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Prisoners’ other Dilemma

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  • Matthias Blonski

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  • Giancarlo Spagnolo

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Abstract

We introduce a measure for the riskiness of cooperation in the infinitely repeated discounted Prisoner’s Dilemma and use it to explore how players cooperate once cooperation is an equilibrium. Riskiness of a cooperative equilibrium is based on a pairwise comparison between this equilibrium and the uniquely safe all defect equilibrium. It is a strategic concept heuristically related to Harsanyi and Selten’s risk dominance. Riskiness 0 defines the same critical discount factor $$\delta ^{*}$$ δ ∗ that was derived with an axiomatic approach for equilibrium selection in Blonski et al. (Am Econ J 3:164–192, 2011 ). Our theory predicts that the less risky cooperation is the more forgiving can parties afford to be if a deviator needs to be punished. Further, we provide sufficient conditions for cooperation equilibria to be risk perfect, i.e. not to be risky in any subgame, and we extend the theory to asymmetric settings. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Matthias Blonski & Giancarlo Spagnolo, 2015. "Prisoners’ other Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 61-81, February.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:1:p:61-81
    DOI: 10.1007/s00182-014-0419-9
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    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.
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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. repec:spr:sochwe:v:51:y:2018:i:1:d:10.1007_s00355-017-1107-z is not listed on IDEAS
    5. repec:eee:jeborg:v:155:y:2018:i:c:p:445-457 is not listed on IDEAS
    6. 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.
    7. 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.
    8. Camera, Gabriele & Gioffré, Alessandro, 2017. "Asymmetric social norms," Economics Letters, Elsevier, vol. 152(C), pages 27-30.
    9. 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.
    10. 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.
    11. 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.
    12. 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..
    13. 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.
    14. 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.
    15. Pablo Hernandez-Lagos & Dylan Minor & Dana Sisak, 2017. "Do people who care about others cooperate more? Experimental evidence from relative incentive pay," Experimental Economics, Springer;Economic Science Association, vol. 20(4), pages 809-835, December.
    16. 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.
    17. repec:pit:wpaper:532 is not listed on IDEAS
    18. 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.
    19. 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.
    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

    Cooperation; Repeated Prisoner’s Dilemma; Equilibrium selection; Forgiveness; Perfection; Strategic risk; Strategic uncertainty; Sucker’s payoff; Collusion; Coordination; C72; C73; C92; L13; L14; M50;

    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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