IDEAS home Printed from https://ideas.repec.org/p/ags/isfiwp/275511.html
   My bibliography  Save this paper

Repeated Games with Finite Automata

Author

Listed:
  • Ben-Porath, Elchanan

Abstract

The paper examines the asymptotic behavior of the set of equilibrium payoffs in a repeated game when there are bounds on the complexity of the strategies players may select. The complexity of a strategy is measured by the size of the minimal automaton that can implement it. The main result is that in a zero—sum game, when the size of the automata of both players go together to infinity, the sequence of values converges to the value of the one—shot game. This is true even if the size of the automata of one player is a polynomial of the size of the automata of the other player. The result for the zero—sum games gives an estimation for the general case.

Suggested Citation

  • Ben-Porath, Elchanan, 1991. "Repeated Games with Finite Automata," Foerder Institute for Economic Research Working Papers 275511, Tel-Aviv University > Foerder Institute for Economic Research.
    • Handle: RePEc:ags:isfiwp:275511
    DOI: 10.22004/ag.econ.275511
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/275511/files/TEL-AVIV-FSWP-180.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.275511?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sylvain Béal, 2010. "Perceptron versus automaton in the finitely repeated prisoner’s dilemma," Theory and Decision, Springer, vol. 69(2), pages 183-204, August.
    2. Mehmet Barlo & Guilherme Carmona, 2007. "One - memory in repeated games," Nova SBE Working Paper Series wp500, Universidade Nova de Lisboa, Nova School of Business and Economics.
    3. David Baron & Ehud Kalai, 1990. "Dividing a Cake by Majority: The Simplest Equilibria," Discussion Papers 919, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Gilboa Itzhak & Schmeidler David, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 370-399, May.
    5. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
    6. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    7. Karl WÄrneryd, 1998. "Communication, complexity, and evolutionary stability," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 599-609.
    8. Hamid Sabourian & Jihong Lee, 2004. "Complexity and Efficiency in Repeated Games with Negotiation," Econometric Society 2004 Far Eastern Meetings 401, Econometric Society.
    9. Ho, Teck-Hua, 1996. "Finite automata play repeated prisoner's dilemma with information processing costs," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 173-207.
    10. Beal, Sylvain & Querou, Nicolas, 2007. "Bounded rationality and repeated network formation," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 71-89, July.
    11. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    12. Hannu Vartiainen, 2009. "A Simple Model of Secure Public Communication," Theory and Decision, Springer, vol. 67(1), pages 101-122, July.
    13. Horaguchi, Haruo, 1996. "The role of information processing cost as the foundation of bounded rationality in game theory," Economics Letters, Elsevier, vol. 51(3), pages 287-294, June.
    14. Monte, Daniel, 2013. "Bounded memory and permanent reputations," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 345-354.
    15. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 593-611, August.
    16. Katerina Sherstyuk, 2011. "Complexity and bidder behavior in iterative auctions," Economics Bulletin, AccessEcon, vol. 31(4), pages 2769-2776.
    17. George J. Mailath & : Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Second Version," PIER Working Paper Archive 08-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2008.
    18. Nachbar, John H & Zame, William R, 1996. "Non-computable Strategies and Discounted Repeated Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 103-122, June.
    19. Kenneth R. Mount & Stanley Reiter, 1996. "A lower bound on computational complexity given by revelation mechanisms (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 237-266.
    20. Spiegler, Ran, 2004. "Simplicity of beliefs and delay tactics in a concession game," Games and Economic Behavior, Elsevier, vol. 47(1), pages 200-220, April.

    More about this item

    Keywords

    Financial Economics;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ags:isfiwp:275511. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/fotauil.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.