Generalized Nash Equilibrium Problems and Fuzzy ASA

Abstract

As an extension of the standard Nash equilibrium concept, the generalized Nash equilibrium (GNE) makes it possible to model and solve more general problems in several scenarios. Its most prominent advantage resides in that the GNE concept allows objective functions and constraints associated to each player to depend on the strategies of other agents, creating a more realistic environment. By studying GNE properties, problems in several fields, including Engineering and Economics, may be modelled and solved in an easier way. In this chapter a solution algorithm based on the Fuzzy ASA algorithm is introduced , evidencing that it is possible to transform many complex tasks into constrained global optimization problems—as such, they can be solved, in principle, by any effective global optimization algorithm, but here the main tool is Fuzzy ASA. The intention is to show that the presented approach may offer a simpler alternative for solving this type of problem in a less limited way, that is, not imposing strong conditions on the defining functions. After the theoretical explanation, many examples are presented in order to demonstrate the efficacy of the method.