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Optimal Collusion with Limited Severity Constraint

  • Etienne Billette de Villemeur

    ()

    (Toulouse School of Economics, IDEI & GREMAQ, 21 allée de Brienne, 31000 Toulouse, France)

  • Laurent Flochel

    ()

    (Charles River Associates International, 27 Avenue de l'Opéra, 75001 Paris, France)

  • Bruno Versaevel

    ()

    (EMLYON Business School & CNRS, GATE, 69134 Ecully cedex France)

Collusion sustainability depends on firms' aptitude to impose suffciently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic ï¬rms 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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Paper provided by Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure in its series Working Papers with number 0909.

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Length: 51 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:gat:wpaper:0909
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  1. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
  2. 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.
  3. Kyle Bagwell, 2004. "Collusion and Price Rigidity," Theory workshop papers 658612000000000081, UCLA Department of Economics.
  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.
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  6. 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.
  7. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, 05.
  8. 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.
  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.
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  12. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
  13. 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.
  14. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  15. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  16. Tom Ross, 1990. "Cartel Stability And Product Differentiation," Carleton Industrial Organization Research Unit (CIORU) 90-04, Carleton University, Department of Economics.
  17. 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.
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  19. 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.
  20. Kyle Bagwell & Robert W. Staiger, 1995. "Collusion Over the Business Cycle," Discussion Papers 1118, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. 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.
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  30. Helder Vasconcelos, 2005. "Tacit Collusion, Cost Asymmetries, and Mergers," RAND Journal of Economics, The RAND Corporation, vol. 36(1), pages 39-62, Spring.
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  32. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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