Congestion games and applications, nash equilibrium and anarchy price

Abstract

This thesis examines singleton congestion games in the non-symmetric case. We proposed simplified analytical formulations that allow for an accurate description of the possible sets of equilibria, including the classical Nash equilibrium and the strong Nash equilibrium in the case of two resources. Furthermore, we developed a general methodology for computing the Nash equilibrium in the general case, supported by practical and efficient algorithms. These algorithms enabled the evaluation of the proposed solutions’ performance and the calculation of the difference between the Price of Anarchy and the Price of Stability, thereby highlighting the theoretical and practical value of this work.