IDEAS home Printed from https://ideas.repec.org/p/pur/prukra/1260.html
   My bibliography  Save this paper

Finite Automata in Undiscounted Repeated Games with Private Monitoring

Author

Listed:
  • Julian Romero

Abstract

I study two-player undiscounted repeated games with imperfect private monitoring. When strategies are restricted to those implementable by nite automata, fewer equilibrium outcomes are possible. When only two-state automata are allowed, a simple strategy, "Win-Stay, Lose-Shift," leads to cooperation. WSLS has the nice property that it is able to endogenously recoordinate back to cooperation after an incorrect signal. I show that WSLS is essentially the only equilibrium that leads to cooperation in the in nitely repeated Prisoner's Dilemma game. In addition, it is also an equilibrium for a wide range of 2 x 2 games. I also give necessary and su cient conditions on the structure of equilibrium strategies when players can use strategies implementable by fnite automata.

Suggested Citation

  • Julian Romero, 2011. "Finite Automata in Undiscounted Repeated Games with Private Monitoring," Purdue University Economics Working Papers 1260, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1260
    as

    Download full text from publisher

    File URL: https://business.purdue.edu/research/Working-papers-series/2011/1260.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    2. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    3. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    4. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    5. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    6. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    7. Roy Radner, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 43-57.
    8. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    9. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    10. 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.
    11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    12. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    13. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    14. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    15. Pedro Dal Bo & Guillaume R. Frechette, 2007. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," Working Papers 2007-7, Brown University, Department of Economics.
    16. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
    17. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    18. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    19. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
    20. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 211-226.
    21. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    22. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    23. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Monte & Maher Said, 2014. "The value of (bounded) memory in a changing world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 59-82, May.

    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. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    2. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    3. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    4. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    5. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "What you get is what you see: Cooperation in repeated games with observable payoffs," Journal of Economic Theory, Elsevier, vol. 181(C), pages 197-237.
    6. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    7. Fong, Kyna & Sannikov, Yuliy, 2007. "Efficiency in a Repeated Prisoners' Dilemma with Imperfect Private Monitoring," Department of Economics, Working Paper Series qt8vz4q9tr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    8. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    9. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    10. repec:pra:mprapa:64485 is not listed on IDEAS
    11. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    12. Drew Fudenberg & David K. Levine, 2008. "The Nash-threats folk theorem with communication and approximate common knowledge in two player games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 15, pages 331-343, World Scientific Publishing Co. Pte. Ltd..
    13. Ueda, Masahiko, 2023. "Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners’ dilemma game," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    14. Michihiro Kandori, 2011. "Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring," Econometrica, Econometric Society, vol. 79(3), pages 877-892, May.
    15. McLean, Richard & Obara, Ichiro & Postlewaite, Andrew, 2014. "Robustness of public equilibria in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 153(C), pages 191-212.
    16. Yamamoto, Yuichi, 2007. "Efficiency results in N player games with imperfect private monitoring," Journal of Economic Theory, Elsevier, vol. 135(1), pages 382-413, July.
    17. Fabian Dvorak & Sebastian Fehrler, 2018. "Negotiating Cooperation Under Uncertainty: Communication in Noisy, Indefinitely Repeated Interactions," TWI Research Paper Series 112, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    18. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    19. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    20. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    21. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    More about this item

    Keywords

    Bounded Rationality; Finite Automata; Prisoner's Dilemma; Private Monitoring; Tit-For-Tat; Win-Stay Lose-Shift;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:pur:prukra:1260. 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: Business PHD (email available below). General contact details of provider: https://edirc.repec.org/data/kspurus.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.