[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/38481.html
   My bibliography  Save this paper

Optimal collusion with limited liability

Author

Listed:
  • Billette de Villemeur, Etienne
  • Flochel, Laurent
  • Versaevel, Bruno
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.

Suggested Citation

  • Billette de Villemeur, Etienne & Flochel, Laurent & Versaevel, Bruno, 2012. "Optimal collusion with limited liability," MPRA Paper 38481, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:38481
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/38481/1/MPRA_paper_38481.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/42638/1/MPRA_paper_42658.pdf
    File Function: revised version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/53600/1/MPRA_paper_42658.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Val Eugene Lambson, 1987. "Optimal Penal Codes in Price-setting Supergames with Capacity Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 385-397.
    2. Malcolm Baker & Jeremy C. Stein & Jeffrey Wurgler, 2003. "When Does the Market Matter? Stock Prices and the Investment of Equity-Dependent Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 969-1005.
    3. Susan Athey & Kyle Bagwell & Chris Sanchirico, 2004. "Collusion and Price Rigidity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 317-349.
    4. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    5. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    6. Robert Gagné & Simon van Norden & Bruno Versaevel, 2003. "Testing Optimal Punishment Mechanisms Under Price Regulation: the Case of the Retail Market for Gasoline," CIRANO Working Papers 2003s-57, CIRANO.
    7. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    8. John Haltiwanger & Joseph E. Harrington Jr., 1991. "The Impact of Cyclical Demand Movements on Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 22(1), pages 89-106, Spring.
    9. Hackner, Jonas, 1996. "Optimal symmetric punishments in a Bertrand differentiated products duopoly," International Journal of Industrial Organization, Elsevier, vol. 14(5), pages 611-630, July.
    10. Kyle Bagwell & Robert Staiger, 1997. "Collusion Over the Business Cycle," RAND Journal of Economics, The RAND Corporation, vol. 28(1), pages 82-106, Spring.
    11. Michael D. Noel, 2007. "Edgeworth Price Cycles: Evidence From The Toronto Retail Gasoline Market," Journal of Industrial Economics, Wiley Blackwell, vol. 55(1), pages 69-92, March.
    12. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    13. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    14. Carmen Beviá & Luis C. Corchón & Yosuke Yasuda, 2020. "Oligopolistic equilibrium and financial constraints," RAND Journal of Economics, RAND Corporation, vol. 51(1), pages 279-300, March.
    15. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
    16. Scott Baker & Pak Yee Lee & Claudio Mezzetti, 2011. "Intellectual property disclosure as threat," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(1), pages 21-38, March.
    17. Rothschild, R., 1999. "Cartel stability when costs are heterogeneous," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 717-734, July.
    18. Luca Lambertini & Dan Sasaki, 2002. "Non‐Negative Quantity Constraints and the Duration of Punishment," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 77-93, March.
    19. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
    20. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    21. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    22. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
    23. George Symeonidis, 2003. "In Which Industries is Collusion More Likely? Evidence from the UK," Journal of Industrial Economics, Wiley Blackwell, vol. 51(1), pages 45-74, March.
    24. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    25. Helder Vasconcelos, 2005. "Tacit Collusion, Cost Asymmetries, and Mergers," RAND Journal of Economics, The RAND Corporation, vol. 36(1), pages 39-62, Spring.
    26. Osterdal, Lars Peter, 2003. "A note on the stability of collusion in differentiated oligopolies," Research in Economics, Elsevier, vol. 57(1), pages 53-64, March.
    27. Wernerfelt, Birger, 1989. "Tacit collusion in differentiated cournot games," Economics Letters, Elsevier, vol. 29(4), pages 303-306.
    28. Lambson Val Eugene, 1994. "Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames," Journal of Economic Theory, Elsevier, vol. 62(2), pages 444-468, April.
    29. Motta,Massimo, 2004. "Competition Policy," Cambridge Books, Cambridge University Press, number 9780521016919, January.
    30. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    31. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    32. Eckert, Andrew & West, Douglas S, 2004. "Retail Gasoline Price Cycles across Spatially Dispersed Gasoline Stations," Journal of Law and Economics, University of Chicago Press, vol. 47(1), pages 245-273, April.
    33. Lambertini, Luca & Sasaki, Dan, 2001. "Marginal costs and collusive sustainability," Economics Letters, Elsevier, vol. 72(1), pages 117-120, July.
    34. Jean-François Houde, 2010. "gasoline markets," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    35. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    36. Andrew Eckert, 2002. "Retail price cycles and response asymmetry," Canadian Journal of Economics, Canadian Economics Association, vol. 35(1), pages 52-77, February.
    37. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Konov, Joshua Ioji / JK, 2013. "Enhancing Markets (i.e. Economies) Transmissionability to Optimize Monetary Policies’ Effect," MPRA Paper 46950, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2009. "Optimal Collusion with Limited Severity Constraint," Post-Print halshs-00375798, HAL.
    2. Flochel, Laurent & Versaevel, Bruno & de Villemeur, Étienne, 2009. "Optimal Collusion with Limited Liability and Policy Implications," TSE Working Papers 09-027, Toulouse School of Economics (TSE), revised Jul 2011.
    3. Panayiotis Agisilaou, 2013. "Collusion in Industrial Economics and Optimally Designed Leniency Programmes - A Survey," Working Paper series, University of East Anglia, Centre for Competition Policy (CCP) 2013-03, Centre for Competition Policy, University of East Anglia, Norwich, UK..
    4. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    5. Robert Gagné & Simon van Norden & Bruno Versaevel, 2003. "Testing Optimal Punishment Mechanisms Under Price Regulation: the Case of the Retail Market for Gasoline," CIRANO Working Papers 2003s-57, CIRANO.
    6. Switgard Feuerstein, 2005. "Collusion in Industrial Economics—A Survey," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 163-198, December.
    7. Labrecciosa Paola & Colombo Luca, 2010. "Technology Uncertainty and Market Collusion," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-17, March.
    8. Joseph E. Harrington, Jr, 2005. "Detecting Cartels," Economics Working Paper Archive 526, The Johns Hopkins University,Department of Economics.
    9. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    10. Dou, Winston Wei & Ji, Yan & Wu, Wei, 2021. "Competition, profitability, and discount rates," Journal of Financial Economics, Elsevier, vol. 140(2), pages 582-620.
    11. Garrod, Luke, 2012. "Collusive price rigidity under price-matching punishments," International Journal of Industrial Organization, Elsevier, vol. 30(5), pages 471-482.
    12. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    13. Leonardo Madio & Aldo Pignataro, 2022. "Collusion sustainability with a capacity constrained firm," "Marco Fanno" Working Papers 0295, Dipartimento di Scienze Economiche "Marco Fanno".
    14. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.
    15. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, September.
    16. de Roos, Nicolas, 2006. "Examining models of collusion: The market for lysine," International Journal of Industrial Organization, Elsevier, vol. 24(6), pages 1083-1107, November.
    17. Leonardo Madio & Aldo Pignataro, 2022. "Collusion Sustainability with a Capacity Constrained Firm," CESifo Working Paper Series 10170, CESifo.
    18. Marcel Canoy & Patrick Rey & Eric van Damme, 2004. "Dominance and Monopolization," Chapters, in: Manfred Neumann & Jürgen Weigand (ed.), The International Handbook of Competition, chapter 7, Edward Elgar Publishing.
    19. Ivaldi, Marc & Jullien, Bruno & Rey, Patrick & Seabright, Paul & Tirole, Jean, 2003. "The Economics of Tacit Collusion," IDEI Working Papers 186, Institut d'Économie Industrielle (IDEI), Toulouse.
    20. Susan Athey & Kyle Bagwell & Chris Sanchirico, 2004. "Collusion and Price Rigidity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 317-349.

    More about this item

    Keywords

    Collusion; Oligopoly; Limited Liability;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:38481. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.