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Prisoners' Other Dilemma

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  • Blonski, Matthias
  • Spagnolo, Giancarlo

Abstract

Collusive agreements and relational contracts are commonly modeled as equilibria of dynamic games with the strategic features of the repeated Prisoner's Dilemma. The pay-offs agents obtain when being ‘cheated upon’ by other agents play no role in these models. We propose a way to take these pay-offs into account, and find that cooperation as equilibrium of the infinitely repeated discounted Prisoner's Dilemma is often implausible: for a significant subset of the pay-off discount factor parameter space, all cooperation equilibria are strictly risk dominated in the sense of Harsanyi and Selten (1988). We derive an easy-to-calculate critical level for the discount factor below which this happens, also function of pay-offs obtained when others defect, and argue it is a better measure for the ‘likelihood’ of cooperation than the critical level at which cooperation is supportable in equilibrium. Our results apply to other games sharing the strategic structure of the Prisoner's Dilemma (repeated oligopolies, relational-contracting models, etc.). We illustrate our main result for collusion equilibria in the repeated Cournot duopoly.

Suggested Citation

  • Blonski, Matthias & Spagnolo, Giancarlo, 2003. "Prisoners' Other Dilemma," CEPR Discussion Papers 3856, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:3856
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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. van Damme, Eric & Hurkens, Sjaak, 2004. "Endogenous price leadership," Games and Economic Behavior, Elsevier, vol. 47(2), pages 404-420, May.
    5. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    6. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    7. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    8. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    9. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    10. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
    11. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    12. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    13. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    14. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    15. Schmidt, David & Shupp, Robert & Walker, James M. & Ostrom, Elinor, 2003. "Playing safe in coordination games:: the roles of risk dominance, payoff dominance, and history of play," Games and Economic Behavior, Elsevier, vol. 42(2), pages 281-299, February.
    16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    17. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
    18. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    19. Tore Ellingsen & Robert Östling, 2010. "When Does Communication Improve Coordination?," American Economic Review, American Economic Association, vol. 100(4), pages 1695-1724, September.
    20. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-192, August.
    21. van Damme, E.E.C. & Carlsson, H., 1993. "Equilibrium selection in stag hunt games," Other publications TiSEM 8951ae88-c6e4-42e6-b253-b, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Leliefeld, Daniel & Motchenkova, Evgenia, 2007. "To protect in order to serve, adverse effects of leniency programs in view of industry asymmetry," Serie Research Memoranda 0002, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Giancarlo Spagnolo, 2004. "Divide et Impera. Optimnal Deterrence Mechanisms Against Cartels and Organized Crime," Econometric Society 2004 North American Winter Meetings 485, Econometric Society.
    3. Douglas Davis & Asen Ivanov & Oleg Korenok, 2014. "Aspects of Behavior in Repeated Games: An Experimental Study," Working Papers 727, Queen Mary University of London, School of Economics and Finance.
    4. Bigoni, Maria & Le Coq, Chloé & Fridolfsson, Sven-Olof & Spagnolo, Giancarlo, 2008. "Risk Aversion, Prospect Theory, and Strategic Risk in Law Enforcement: Evidence From an Antitrust Experiment," SSE/EFI Working Paper Series in Economics and Finance 696, Stockholm School of Economics.
    5. Gabriele Camera & Marco Casari & Maria Bigoni, 2010. "Cooperative Strategies in Groups of Strangers: An Experiment," Purdue University Economics Working Papers 1237, Purdue University, Department of Economics.
    6. Camera, Gabriele & Gioffré, Alessandro, 2017. "Asymmetric social norms," Economics Letters, Elsevier, vol. 152(C), pages 27-30.
    7. Chen, Zhiqi & Ghosh, Subhadip & Ross, Thomas W., 2015. "Denying leniency to cartel instigators: Costs and benefits," International Journal of Industrial Organization, Elsevier, vol. 41(C), pages 19-29.
    8. Dijkstra, Peter T., 2015. "Price leadership and unequal market sharing: Collusion in experimental markets," International Journal of Industrial Organization, Elsevier, vol. 43(C), pages 80-97.
    9. Landeo, Claudia & Spier, Kathryn, 2015. "Incentive Contracts for Teams: Experimental Evidence," Working Papers 2015-9, University of Alberta, Department of Economics.
    10. Carsten J. Crede & Liang Lu, 2016. "The effects of endogenous enforcement on strategic uncertainty and cartel deterrence," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 16-08, School of Economics, University of East Anglia, Norwich, UK..
    11. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    12. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-192, August.
    13. Pablo Hernandez & Dylan Minor & Dana Sisak, 2015. "Do People Who Care About Others Cooperate More? Experimental Evidence from Relative Incentive Pay," Harvard Business School Working Papers 16-040, Harvard Business School.
    14. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-749, April.
    15. Landeo, Claudia M. & Spier, Kathryn E., 2015. "Incentive contracts for teams: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 496-511.
    16. repec:pit:wpaper:532 is not listed on IDEAS
    17. Marvao, Catarina & Spagnolo, Giancarlo & Buccirossi, Paolo, 2015. "Leniency and Damages," SITE Working Paper Series 32, Stockholm School of Economics, Stockholm Institute of Transition Economics, revised 13 Jan 2016.
    18. Tatsuyoshi Saijo & Takehito Masuda & Takafumi Yamakawa, "undated". "Approval Mechanism to Solve Prisoner’s Dilemma: Comparison with Varian’s Compensation Mechanism," Working Papers SDES-2016-15, Kochi University of Technology, School of Economics and Management.
    19. Claudia M. Landeo & Kathryn E. Spier, 2015. "Incentive Contracts for Teams: Experimental Evidence," Working Papers 2015-53, Peruvian Economic Association.
    20. Blonski, Matthias & Spagnolo, Giancarlo, 2002. "Relational Contracts and Property Rights," CEPR Discussion Papers 3460, C.E.P.R. Discussion Papers.
    21. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2016. "Intelligence, Personality and Gains from Cooperation in Repeated Interactions," CESifo Working Paper Series 6121, CESifo Group Munich.

    More about this item

    Keywords

    cartel stability; collusion; cooperation; relational contracts; repeated games; risk dominance; strategic risk;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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