Working paper

Optimal Collusion with Limited Liability and Policy Implications

Laurent Flochel, Bruno Versaevel, and Étienne de Villemeur


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.

JEL codes

  • C72: Noncooperative Games
  • D43: Oligopoly and Other Forms of Market Imperfection
  • L13: Oligopoly and Other Imperfect Markets

See also

Published in

TSE Working Paper, n. 09-027, March 2009, revised July 2011