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Prisoners` Dilemma in Duopoly Supergames

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  • L. Lambertini

Abstract

The choice between quantity and price in order to stabilize collusion is modeled here. It is shown that this relocates the prisoners’ dilemma backwards, from the market stage to the stage where the market variable is chosen in order to sustain collusion, and where discount rates appear as the payo¤s. Likewise, a prisoners’ dilemma arises also when both the market variable and the type of behavior (cooperative or non-cooperative) are simultaneously chosen.

Suggested Citation

  • L. Lambertini, 1996. "Prisoners` Dilemma in Duopoly Supergames," Working Papers 264, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:264
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    References listed on IDEAS

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    1. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
    2. Val Eugene Lambson, 1987. "Optimal Penal Codes in Price-setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 385-397.
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    5. 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.
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    7. Rothschild, R., 1992. "On the sustainability of collusion in differentiated duopolies," Economics Letters, Elsevier, vol. 40(1), pages 33-37, September.
    8. 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.
    9. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
    10. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    11. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    12. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    13. Boyer, Marcel & Moreaux, Michel, 1987. "On Stackelberg Equilibria with Differentiated Products: The Critical Role of the Strategy Space," Journal of Industrial Economics, Wiley Blackwell, vol. 36(2), pages 217-230, December.
    14. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
    15. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
    16. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
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    Citations

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    Cited by:

    1. Lambertini, L. & Sasaki, D., 1999. "A Cost-Side Analysis on Collusive Sustainability," Department of Economics - Working Papers Series 710, The University of Melbourne.
    2. F. Delbono & L. Lambertini, 2016. "On Globally Optimal Punishments in the Repeated Cournot Game," Working Papers wp1091, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. L. Lambertini & L. Marattin, 2016. "On Prices' Cyclical Behaviour in Oligopolistic Markets," Working Papers wp1064, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. Lambertini, Luca & Poddar, Sougata & Sasaki, Dan, 1998. "Standardization and the stability of collusion," Economics Letters, Elsevier, vol. 58(3), pages 303-310, March.
    5. Choi, Kangsik & Lim, Seonyoung, 2014. "Strategic Trade Policies with Endogenous Choice of Competition Mode under a Vertical Structure," MPRA Paper 59074, University Library of Munich, Germany.
    6. Luca Lambertini & Sougata Poddar & Dan Sasaki, 1997. "RJVs and Price Collusion under Endogenous Product Differentiation," Discussion Papers 97-09, University of Copenhagen. Department of Economics.
    7. L. Lambertini & S. Poddar & D. Sasaki, 1998. "Price versus Quantity Competition with Cost Sharing," Working Papers 343, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Baldelli, Serena & Lambertini, Luca, 2006. "Price vs quantity in a duopoly supergame with Nash punishments," Research in Economics, Elsevier, vol. 60(3), pages 121-130, September.
    9. repec:wsi:igtrxx:v:06:y:2004:i:04:n:s0219198904000320 is not listed on IDEAS
    10. Roberto Cellini & Luca Lambertini, 2004. "Private And Social Incentives Towards Investment In Product Differentiation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 493-508.
    11. Alipranti, Maria & Milliou, Chrysovalantou & Petrakis, Emmanuel, 2014. "Price vs. quantity competition in a vertically related market," Economics Letters, Elsevier, vol. 124(1), pages 122-126.
    12. Trishita Bhattacharjee & Rupayan Pal, 2013. "Price vs. Quantity in duopoly with strategic delegation: Role of network externalities," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2013-010, Indira Gandhi Institute of Development Research, Mumbai, India.
    13. Lee, DongJoon & Choi, Kangsik & Nariu, Tatsuhiko, 2016. "Endogenous Choice of Price or Quantity Contract with Upstream R&D Investment: Linear Pricing and Two-part Tariff Contract with Bargaining," MPRA Paper 72752, University Library of Munich, Germany.
    14. Etro, Federico, 2016. "Research in economics and industrial organization," Research in Economics, Elsevier, vol. 70(4), pages 511-517.
    15. Lim, Seonyoung & Choi, Kangsik, 2014. "Strategic Subsidy Policies with Endogenous Choice of Competition Mode," MPRA Paper 59462, University Library of Munich, Germany.
    16. Poddar, Sougata & Sasaki, Dan, 2002. "The strategic benefit from advance production," European Journal of Political Economy, Elsevier, vol. 18(3), pages 579-595, September.
    17. Kangsik, Choi, 2011. "Cournot and Bertrand competition with asymmetric costs in a mixed duopoly," MPRA Paper 34100, University Library of Munich, Germany.
    18. Choi, Kangsik & Lee, Ki-Dong & Lim, Seonyoung, 2016. "Strategic Trade Policies In International Rivalry When Competition Mode Is Endogenous," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(2), pages 223-241, December.
    19. Kangsik, Choi, 2008. "Cournot-Bertrand competition in a unionized mixed duopoly," MPRA Paper 12787, University Library of Munich, Germany, revised 26 Dec 2008.
    20. Lee, DongJoon & Choi, Kangsik & Hwang, Kyu-Chan, 2014. "Reverse First-mover and Second-mover Advantage in a Vertical Structure," MPRA Paper 59803, University Library of Munich, Germany.
    21. Luciano Fanti & Marcella Scrimitore, 2017. "How to compete? Cournot vs. Bertrand in a vertical structure with an integrated input supplier," Discussion Papers 2017/221, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    22. Kangsik, Choi, 2012. "Cournot and Bertrand competition with asymmetric costs in a mixed duopoly revisited," MPRA Paper 37704, University Library of Munich, Germany, revised 28 Mar 2012.
    23. R. Cellini & L. Lambertini, 2002. "Advertising with Spillover Effects in a Differential Oligopoly Game With Differentiated Goods," Working Papers 430, Dipartimento Scienze Economiche, Universita' di Bologna.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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