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On the convergence to the Cournot equilibrium in a productive asset oligopoly

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  • Colombo, Luca
  • Labrecciosa, Paola

Abstract

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.

Suggested Citation

  • Colombo, Luca & Labrecciosa, Paola, 2013. "On the convergence to the Cournot equilibrium in a productive asset oligopoly," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 441-445.
  • Handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:441-445
    DOI: 10.1016/j.jmateco.2013.09.008
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    References listed on IDEAS

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    1. repec:eee:jeborg:v:140:y:2017:i:c:p:91-119 is not listed on IDEAS
    2. Benchekroun, H. & Ray Chaudhuri, A. & Tasneem, Dina, 2019. "On the Impact of Trade in a Common Property Renewable Resource Oligopoly," Discussion Paper 2019-021, Tilburg University, Center for Economic Research.
    3. L. Lambertini & G. Leitmann, 2017. "On the attainment of the maximum sustainable yield in the Verhulst-Lotka-Volterra model," Working Papers wp1112, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. repec:wsi:igtrxx:v:20:y:2018:i:03:n:s0219198917500359 is not listed on IDEAS
    5. repec:eee:jeeman:v:92:y:2018:i:c:p:185-193 is not listed on IDEAS
    6. Benchekroun, Hassan & Long, Ngo Van, 2016. "Status concern and the exploitation of common pool renewable resources," Ecological Economics, Elsevier, vol. 125(C), pages 70-82.
    7. Tasneem, Dina & Engle-Warnick, Jim & Benchekroun, Hassan, 2017. "An experimental study of a common property renewable resource game in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 91-119.
    8. repec:wsi:igtrxx:v:19:y:2017:i:04:n:s0219198917500189 is not listed on IDEAS
    9. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0189-5 is not listed on IDEAS

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