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Modeling and Computation of Mean Field Equilibria in Producers' Game with Emission Permits Trading

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  • Shuhua Chang
  • Xinyu Wang
  • Alexander Shananin

Abstract

In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.

Suggested Citation

  • Shuhua Chang & Xinyu Wang & Alexander Shananin, 2015. "Modeling and Computation of Mean Field Equilibria in Producers' Game with Emission Permits Trading," Papers 1506.04869, arXiv.org.
    • Handle: RePEc:arx:papers:1506.04869
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    File URL: http://arxiv.org/pdf/1506.04869
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Hai-Feng & Jin, Zhen & Wang, Zhen, 2014. "Cooperation and popularity in spatial games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 86-94.
    3. Seifert, Jan & Uhrig-Homburg, Marliese & Wagner, Michael, 2008. "Dynamic behavior of CO2 spot prices," Journal of Environmental Economics and Management, Elsevier, vol. 56(2), pages 180-194, September.
    4. Shoude Li, 2014. "A Differential Game of Transboundary Industrial Pollution with Emission Permits Trading," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 642-659, November.
    5. Shuhua Chang & Xinyu Wang, 2015. "Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-35, May.
    6. repec:dau:papers:123456789/3001 is not listed on IDEAS
    7. Daskalakis, George & Psychoyios, Dimitris & Markellos, Raphael N., 2009. "Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1230-1241, July.
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    Cited by:

    1. Wang, Xinyu & Zhang, Shuhua & Hao, Wenwei, 2022. "Myopic vs. foresighted behaviors in a transboundary pollution game with abatement policy and emission permits trading," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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