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On the complexity of coordination

  • O. Gossner
  • P. Hernandez

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. Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
  3. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
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