Optimización lineal aplicada a teoría de juegos

Abstract

In the following TFG we deal with the Game Theory and with the application that the Linear Programming has on it. We start defining some key concepts that will serve us as a base. Within the Game Theory there are manly two theories: the cooperative one and the non-cooperative one. We consider that the non-cooperative approach is the most appropriate to analyse our problem, that is: every single player might find its own strategies considering that the others will use their best strategies as well. To this effect, we will use the Linear Programming to obtain the most accurate solution. On the other side, the cooperative approach deals with the assumption that the hypothetical players are going to cooperate and, to this respect, they will act according to the most suitable social way, focusing on how the players should divide out the benefits of its cooperation. Due to those reasons, we will use the Core and the Nucleolus and revise the Linear Production Games, in which the Linear Programming furnishes on how to spread the benefits within extensive coalitions.