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Folk theorems in a class of additively separable games

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  • Delbono, Flavio
  • Lambertini, Luca

Abstract

We study a class of games featuring payoff functions 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 infinite supergames is independent of the number of players. This holds irrespective of whether punishment is based on infinite Nash reversion or one-shot stick-and-carrot strategy. We outline two examples stemming from economic theory and one from international relations.

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  • Delbono, Flavio & Lambertini, Luca, 2018. "Folk theorems in a class of additively separable games," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 10-15.
    • Handle: RePEc:eee:matsoc:v:92:y:2018:i:c:p:10-15
    DOI: 10.1016/j.mathsocsci.2017.12.004
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    1. 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.
    2. 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.
    3. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    4. Martin Shubik, 1971. "The Dollar Auction game: a paradox in noncooperative behavior and escalation," Journal of Conflict Resolution, Peace Science Society (International), vol. 15(1), pages 109-111, March.
    5. Ivaldi, Marc & Jullien, Bruno & Rey, Patrick & Seabright, Paul & Tirole, Jean, 2003. "The Economics of Tacit Collusion," IDEI Working Papers 186, Institut d'Économie Industrielle (IDEI), Toulouse.
    6. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
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    Cited by:

    1. Delbono, Flavio & Lambertini, Luca, 2023. "Stackelberg leadership and managerial delegation under hyperbolic demand," Economics Letters, Elsevier, vol. 224(C).

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