Advanced Search
MyIDEAS: Login

Optimal collusion with limited liability

Contents:

Author Info

  • 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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/38481/
File Function: original version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/42638/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/53600/
File Function: revised version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38481.

as in new window
Length:
Date of creation: 30 Apr 2012
Date of revision:
Handle: RePEc:pra:mprapa:38481

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Collusion; Oligopoly; Limited Liability;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. 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.
  2. 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, 03.
  3. 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 245-73, April.
  4. 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.
  5. Jean-François Houde, 2010. "gasoline markets," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  6. Carmen Beviá & Luis C. Corchón & Yosuke Yasuda, 2011. "Oligopolistic Equilibrium and Financial Constraints," Working Papers 547, Barcelona Graduate School of Economics.
  7. Motta,Massimo, 2004. "Competition Policy," Cambridge Books, Cambridge University Press, number 9780521016919, October.
  8. Kyle Bagwell, 2004. "Collusion and Price Rigidity," Theory workshop papers 658612000000000081, UCLA Department of Economics.
  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. Lambertini, Luca & Sasaki, Dan, 2001. "Marginal costs and collusive sustainability," Economics Letters, Elsevier, vol. 72(1), pages 117-120, July.
  11. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  12. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  13. 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.
  14. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  15. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
  16. Lambson, Val Eugene, 1987. "Optimal Penal Codes in Price-Setting Supergames with Capacity Constraints," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 385-97, July.
  17. Malcolm Baker & Jeremy C. Stein & Jeffrey Wurgler, 2002. "When Does the Market Matter? Stock Prices and the Investment of Equity-Dependent Firms," NBER Working Papers 8750, National Bureau of Economic Research, Inc.
  18. Susan Athey & Kyle Bagwell, 2007. "Collusion with Persistent Cost Shocks," Levine's Bibliography 321307000000000898, UCLA Department of Economics.
  19. Bagwell, K. & Staiger, R.W., 1995. "Collusion Over the Business Cycle," Working papers 9504, Wisconsin Madison - Social Systems.
  20. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  21. Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
  22. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
  23. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  24. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  25. 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.
  26. Wernerfelt, Birger, 1989. "Tacit collusion in differentiated cournot games," Economics Letters, Elsevier, vol. 29(4), pages 303-306.
  27. Andrew Eckert, 2002. "Retail price cycles and response asymmetry," Canadian Journal of Economics, Canadian Economics Association, vol. 35(1), pages 52-77, February.
  28. Helder Vasconcelos, 2005. "Tacit Collusion, Cost Asymmetries, and Mergers," RAND Journal of Economics, The RAND Corporation, vol. 36(1), pages 39-62, Spring.
  29. 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.
  30. Rothschild, R., 1999. "Cartel stability when costs are heterogeneous," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 717-734, July.
  31. 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.
  32. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
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 in new window

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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:38481. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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