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Finitely Repeated Games with Small Side Payments

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Author Info
Hitoshi Matsushima (Faculty of Economics, University of Tokyo)

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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.

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Publisher Info
Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-179.

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Length: 30 pages
Date of creation: Oct 2002
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Handle: RePEc:tky:fseres:2002cf179

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  1. 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. [Downloadable!] (restricted)
  2. 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.
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  3. Conlon, John R., 1996. "Cooperation for Pennies: A Note on[epsiv]-Equilibria," Journal of Economic Theory, Elsevier, vol. 70(2), pages 489-500, August. [Downloadable!] (restricted)
  4. Rey, Patrick & Salanie, Bernard, 1990. "Long-term, Short-term and Renegotiation: On the Value of Commitment in Contracting," Econometrica, Econometric Society, vol. 58(3), pages 597-619, May. [Downloadable!] (restricted)
  5. Ma, Ching-to & Moore, John & Turnbull, Stephen, 1988. "Stopping agents from "cheating"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 355-372, December. [Downloadable!] (restricted)
  6. Ma, Ching-To, 1988. "Unique Implementation of Incentive Contracts with Many Agents," Review of Economic Studies, Blackwell Publishing, vol. 55(4), pages 555-72, October. [Downloadable!] (restricted)
  7. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December. [Downloadable!] (restricted)
  8. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August. [Downloadable!] (restricted)
  9. David G. Pearce, 1987. "Renegotiation-Proof Equilibria: Collective Rationality and Intertemporal Cooperation," Cowles Foundation Discussion Papers 855, Cowles Foundation, Yale University. [Downloadable!]
  10. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December. [Downloadable!] (restricted)
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  11. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August. [Downloadable!] (restricted)
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  12. Dutta, Prajit K. & Radner, Roy, 1994. "Moral hazard," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 26, pages 869-903 Elsevier. [Downloadable!] (restricted)
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  14. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August. [Downloadable!] (restricted)
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  15. Hitoshi Matsushima, 2000. "Small Verifiability in Long-Term Relationships," CIRJE F-Series CIRJE-F-98, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  16. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December. [Downloadable!] (restricted)
  17. Benoit, Jean-Pierre & Krishna, Vijay, 1993. "Renegotiation in Finitely Repeated Games," Econometrica, Econometric Society, vol. 61(2), pages 303-23, March. [Downloadable!] (restricted)
  18. John Geanakoplos & Chien-fu Chou, 1988. "The Power of Commitment," Cowles Foundation Discussion Papers 885, Cowles Foundation, Yale University. [Downloadable!]
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  20. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May. [Downloadable!] (restricted)
  21. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, vol. 57(2), pages 447-80, March. [Downloadable!] (restricted)
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  22. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn. [Downloadable!] (restricted)
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