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S-Adapted Oligopoly Equilibria and Approximations in Stochastic Variational Inequalities

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  • Alain Haurie
  • Francesco Moresino

Abstract

This paper deals with a class of dynamic games that are used for modelling oligopolistic competition in discrete time with random disturbances that can be described as an event tree with exogenously given probabilities. The concepts of S-adapted information structure and S-adapted equilibrium are reviewed and a characterization of the equilibrium as the solution of a variational inequality (VI) is proposed. Conditions for existence and uniqueness of the equilibrium are provided. In order to deal with the large dimension of the VI an approximation method is proposed which is based on the use of random sampling of scenarios in the event tree. A proof of convergence is provided and these results are illustrated numerically on two dynamic oligopoly models. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Alain Haurie & Francesco Moresino, 2002. "S-Adapted Oligopoly Equilibria and Approximations in Stochastic Variational Inequalities," Annals of Operations Research, Springer, vol. 114(1), pages 183-201, August.
    • Handle: RePEc:spr:annopr:v:114:y:2002:i:1:p:183-201:10.1023/a:1021018421126
    DOI: 10.1023/A:1021018421126
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    Cited by:

    1. S. Gabriel & J. Fuller, 2010. "A Benders Decomposition Method for Solving Stochastic Complementarity Problems with an Application in Energy," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 301-329, April.
    2. Genc, Talat S. & Sen, Suvrajeet, 2008. "An analysis of capacity and price trajectories for the Ontario electricity market using dynamic Nash equilibrium under uncertainty," Energy Economics, Elsevier, vol. 30(1), pages 173-191, January.
    3. Genc, Talat S. & Thille, Henry, 2011. "Investment in electricity markets with asymmetric technologies," Energy Economics, Elsevier, vol. 33(3), pages 379-387, May.
    4. Bernard, A. & Haurie, A. & Vielle, M. & Viguier, L., 2008. "A two-level dynamic game of carbon emission trading between Russia, China, and Annex B countries," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1830-1856, June.
    5. Gabriel, Steven A. & Zhuang, Jifang & Egging, Ruud, 2009. "Solving stochastic complementarity problems in energy market modeling using scenario reduction," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1028-1040, September.
    6. Simone Balmelli & Francesco Moresino, 2023. "Coordination of Plug-In Electric Vehicle Charging in a Stochastic Framework: A Decentralized Tax/Incentive-Based Mechanism to Reach Global Optimality," Mathematics, MDPI, vol. 11(4), pages 1-24, February.
    7. Filomena, Tiago Pascoal & Campos-Náñez, Enrique & Duffey, Michael Robert, 2014. "Technology selection and capacity investment under uncertainty," European Journal of Operational Research, Elsevier, vol. 232(1), pages 125-136.
    8. Genc, Talat S. & Reynolds, Stanley S. & Sen, Suvrajeet, 2007. "Dynamic oligopolistic games under uncertainty: A stochastic programming approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 55-80, January.
    9. Paulus, Moritz, 2012. "How are investment decisions in the steam coal market affected by demand uncertainty and buyer-side market power?," EWI Working Papers 2012-3, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI).
    10. Elnaz Kanani Kuchesfehani & Georges Zaccour, 2015. "S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 644-658, August.
    11. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.

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