Optimal Collusion with Limited Liability

Collusion sustainability depends on firms' ability to impose sufficiently severe punishments in the event of deviation from the collusive rule. We extend results from the literature on optimal collusion by investigating the role of a limited liability constraint. We examine all situations in which either structural conditions, financial considerations, or institutional circumstances set a lower bound, possibly negative, to firms' profits. For a large class of repeated games we show that, when the limited liability constraint binds, 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.