[en] The main idea of this project is to find a way to represent mathematically different situations where various agents are involved to take each of them a decision. The decision taken by each agent will affect the others results. This is the reason why we need to consider the others strategies by the time we choose our own game strategy. In this project we will study what is a cooperative game in game theory, and how we can restrict this cooperation by introducing some affinities and incompatibilities between the players. This restrictions are represented by communication graphs where the vertices represent the players and the edges show the connexions between them. Finally, we will apply the graph-restricted cooperation games to a real case, in order to do a research of the possible post-election coalitions that can be formed between the players, after some political elections and by the initial situation where none of the electoral parties have got an absolute majority of votes.

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