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Finitely Repeated Prisoners' Dilemma with Small Fines: Penance Contract

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

We investigate the finitely repeated prisoners' dilemma with explicit contractual devices. We show that full collusion can be achieved by incentivizing the players' final period of play with small fines. Our incentivizing modality is the penance contract, by which a player is penalized if (and only if) he deviates from the penance strategy in the final period. We show that using this contractual agreement brings the penance strategy profile into unique subgame perfect equilibrium and achieves full collusion without being overturned by renegotiation.

Suggested Citation

  • Hitoshi Matsushima, 2010. "Finitely Repeated Prisoners' Dilemma with Small Fines: Penance Contract," CARF F-Series CARF-F-208, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf208
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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. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    3. 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.
    4. Benoit, Jean-Pierre & Krishna, Vijay, 1993. "Renegotiation in Finitely Repeated Games," Econometrica, Econometric Society, vol. 61(2), pages 303-323, March.
    5. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    6. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    7. Lipman, Barton L. & Wang, Ruqu, 2000. "Switching Costs in Frequently Repeated Games," Journal of Economic Theory, Elsevier, vol. 93(2), pages 149-190, August.
    8. 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.
    9. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    10. Joel Sobel, 1985. "A Theory of Credibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 557-573.
    11. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    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. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, Decembrie.
    14. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
    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. 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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    1. Malcolm Kass & Enrique Fatas & Catherine Eckel & Daniel Arce, 2015. "The UN in the lab," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 625-651, October.

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