Optimal collusion with limited liability

Etienne Billette de Villemeur, Laurent Flochel and Bruno Versaevel

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Collusion; Oligopoly; Limited Liability (search for similar items in EconPapers)
JEL-codes: C72 D43 L13 (search for similar items in EconPapers)
Date: 2012-04-30
New Economics Papers: this item is included in nep-bec, nep-com and nep-ind
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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https://mpra.ub.uni-muenchen.de/42638/1/MPRA_paper_42658.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/53600/1/MPRA_paper_42658.pdf revised version (application/pdf)

Related works:
Journal Article: Optimal collusion with limited liability (2013)
Working Paper: Optimal Collusion with Limited Liability (2013)
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