A new approach to the potential concept for bisemivalues on bicooperative games

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.

Keywords: cooperative game, bicooperative game, semivalues, bisemivalues, potential.

Game Theory
November 9, 2023  4:50 PM
CC2: Conference Room

M. Domènech Blàzquez, J. M. Giménez Pradales, M. A. Puente del Campo

D. Martín García, C. M. Manuel García, E. C. Gavilan García

A. Jiménez Losada, M. Basallote Galvan, J. M. Gallardo Morilla, C. Hernández Mancera

J. Castro, I. Gutiérrez, D. Gómez, D. Santos, R. Espínola, J. A. Guevara