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Prisoners’ other Dilemma

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  • Matthias Blonski
  • Giancarlo Spagnolo

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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    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;
    All these keywords.

    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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