Abstract
We present two solution algorithms for a large-scale integrated assessment model of climate change mitigation: the well known Negishi algorithm and a newly developed Nash algorithm. The algorithms are used to calculate the Pareto-optimum and competitive equilibrium, respectively, for the global model that includes trade in a number of goods as an interaction between regions. We demonstrate that in the absence of externalities both algorithms deliver the same solution. The Nash algorithm is computationally much more effective, and scales more favorably with the number of regions. In the presence of externalities between regions the two solutions differ, which we demonstrate by the inclusion of global spillovers from learning-by-doing in the energy sector. The non-cooperative treatment of the spillover externality in the Nash algorithm leads to a delay in the expansion of renewable energy installations compared to the cooperative solution derived using the Negishi algorithm.
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Notes
Within an iterative sequence (Nordhaus and Yang 1996) compute a closed-loop Nash equilibrium (Fudenberg and Levine 1988). Technically, this is an outcome of a finite game with perfect information and calculated through backward induction (Mas-Colell et al. 1995, Chapter 9; Kicsiny et al. 2014). A survey on Generalized Nash equilibrium problems is provided by Facchinei and Kanzow (2010). Yang (2003) demonstrated how the closed-loop solution can be found by a computationally more tractable sequence of open-loop equilibria.
We solve the model on a high-performance computer cluster equipped with Intel Xeon E5472 CPUs at 3.0 GHz.
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Funding from the German Federal Ministry of Education and Research (BMBF) in the Call Economics of Climate Change (funding code 01LA1105A CliPoN) is gratefully acknowledged.
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Marian Leimbach and Anselm Schultes have contributed equally to this study.
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Leimbach, M., Schultes, A., Baumstark, L. et al. Solution algorithms for regional interactions in large-scale integrated assessment models of climate change. Ann Oper Res 255, 29–45 (2017). https://doi.org/10.1007/s10479-016-2340-z
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DOI: https://doi.org/10.1007/s10479-016-2340-z