A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games

2020

Energies

Self Cite

In this paper, we present a stylized dynamic interdependent multi-country energy transition model. The goal of this paper is to provide a starting point for examining the impact of uncertainty in such models. To do this, we define a simple model based on the standard Solow macroeconomic growth model. We consider this model in a two-country setting using a non-cooperative dynamic game perspective. Total carbon dioxide (CO2) emission is added in this growth model as a factor that has a negative impact on economic growth, whereas production can be realized using either green or fossil energy. Additionally, a factor is incorporated that captures the difficulties of using green energy, such as accessibility per country. We calibrate this model for a two-player setting, in which one player represents all countries affiliated with the Organization for Economic Cooperation and Development (OECD) and the other player represents countries not affiliated with the OECD. It is shown that, in general, the model is capable to describe energy transitions towards quite different equilibrium constellations. It turns out that this is mainly caused by the choice of policy parameters chosen in the objective function. We also analyze the optimal response strategies of both countries if the model in equilibrium would be hit by a CO2 shock. Also, here we observe a quite natural response. As the model is quite stylized, a serious study is performed to the impact several model uncertainties have on the results. It turns out that, within the OECD/non-OECD framework, most of the considered uncertainties do not impact results much. However, the way we calibrate policy parameters does carry much uncertainty and, as such, influences equilibrium outcomes a lot.

Section: Benchmark Model Simulationsmentioning

confidence: 99%

Measuring Impact of Uncertainty in a Stylized Macroeconomic Climate Model within a Dynamic Game Perspective

Stienen

2020

Energies

Self Cite

“…To perform the simulations, we used the numerical toolbox developed by [16] to solve N -player affine linear-quadratic open-loop differential games. Clearly, the use of open-loop strategies is made to simplify the analysis.…”

Section: Benchmark Model Simulationsmentioning

confidence: 99%

Measuring impact of uncertainty in a stylized macro-economic climate model within a dynamic game perspective

Stienen

2018

IFAC-PapersOnLine

In this paper we try to quantify/measure the main factors that influence the equilibrium outcome and pursued strategies in a simplistic model for the use of fossil versus green energy over time. The model is derived using the standard Solow macro-economic growth model in a twocountry setting within a dynamic game perspective. After calibrating the model for a setting of OECD versus non-OECD countries we study what kind of uncertainties affect the outcomes of the linearized model most, assuming both countries use Nash strategies to cope with shocks that impact the model. The main outcome of this study is that the parameters that occur in the objective of both players seem to carry the most uncertainty for both the outcome of the model and strategies.

“…To perform the simulations, we used the numerical toolbox developed by [31] to solve N-player affine LQ open-loop differential games. The discrepancy between the loss of NDC and other players stems from the quadratic nature of the loss function.…”

Section: A Simulation Studymentioning

confidence: 99%

Economic Growth and Choice of Energy: A Simplistic Strategic Approach

Michalak

2014

Environ Model Assess

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In this paper, we present a simplistic dynamic model to analyze the tradeoff between the use of environment-friendly energy and the use of environmentpolluting energy in a dynamic world characterized by players that have different interests. Our approach builds upon a neoclassical growth model, integrating different economies, and including pollution as a separate growth factor. The model is cast in a differential game framework with the open-loop information structure. In this setting, we analyze the impact of pollution over time on the fossil fuel/"green" energy ratio. Furthermore, based on a simulation study for the linearized model, we consider the question whether certain cooperative arrangements between countries having different interests can be expected in case pollution shocks occur.