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Optimal Collusion with Limited Severity Constraint

  • Etienne Billette De Villemeur

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - CNRS : UMR5604 - Université des Sciences Sociales - Toulouse I - École des Hautes Études en Sciences Sociales (EHESS) - Institut national de la recherche agronomique (INRA) : UMR)

  • Laurent Flochel

    (CRA - Charles River Associates International - Charles River Associates International)

  • Bruno Versaevel

    ()

    (EMLYON RECHERCHE - EMLYON Business School, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure (ENS) - Lyon - PRES Université de Lyon - Université Jean Monnet - Saint-Etienne - Université Claude Bernard - Lyon I)

Collusion sustainability depends on firms' aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic firms to implement a collusive strategy when their ability to punish deviations over one or several periods is limited by a severity constraint. It captures all situations in which either structural conditions (the form of payoff functions), institutional circumstances (a regulation), or financial considerations (profitability requirements) set a lower bound to firms' losses. The model specifications encompass the structural assumptions (A1-A3) in Abreu (1986) [Journal of Economic Theory, 39, 191-225]. The optimal punishment scheme is characterized, and the expression of the lowest discount factor for which collusion can be sustained is computed, that both depend on the status of the severity constraint. This extends received results from the literature to a large class of models that include a severity constraint, and uncovers the role of structural parameters that facilitate collusion by relaxing the constraint.

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Date of creation: 2009
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Handle: RePEc:hal:journl:halshs-00375798
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  1. Ross, Thomas W., 1992. "Cartel stability and product differentiation," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 1-13, March.
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  8. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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  13. Susan Athey & Kyle Bagwell, 2004. "Collusion with Persistent Cost Shocks," Levine's Bibliography 122247000000000334, UCLA Department of Economics.
  14. Lambson Val Eugene, 1994. "Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames," Journal of Economic Theory, Elsevier, vol. 62(2), pages 444-468, April.
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