7. Studying Coalitions

A deep study assessing the feasibility of coalition formation in electric energy auctions is presented. A stochastic global optimization algorithm, when applied to the calculation of Nash–Cournot equilibria in several scenarios, makes it possible to obtain quantitative results concerning the profitability of coalition formation processes in diverse environments. Auxiliary Nash equilibrium problems are solved by transforming the original problem into a global optimization one and constructing cost functions which translate the associated constraints into mathematical relations, reflecting the benefit maximization trend of typical energy conversion and transmission firms. It is also indicated how to use the algorithm to estimate coupled constraint equilibria occurring when restrictions are imposed to businesses or marketplaces. In addition, the suggested method computes players’ payoffs in many configurations, comparing their profits and production levels under different market elasticities. Furthermore, solutions are based on cooperative game theory concepts, such as the bilateral Shapley value. It is shown that the adequacy of creating certain coalition configurations depends critically on demand \(\times \) price elasticity relationships. A case study based on the IEEE 30-bus system is used, for the sake of presenting and discussing in detail the paradigm. The presented method is far-reaching and uses the solution of generalized Nash equilibrium problems to obtain numerical data that will take us to the final decisions. As seen in the previous chapter, generalized Nash equilibrium problems address extensions of the well-known standard Nash equilibrium concept, making it possible to model and study more general configurations. As said before, GNEP’s have a larger scope, considering that they allow both objective functions and constraints of each player to depend on the strategies of other players. As can be observed from the literature, the study of such problems finds endless applications in several areas, including Medicine, Engineering, and Management Science, for example.