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An integral transformation approach to differential games: a climate model application

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  • Raouf Boucekkine
  • Giorgio Fabbri
  • Salvatore Federico
  • Fausto Gozzi
  • Ted Loch-Temzelides
  • Cristiano Ricci

Abstract

We develop an Integral Transformation Method (ITM) for the study of suitable optimal control and differential game models. This allows for a solution to such dynamic problems to be found through solving a family of optimization problems parametrized by time. The method is quite flexible, and it can be used in several economic applications where the state equation and the objective functional are linear in a state variable. We illustrate the ITM in the context of a two-country integrated assessment climate model. We characterize emissions, consumption, transfers, and welfare by computing the Nash equilibria of the associated dynamic game. We then compare them to efficiency benchmarks. Further, we apply the ITM in a robust control setup, where we investigate how (deep) uncertainty affects climate outcomes.

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  • Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi & Ted Loch-Temzelides & Cristiano Ricci, 2025. "An integral transformation approach to differential games: a climate model application," Papers 2501.01749, arXiv.org.
    • Handle: RePEc:arx:papers:2501.01749
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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies

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