Optimal Collusion with Limited Severity Constraint

Etienne Billette de Villemeur (1) , Laurent Flochel (2) , Bruno Versaevel (3, 4)

1 GREMAQ - Groupe de recherche en économie mathématique et quantitative
2 CRA - Charles River Associates International
3 EM - EMLyon Business School
4 GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne

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.

Mots clés: Collusion; Oligopoly; Penal codes

Domaines: Economies et finances

Etienne Billette de Villemeur, Laurent Flochel, Bruno Versaevel. Optimal Collusion with Limited Severity Constraint. 2009. ⟨halshs-00375798⟩