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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
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Handle: RePEc:bol:bodewp:510
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  1. Rothschild, R., 1995. "Sustaining collusion when the choice of strategic variable is endogenous," Journal of Economic Behavior & Organization, Elsevier, vol. 28(3), pages 373-385, December.
  2. 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.
  3. Lambertini, Luca & Schultz, Christian, 2003. "Price or quantity in tacit collusion?," Economics Letters, Elsevier, vol. 78(1), pages 131-137, January.
  4. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  5. Luca Lambertini, 1997. "Prisoners’ Dilemma in Duopoly (Super)games," CIE Discussion Papers 1997-08, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  6. Majerus, David W., 1988. "Price vs. quantity competition in oligopoly supergames," Economics Letters, Elsevier, vol. 27(3), pages 293-297.
  7. Amir, Rabah, 2000. "Modelling imperfectly appropriable R&D via spillovers," International Journal of Industrial Organization, Elsevier, vol. 18(7), pages 1013-1032, October.
  8. 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.
  9. 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.
  10. Ross, Thomas W., 1992. "Cartel stability and product differentiation," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 1-13, March.
  11. Amir, Rabah & Evstigneev, Igor & Wooders, John, 2003. "Noncooperative versus cooperative R&D with endogenous spillover rates," Games and Economic Behavior, Elsevier, vol. 42(2), pages 183-207, February.
  12. L. Lambertini & C. Schultz, 2000. "Price vs Quantityin a Repeated Differentiated Duopoly," Working Papers 379, Dipartimento Scienze Economiche, Universita' di Bologna.
  13. 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.
  14. 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.
  15. 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.
  16. Cellini, Roberto & Lambertini, Luca, 2009. "Dynamic R&D with spillovers: Competition vs cooperation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 568-582, March.
  17. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  18. Katsoulacos, Yannis & Ulph, David, 1998. "Endogenous Spillovers and the Performance of Research Joint Ventures," Journal of Industrial Economics, Wiley Blackwell, vol. 46(3), pages 333-57, September.
  19. d'Aspremont, Claude & Jacquemin, Alexis, 1988. "Cooperative and Noncooperative R&D in Duopoly with Spillovers," American Economic Review, American Economic Association, vol. 78(5), pages 1133-37, December.
  20. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
  21. 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.
  22. Rabah Amir & John Wooders, 1998. "Cooperation vs. competition in R&D: The role of stability of equilibrium," Journal of Economics, Springer, vol. 67(1), pages 63-73, February.
  23. 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.
  24. Kotaro Suzumura, 1990. "Cooperative and Non-cooperative R&D in Oligopoly with Spillovers," Discussion Paper Series a218, Institute of Economic Research, Hitotsubashi University.
  25. Rothschild, R., 1992. "On the sustainability of collusion in differentiated duopolies," Economics Letters, Elsevier, vol. 40(1), pages 33-37, September.
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