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Small Verifiability in Long-Term Relationships

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  • 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
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2000/2000cf98.pdf
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    References listed on IDEAS

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    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. Glazer, Jacob & Perry, Motty, 1996. "Virtual Implementation in Backwards Induction," Games and Economic Behavior, Elsevier, vol. 15(1), pages 27-32, July.
    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. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December.
    5. 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..
    6. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    9. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    10. 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.
    11. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, vol. 58(6), pages 1279-1319, November.
    12. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    13. Ma, Ching-to & Moore, John & Turnbull, Stephen, 1988. "Stopping agents from "cheating"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 355-372, December.
    14. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, vol. 57(2), pages 447-480, March.
    15. 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.
    16. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    17. 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.
    18. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August.
    19. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    20. 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.
    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.
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    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.

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