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.