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Optimal Collusion with Limited Liability

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  • Etienne Billette de Villemeur

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRA - Institut National de la Recherche Agronomique - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées)

  • Laurent Flochel

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

  • Bruno Versaevel

    (emlyon business school, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon)

Abstract

Collusion sustainability depends on firms' aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We extend results from the literature on optimal collusion by investigating the role of limited liability. We examine all situations in which either structural conditions (demand and technology), financial considerations (a profitability target), or institutional circumstances (a regulation) set a lower bound, possibly negative, to firms' profits. For a large class of repeated games with discounting, we show that, absent participation and limited liability constraints, there exists a unique optimal penal code. It commands a severe single-period punishment immediately after a firm deviates from the collusive stage-game strategy. When either the participation constraint or the limited liability constraint bind, there exists an infinity of multi-period punishment paths that permit firms to implement the optimal collusive strategy. The usual front-loading scheme is only a specific case and an optimal punishment profile can take the form of a price asymmetric cycle. We characterize the situations in which a longer punishment does not perform as a perfect substitute for more immediate severity. In this case the lowest discount factor that permits collusion is strictly higher than without the limited liability constraint, which hinders collusion.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2013. "Optimal Collusion with Limited Liability," Post-Print halshs-00755569, HAL.
  • Handle: RePEc:hal:journl:halshs-00755569
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00755569
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    More about this item

    Keywords

    optimal collusion;

    JEL classification:

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

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