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Price vs Quantity in a Duopoly Supergame with Nash Punishments

  • S. Baldelli
  • L. Lambertini

We examine the endogenous choice between price and quantity behaviour in a duopoly supergame with product differentiation. We find that (i) if cartel profits are evenly split between firms, then only symmetric equilibria obtains; (i) if instead the additional profits available through collusion are split according to the Nash bargaining solution, there are parameter regions where all subgame perfect equilibria are asymmetric, with firms colluding in price-quantity supergames.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number 510.

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Date of creation: 2004
Handle: RePEc:bol:bodewp:510
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  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. L. Lambertini, 1996. "Prisoners` Dilemma in Duopoly Supergames," Working Papers 264, Dipartimento Scienze Economiche, Universita' di Bologna.
  3. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
  4. 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.
  5. Rothschild, R., 1992. "On the sustainability of collusion in differentiated duopolies," Economics Letters, Elsevier, vol. 40(1), pages 33-37, September.
  6. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 371-382.
  7. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 23-35.
  8. Tom Ross, 1990. "Cartel Stability And Product Differentiation," Carleton Industrial Organization Research Unit (CIORU) 90-04, Carleton University, Department of Economics.
  9. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  10. Lambertini, Luca & Schultz, Christian, 2003. "Price or quantity in tacit collusion?," Economics Letters, Elsevier, vol. 78(1), pages 131-137, January.
  11. Majerus, David W., 1988. "Price vs. quantity competition in oligopoly supergames," Economics Letters, Elsevier, vol. 27(3), pages 293-297.
  12. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
  13. Luca Lambertini & Dan Sasaki, 1999. "Optimal punishments in linear duopoly supergames with product differentiation," Journal of Economics, Springer, vol. 69(2), pages 173-188, June.
  14. R.Rothschild, . "Sustaining Collusion When the Choice of Strategic Variable is Endogenous," Working Papers ec3/93, Department of Economics, University of Lancaster.
  15. Chang, Myong-Hun, 1992. "Intertemporal Product Choice and Its Effects on Collusive Firm Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 773-93, November.
  16. L. Lambertini & C. Schultz, 2000. "Price vs Quantity in a Repeated Differentiated Duopoly," Working Papers 379, Dipartimento Scienze Economiche, Universita' di Bologna.
  17. Macleod, W. Bentley, . "A theory of conscious parallelism," CORE Discussion Papers RP 629, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
  19. Albaek, Svend & Lambertini, Luca, 1998. "Collusion in differentiated duopolies revisited," Economics Letters, Elsevier, vol. 59(3), pages 305-308, June.
  20. 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.
  21. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
  22. Davidson, Carl & Deneckere, Raymond J, 1990. "Excess Capacity and Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 521-41, August.
  23. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  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.
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