Competition among Several Gas Pipelines: A Game Model with Exponential Functions

The process of competition of large-scale projects is studied in a setting motivated by real-life problems of optimization of gas and oil transportation networks and optimization of the corresponding investment. The employed mathematical model is a noncooperative game of several players with choice of time moments and payoff functions that contain improper integrals. It is assumed that the investigated processes are described by exponential functions. This assumption is reasonable because of the economic sense of the problem. Also, this assumption simplifies the mathematical model and the implementation of the corresponding algorithms. The use of exponential functions makes it possible to create effective codes for computer modelling of these problems. The paper contains detailed consideration of the involved mathematical assumptions, description of the algorithms for finding points of Nash equilibrium and the best responses of investors to actions of other investors, and description of the developed software. An illustrative numerical example is also given