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Parabolic Cylinders and Folk Theorems

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  • F. Delbono
  • L. Lambertini

Abstract

We study a class of games featuring payoff functions being parabolic cylinders where best reply functions are orthogonal and therefore the pure-strategy non-cooperative solution is attained as a Nash equilibrium in dominant strategies. We prove that the resulting threshold of the discount factor above which implicit collusion on the Pareto frontier is stable in the infi?nite supergames is independent of the number of players. This holds irrespective of whether punishment is based on in?finite Nash reversion or one-shot stick-and-carrot strategy. We outline two examples stemming from economic theory and one from international relations.

Suggested Citation

  • F. Delbono & L. Lambertini, 2015. "Parabolic Cylinders and Folk Theorems," Working Papers wp1043, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:wp1043
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    References listed on IDEAS

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    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    3. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    4. Luca Lambertini & Dan Sasaki, 2002. "Non‐Negative Quantity Constraints and the Duration of Punishment," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 77-93, March.
    5. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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