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Optimal Collusion with Limited Liability and Policy Implications

  • Flochel, Laurent
  • Versaevel, Bruno
  • de Villemeur, Étienne

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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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 547.

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Date of creation: Mar 2009
Date of revision: Jul 2011
Handle: RePEc:ide:wpaper:11169
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  1. 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.
  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. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  4. 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.
  5. 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.
  6. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  7. Robert Gagné & Simon Van Norden & Bruno Versaevel, 2006. "Testing Optimal Punishment Mechanisms under Price Regulation: the Case of the Retail Market for Gasoline," Post-Print halshs-00142516, HAL.
  8. 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.
  9. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  10. 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.
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