Author(s)

Néstor Bravo

Departamento de Matemáticas, Universidad de Guanajuato, Guanajuato, Mexico.

Given a graph $g=\left(V,A\right)$, we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Graph Theory, Values for Graphs, Cooperation Games, Potential Function

Bravo, N. (2024) A Value for Games Defined on Graphs. Applied Mathematics, 15, 331-348. doi: 10.4236/am.2024.155020.