

    (CORE, 34 Voie du Roman Pays, Université Catholique de Louvain, Louvain, Belgique)

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 ln m )/ n (ge) C , for almost any sequence of length n , there exists an automaton of size m that achieves a coordination ratio close to 1 with it. Moreover, we show that one can take any constant C such that C > e| X | ln | X |, where | X | is the size of the alphabet from which the sequence is drawn. Our result contrasts with Neyman (1997) that shows that when ( m ln m )/ n is close to 0, for almost no sequence of length n there exists an automaton of size m that achieves a coordination ratio significantly larger 1/| X | with it.

Suggested Citation

  • Olivier Gossner & Penélope Hernández, 2003. "On the Complexity of Coordination," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 127-140, February.
    • Handle: RePEc:inm:ormoor:v:28:y:2003:i:1:p:127-140
    DOI: 10.1287/moor.28.1.127.14257
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    References listed on IDEAS

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    13. 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).
    14. Amparo Urbano & Penélope Hernández, 2001. "Pseudorandom Processes: Entropy And Automata," Working Papers. Serie AD 2001-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    Cited by:

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    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.
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