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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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Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2001-21.

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Date of creation: 2001
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Handle: RePEc:ema:worpap:2001-21

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  1. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1259-81, November.
  2. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 17-32, February.
  3. Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Stephen Coate & Marco Battaglini, 2007. "A Dynamic Theory of Public Spending, Taxation and Debt," 2007 Meeting Papers, Society for Economic Dynamics 573, Society for Economic Dynamics.
  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, MIT Press, vol. 1(1), pages 212-223, 03.
  3. Olivier Gossner & Jöhannes Horner, 2006. "When is the individually rational payoff in a repeated game equal to the minmax payoff?," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1440, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Amparo Urbano Salvador & Penélope Hernández Rojas, 2000. "Codification schemes and finite automata," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2006-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, Elsevier, vol. 56(2), pages 207-223, September.
  6. Yair Goldberg, 2003. "On the Minmax of Repeated Games with Imperfect Monitoring: A Computational Example," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp345, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Olivier Gossner & Penélope Hernández, 2005. "Coordination Through De Bruijn Sequences," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2005-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Fernando Oliveira, 2010. "Bottom-up design of strategic options as finite automata," Computational Management Science, Springer, Springer, vol. 7(4), pages 355-375, October.

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