Billette de Villemeur, Etienne and Flochel, Laurent and Versaevel, Bruno (2012): Optimal collusion with limited liability.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Optimal collusion with limited liability|
|Keywords:||Collusion; Oligopoly; Limited Liability|
|Subjects:||L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets
D - Microeconomics > D4 - Market Structure and Pricing > D43 - Oligopoly and Other Forms of Market Imperfection
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Etienne Billette de Villemeur|
|Date Deposited:||30. Apr 2012 17:01|
|Last Modified:||20. Feb 2013 14:39|
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