Mathematics of Sustainability - Modelling Investments in Energy Production with game Theory

Titel: Mathematics of Sustainability - Modelling Investments in Energy Production with Game Theory  

Abstract: This thesis investigates the choice between   investing in renewable energies and fossil fuels. The aim is to construct a model that can be extended   to a game for two agents. We begin by introducing the investment choice and establish two   basic assumptions. We define different maximization problems to describe the choices   mathematically; both short term and long term problems are given as well as with and without the   choice of investing in renewables. Thus in total four maximization problems are given. We   define when the model is well defined with respect to investment variables and marginal   utility. We consider properties of the model and from these properties we are able to construct an   algorithm to find a set of parameters for which the short term of the model is well defined with   respect to investment variabels and marginal utility Furthermore we construct an extension of the   algorithm to find additional parameters for the long term of the model   however we can not ensure that the long term of the model is well defined. Then we link the model to the problem initially   introduced and define when the mathematical model is well defined with respect to utility. It is   possible to adjust the parameters from the algorithm so that the short term of the model is also well defined   with respect to utility. Finally, we expand the short term model to a game   for two agents. The Nash equilibrium is found for a Cournot game given one set of feasible parameters and subgame   perfect equilibria are found for a Stackelberg game given three different   feasible set of parameters.