M. A. Puente del Campo, M. Domènech Blàzquez, J. M. G. Giménez Pradales, A. Jiménez Losada
Bicooperative games were introduced by Bilbao as a generalization of cooperative games. The potential notion was first introduced for the Shapley value by Hart and Mas-Colell and it was translated to the Banzhaf value and to all semivalues by Dragan. In all these cases, a single number describes any game for each solution. Thus, if a value can be viewed as a vector-valued function on games, is just the discrete gradient of the potential function.
The main goal of the work is giving a new approach to the concept of the potential function based on games with a fixed number of players. That is, whereas the classical definition consider subgames, in the new one, modified games without removing players are introduced. Following this new approach, we introduce a pair of potential functions on the space of bicooperative games for each solution belonging to the family of bisemivalues.
Palabras clave: cooperative game, bicooperative game, semivalues, bisemivalues, potential.
Programado
Teoría de Juegos
9 de noviembre de 2023 16:50
CC2: Sala Conferencias