[en] John F. Nash work was a cornerstone in the development of Game Theory, especially with the famous concept of “Nash Equilibrium”, defined in his Ph.D thesis in 1950. Its implications in such a different fields as economics, biology, or social sciences, led to a new insights and results. In this project, the main objective is to analyse the Nash equilibrium from a mathematical perspective, from the basic definitions to the Nash Theorem. As the spirit is to give a didactic explanation, there are several examples in order to illustrate all the concepts and results shown. Besides this, and according to this interdisciplinar field which combines the rigorous mathematical language with the economic applications, some classical economic models will be studied, remarking the power of Nash Equilibria in these situations. Finally, further solution concepts for normal-form games will be presented in the last chapter, in order to show there are some refinements of Nash Equilibrium that can be used taking into account different hypotesis.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Josep Vives i Santa Eulàlia