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Fictitious play in coordination games

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Author Info

  • Aner Sela

    ()
    (Department of Economics, Ben-Gurion University of the Negev, P.O.B 653, Beer-Sheva 84105, Israel)

  • Dorothea Herreiner

    ()
    (Wirtschaftstheorie III, Department of Economics, University of Bonn, Adenauerallee 24-26, D-53113 Bonn, Germany)

Abstract

We study the Fictitious Play process with bounded and unbounded recall in pure coordination games for which failing to coordinate yields a payoff of zero for both players. It is shown that every Fictitious Play player with bounded recall may fail to coordinate against his own type. On the other hand, players with unbounded recall are shown to coordinate (almost surely) against their own type as well as against players with bounded recall. In particular, this implies that a FP player's realized average utility is (almost surely) at least as large as his minmax payoff in 2þ2 coordination games.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 2 ()
Pages: 189-197

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Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:189-197

Note: Received: December 1997/Final version: November 1998
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Related research

Keywords: Learning · fictitious play · (pure) coordination games;

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References

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  1. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  2. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  3. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
  4. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
  5. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  6. Li, Shuhe, 1994. "Dynamic stability and learning processes in 2 x 2 coordination games," Economics Letters, Elsevier, vol. 46(2), pages 105-111, October.
  7. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  8. Gilboa, Itzhak & Samet, Dov, 1989. "Bounded versus unbounded rationality: The tyranny of the weak," Games and Economic Behavior, Elsevier, vol. 1(3), pages 213-221, September.
  9. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  11. Monderer, Dov & Sela, Aner, 1996. "A2 x 2Game without the Fictitious Play Property," Games and Economic Behavior, Elsevier, vol. 14(1), pages 144-148, May.
  12. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
  13. Dov Monderer & Aner Sela, 2010. "A 2 ×2 Game without the Fictitious Play Property," Levine's Working Paper Archive 583, David K. Levine.
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Cited by:
  1. Steffen Huck & Rajiv Sarin, 2000. "Players with Limited Memory," Econometric Society World Congress 2000 Contributed Papers 1645, Econometric Society.
  2. Bryan McCannon, 2011. "Coordination between a sophisticated and fictitious player," Journal of Economics, Springer, vol. 102(3), pages 263-273, April.

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