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Optimal Collusion with Limited Severity Constraint

  • Etienne Billette De Villemeur

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - CNRS : UMR5604 - Université des Sciences Sociales - Toulouse I - École des Hautes Études en Sciences Sociales (EHESS) - Institut national de la recherche agronomique (INRA) : UMR)

  • Laurent Flochel

    (CRA - Charles River Associates International - Charles River Associates International)

  • Bruno Versaevel

    ()

    (EMLYON RECHERCHE - EMLYON Business School, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure (ENS) - Lyon - PRES Université de Lyon - Université Jean Monnet - Saint-Etienne - Université Claude Bernard - Lyon I)

Collusion sustainability depends on firms' aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic firms to implement a collusive strategy when their ability to punish deviations over one or several periods is limited by a severity constraint. It captures all situations in which either structural conditions (the form of payoff functions), institutional circumstances (a regulation), or financial considerations (profitability requirements) set a lower bound to firms' losses. The model specifications encompass the structural assumptions (A1-A3) in Abreu (1986) [Journal of Economic Theory, 39, 191-225]. The optimal punishment scheme is characterized, and the expression of the lowest discount factor for which collusion can be sustained is computed, that both depend on the status of the severity constraint. This extends received results from the literature to a large class of models that include a severity constraint, and uncovers the role of structural parameters that facilitate collusion by relaxing the constraint.

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Date of creation: 2009
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Handle: RePEc:hal:journl:halshs-00375798
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  1. Robert Gagné & Simon van Norden & Bruno Versaevel, 2006. "Testing Optimal Punishment Mechanisms under Price Regulation: the Case of the Retail Market for Gasoline," Working Papers 0611, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  2. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
  3. 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.
  4. Bagwell, K. & Staiger, R.W., 1995. "Collusion Over the Business Cycle," Working papers 9504, Wisconsin Madison - Social Systems.
  5. 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.
  6. Hackner, Jonas, 1994. "Collusive pricing in markets for vertically differentiated products," International Journal of Industrial Organization, Elsevier, vol. 12(2), pages 155-177, June.
  7. 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.
  8. Wernerfelt, Birger, 1989. "Tacit collusion in differentiated cournot games," Economics Letters, Elsevier, vol. 29(4), pages 303-306.
  9. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  10. Kyle Bagwell, 2004. "Collusion and Price Rigidity," Theory workshop papers 658612000000000081, UCLA Department of Economics.
  11. Helder Vasconcelos, 2005. "Tacit Collusion, Cost Asymmetries, and Mergers," RAND Journal of Economics, The RAND Corporation, vol. 36(1), pages 39-62, Spring.
  12. 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.
  13. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
  14. Susan Athey & Kyle Bagwell, 2007. "Collusion with Persistent Cost Shocks," Levine's Bibliography 321307000000000898, UCLA Department of Economics.
  15. Chang, Myong-Hun, 1991. "The effects of product differentiation on collusive pricing," International Journal of Industrial Organization, Elsevier, vol. 9(3), pages 453-469, September.
  16. 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.
  17. Majerus, David W., 1988. "Price vs. quantity competition in oligopoly supergames," Economics Letters, Elsevier, vol. 27(3), pages 293-297.
  18. B. Douglas Bernheim & Michael D. Whinston, 1990. "Multimarket Contact and Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 1-26, Spring.
  19. Lambertini, L. & Sasaki, D., 1998. "Non-Negative Quantity Constraints and the Duration of Punishment," Department of Economics - Working Papers Series 630, The University of Melbourne.
  20. Häckner, Jonas, 1999. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Research Papers in Economics 1999:9, Stockholm University, Department of Economics.
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  22. Ross, Thomas W., 1992. "Cartel stability and product differentiation," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 1-13, March.
  23. 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.
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  25. 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.
  26. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  27. Lambertini, Luca & Sasaki, Dan, 2001. "Marginal costs and collusive sustainability," Economics Letters, Elsevier, vol. 72(1), pages 117-120, July.
  28. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
  29. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  30. Rothschild, R., 1999. "Cartel stability when costs are heterogeneous," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 717-734, July.
  31. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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