‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it  by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in ...

We consider weighted congestion games with polynomial latency functions of maximum degree d≥1. For these games, we investigate the existence and efficiency approximate pure Nash equilibria which are obtained through sequences unilateral improvement moves by players. By exploiting a simple technique, firstly show that admit an infinite set d-approximate potential functions. This implies there al...