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A dynamic theory of spatial externalities

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  • Boucekkine, Raouf
  • Fabbri, Giorgio
  • Federico, Salvatore
  • Gozzi, Fausto
Abstract
We characterize the shape of spatial externalities in a continuous time and space differential game with transboundary pollution. We posit a realistic spatiotemporal law of motion for pollution (diffusion and advection), and tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. We allow for a rich set of geographic heterogeneities across states. We solve analytically the induced non-cooperative differential game and characterize its long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the affine feedbacks. We further provide with a full exploration of the free riding problem and the associated border effect.

Suggested Citation

  • Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:133-165
    DOI: 10.1016/j.geb.2021.12.002
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    Cited by:

    1. Boucekkine, Raouf & Ruan, Weihua & Zou, Benteng, 2023. "The irreversible pollution game," Journal of Environmental Economics and Management, Elsevier, vol. 120(C).
    2. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. Bahlali, Mohamed & Petit, Quentin, 2024. "An equilibrium model of city with atmospheric pollution dispersion," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    4. Jacek Rothert, 2021. "Optimal federal transfers during uncoordinated response to a pandemic," GRAPE Working Papers 58, GRAPE Group for Research in Applied Economics.
    5. Jacek Rothert, 2022. "Optimal federal transfers during uncoordinated response to a pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1124-1153, October.
    6. Rabah Amir & Raouf Boucekkine, 2022. "Introduction to the special issue on new insights into economic epidemiology: Theory and policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 861-872, October.
    7. Basei, Matteo & Ferrari, Giorgio & Rodosthenous, Neofytos, 2024. "Uncertainty over uncertainty in environmental policy adoption: Bayesian learning of unpredictable socioeconomic costs," Journal of Economic Dynamics and Control, Elsevier, vol. 161(C).

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    More about this item

    Keywords

    Spatial externalities; Spatial diffusion; Differential games in continuous time and space; Infinite dimensional optimal control problems; Environmental federalism;
    All these keywords.

    JEL classification:

    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth

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