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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.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2000/2000cf98.pdf
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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-98.

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Length: 39 pages
Date of creation: Dec 2000
Date of revision:
Handle: RePEc:tky:fseres:2000cf98

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  1. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 447-80, March.
  2. Ma, Ching-to & Moore, John & Turnbull, Stephen, 1988. "Stopping agents from "cheating"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 355-372, December.
  3. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  4. Drew Fudenberg & Jean Tirole, 1988. "Moral Hazard and Renegotiation in Agency Contracts," Working papers 494, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
  6. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  7. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August.
  8. Drew Fudenberg & Bengt Holmstrom & Paul Milgrom, 1987. "Short-Term Contracts and Long-Term Agency Relationships," Working papers 468, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Patrick Legros & Hitoshi Matsushima, 1991. "Efficiency in partnerships," ULB Institutional Repository 2013/7044, ULB -- Universite Libre de Bruxelles.
  10. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 993-1008, September.
  11. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 54(3), pages 533-54, May.
  12. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 627-652, May.
  13. Ma, Ching-To, 1988. "Unique Implementation of Incentive Contracts with Many Agents," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 55(4), pages 555-72, October.
  14. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
  15. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.
  16. 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.
  17. Conlon, John R., 1996. "Cooperation for Pennies: A Note on[epsiv]-Equilibria," Journal of Economic Theory, Elsevier, vol. 70(2), pages 489-500, August.
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Cited by:
  1. Hitoshi Matsushima, 2002. "Finitely Repeated Games with Small Side Payments," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-179, CIRJE, Faculty of Economics, University of Tokyo.

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