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An OLG Differential Game of Pollution Control with the Risk of a Catastrophic Climate Change

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  • Stefan Wrzaczek

    (International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria)

Abstract

This paper studies an overlapping generations (OLG) differential game on optimal emissions with continuous age structure and different types of individuals. At the (stochastic) arrival of a catastrophic climate change, the utility and the damage to the stock of pollution change for the rest of the time horizon. We derive the open-loop (OL) Nash equilibrium and show that it is subgame perfect and moreover equal to the feedback Stackelberg one. We compare the solution to the cooperative one (using the social welfare as objective function) and show the different dynamic evolutions of optimal emissions over time. Finally, we derive a time-consistent tax scheme that reaches the cooperative optimal solution in the OL Nash equilibrium. The tax scheme turns out to be heterogeneous with respect to age and type (anticipating and nonanticipating the catastrophic climate change). Setting taxes that are homogeneous across the individual type leads to an OL Nash solution that produces socially optimal total emissions, but lower individual utilities.

Suggested Citation

  • Stefan Wrzaczek, 2021. "An OLG Differential Game of Pollution Control with the Risk of a Catastrophic Climate Change," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-26, December.
    • Handle: RePEc:wsi:igtrxx:v:23:y:2021:i:04:n:s0219198922500025
    DOI: 10.1142/S0219198922500025
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    Cited by:

    1. Feichtinger, Gustav & Wrzaczek, Stefan, 2024. "The optimal momentum of population growth and decline," Theoretical Population Biology, Elsevier, vol. 155(C), pages 51-66.
    2. Feichtinger, Gustav & Lambertini, Luca & Leitmann, George & Wrzaczek, Stefan, 2022. "Managing the tragedy of commons and polluting emissions: A unified view," European Journal of Operational Research, Elsevier, vol. 303(1), pages 487-499.

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