Comparativa del valor de Shapley amb altres solucions igualitàries en els jocs cooperatius. El paper dels jugadors “inútils”

Abstract

[en] The main objective of this research is the study of cooperative games with transferable utility. Specifically, we will examine the three most common used solutions: the Shapley value, the egalitarian solution, and the egalitarian surplus solution. These solutions aim to determine how to reach an agreement in a cooperative situation among players. On one hand, we will present the common properties shared by these solutions, namely efficiency, symmetry, and additivity. On the other hand, we will examine the properties that differentiate them. Additionally, we will deepen into the detailed axiomatic characterizations that are crucial for their proper definition, providing several examples to illustrate the independence of these properties.