IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2000cf98.html
   My bibliography  Save this paper

Small Verifiability in Long-Term Relationships

Author

Listed:
  • Hitoshi Matsushima

    (Faculty of Economics, Universtiy of Tokyo)

Abstract

This paper investigates a finitely repeated game at the beginning of which players agree to write an explicit contract with full commitment. This contract conditions the budget-balancing vector of side payments on the complete history of their action choices. However, this history is not always verifiable to the court, and each player's liability is severely limited. We show, in the general case, that even if the probability of the complete history being verifiable is small and the amount of possible fines is negligible compared with the differences in long-run payoffs, every efficient payoff vector induced by an action profile, which Pareto-dominates a Nash equilibrium action profile, is uniquely and exactly implementable either in terms of perfect equilibrium or in terms of perfect iterative undominance. Moreover, we show, in a wide class of component games, that even if this probability is close to zero and the amount of fines is negligible compared with the differences not only in long-run payoffs but also in instantaneous payoffs, every efficient payoff vector induced by an action profile, which Pareto-dominates a Nash equilibrium action profile, is uniquely and virtually implementable either in terms of perfect equilibrium or in terms of perfect iterative undominance.

Suggested Citation

  • Hitoshi Matsushima, 2000. "Small Verifiability in Long-Term Relationships," CIRJE F-Series CIRJE-F-98, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2000cf98
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2000/2000cf98.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    2. 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..
    3. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    4. Hitoshi Matsushima, 2000. "The Folk Theorem with Private Monitoring and Uniform Sustainability," CIRJE F-Series CIRJE-F-84, CIRJE, Faculty of Economics, University of Tokyo.
    5. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    6. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    7. Ma, Ching-to & Moore, John & Turnbull, Stephen, 1988. "Stopping agents from "cheating"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 355-372, December.
    8. David G. Pearce, 1987. "Renegotiation-Proof Equilibria: Collective Rationality and Intertemporal Cooperation," Cowles Foundation Discussion Papers 855, Cowles Foundation for Research in Economics, Yale University.
    9. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December.
    10. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    11. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August.
    12. Ching-To Ma, 1988. "Unique Implementation of Incentive Contracts with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 555-572.
    13. Glazer, Jacob & Perry, Motty, 1996. "Virtual Implementation in Backwards Induction," Games and Economic Behavior, Elsevier, vol. 15(1), pages 27-32, July.
    14. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.
    15. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    16. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, vol. 58(6), pages 1279-1319, November.
    17. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, vol. 57(2), pages 447-480, March.
    18. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    19. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
    20. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    21. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    22. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    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. Hitoshi Matsushima, 2002. "Finitely Repeated Games with Small Side Payments," CIRJE F-Series CIRJE-F-179, CIRJE, Faculty of Economics, University of Tokyo.

    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. Hitoshi Matsushima, 2002. "Finitely Repeated Games with Small Side Payments," CIRJE F-Series CIRJE-F-179, CIRJE, Faculty of Economics, University of Tokyo.
    2. Hitoshi Matsushima, 2012. "Finitely Repeated Prisoners' Dilemma With Small Fines: The Penance Contract," The Japanese Economic Review, Japanese Economic Association, vol. 63(3), pages 333-347, September.
    3. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    4. Du, Chuang, 2012. "Solving payoff sets of perfect public equilibria: an example," MPRA Paper 38622, University Library of Munich, Germany.
    5. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    6. Hitoshi Matsushima, 2010. "Role Of Relative And Absolute Performance Evaluations In Intergroup Competition," The Japanese Economic Review, Japanese Economic Association, vol. 61(4), pages 443-454, December.
    7. Nuh Aygün Dalkıran, 2016. "Order of limits in reputations," Theory and Decision, Springer, vol. 81(3), pages 393-411, September.
    8. Arya, Anil & Glover, Jonathan & Rajan, Uday, 2000. "Implementation in Principal-Agent Models of Adverse Selection," Journal of Economic Theory, Elsevier, vol. 93(1), pages 87-109, July.
    9. David G. Pearce, 1991. "Repeated Games: Cooperation and Rationality," Cowles Foundation Discussion Papers 983, Cowles Foundation for Research in Economics, Yale University.
    10. Pearce, David G. & Stacchetti, Ennio, 1998. "The Interaction of Implicit and Explicit Contracts in Repeated Agency," Games and Economic Behavior, Elsevier, vol. 23(1), pages 75-96, April.
    11. Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
    12. Gagen, Michael, 2013. "Isomorphic Strategy Spaces in Game Theory," MPRA Paper 46176, University Library of Munich, Germany.
    13. Conlon, John R., 1995. "Continuous time vs. backward induction a new approach to modelling reputation in the finite time horizon context," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1449-1469, November.
    14. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    15. Sandro Brusco, 2002. "Unique Implementation of Action Profiles: Necessary and Sufficient Conditions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 509-532, May.
    16. Rudolf Kerschbamer & Muriel Niederle & Josef Perktold, 2000. "Market Institutions and Quality Enforcement," Econometric Society World Congress 2000 Contributed Papers 1482, Econometric Society.
    17. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.
    18. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Imperfect Monitoring and Impermanent Reputations," Econometrica, Econometric Society, vol. 72(2), pages 407-432, March.
    19. Gintis, Herbert, 2004. "Modeling cooperation among self-interested agents: a critique," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(6), pages 695-714, December.
    20. Radygin Alexandr & Entov Revold & Apevalova E. & Shvetsov P., 2008. "Market Discipline and Contracts: Theory, Empiric Analysis, Law," Research Paper Series, Gaidar Institute for Economic Policy, issue 117P.

    More about this item

    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:tky:fseres:2000cf98. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.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.