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Finitely Repeated Games with Small Side Payments

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

This paper investigates repeated games with perfect monitoring, where the number of repetition is finite, and the discount factor is far less than unity. Players can make a side payment contract, but their liability is severely limited. The history of play may not necessarily be verifiable. With positive interest rate of the contractible asset, we show that, in spite of limited liability and verifiability, efficiency is sustainable in that there exist a contract and an efficient perfect equilibrium in its associated game, and that efficiency is even uniquely sustainable if there exists the unique one-shot Nash equilibrium. In partnership games, efficiency is uniquely and approximately sustainable, even if the interest rate equals zero. In partnership games with two players and positive interest rate, efficient sustainability is robust to renegotiation-proofness on the terms of explicit contracting as well as implicit agreements.

Suggested Citation

  • Hitoshi Matsushima, 2002. "Finitely Repeated Games with Small Side Payments," CIRJE F-Series CIRJE-F-179, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2002cf179
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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. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December.
    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. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    5. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, 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. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, vol. 57(2), pages 447-480, March.
    9. 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.
    10. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    11. 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.
    12. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August.
    13. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    14. 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.
    15. Hitoshi Matsushima, 2000. "Small Verifiability in Long-Term Relationships," CIRJE F-Series CIRJE-F-98, CIRJE, Faculty of Economics, University of Tokyo.
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