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Optimal Collusion with Limited Severity Constraint

Author

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  • Etienne Billette de Villemeur

    () (Toulouse School of Economics, IDEI & GREMAQ, 21 allée de Brienne, 31000 Toulouse, France)

  • Laurent Flochel

    () (Charles River Associates International, 27 Avenue de l'Opéra, 75001 Paris, France)

  • Bruno Versaevel

    () (EMLYON Business School & CNRS, GATE, 69134 Ecully cedex France)

Abstract

Collusion sustainability depends on firms' aptitude to impose suffciently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic ï¬ rms 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.

Suggested Citation

  • Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2009. "Optimal Collusion with Limited Severity Constraint," Working Papers 0909, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
  • Handle: RePEc:gat:wpaper:0909
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    References listed on IDEAS

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    More about this item

    Keywords

    Collusion; Oligopoly; Penal codes;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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