ABSTRACT
In his famous paper of 1953, Shapley proposed his approach to measure the prospects of a player in a multi-person cooperative game, the well-known Shapley value. Following this spirit, it is natural to ask if it would be possible to define a similar measure for a group of players, when they could enter in the game as a coordinated group. In 2017, and based on previous work of Marichal et al. (2007) (Marichal, J.L., Kojadinovic, I., Fujimoto, J. (2007) Axiomatic characterizations of generalized values. Discrete Applied Mathematics 155, 26-43), the authors of this note propose the Shapley group value as a possible answer to the previous question. This chapter presents a comprehensive introduction to this value, describing in particular an axiomatic characterization of it, and using it to discuss the profitability of a group inside a network. It is also studied how the notion is adapted when the communication between players is restricted by a graph. Throughout the text, different examples that show the usefulness of the measure are provided. In particular, the value is applied to a real context, as it is the Spanish Elections of 2015, and also to an inventory cost game.
